Fluidmechanics2labs /civil or mechanical engg
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below are 3 zip files
(1) lab3 and lab4 in 2lab.zp files are labs to be done
(2) in HelpForLab3.zip file is help for lab 3 , you can take help from it and you use excel file for data and calculation
(3)in HelpForLab4.zip file is help for lab 4 , you can take help from it and you use excel file for data and calculation
MECH202 Lab 3.pdf
MECH202 – Fluid Mechanics – 2015 Lab 3
Bernoulli’s Principle
INTRODUCTION
In this experiment you will investigate the flow through a Venturi meter. By observing the flow rate
and pressure variation along the system, you will:
1) Investigate the interchange of pressure and kinetic energy, as dictated by the Bernoulli’s equation
– conservation of energy with assumptions made.
2) Study the application of this equation to flow metering devices.
BACKGROUND
1. Experimental Apparatus
The experimental apparatus is shown in Figure 1. It consists of a horizontal test section with a
constant inlet diameter and a constant outlet diameter.
Figure 1
Experiment 3: Bernoulli’s Principle
As shown in Figure 2, water enters the test section from inlet ( left hand side ). It then flows through
a contraction ( A to C ) , a throat ( E) and an expansion ( E to F ), before exiting through a control
valve used to control the flow rate in this experiment. The length of pipe with the contraction and
expansion is an example of a Venturi flow meter. There are various pressure tappings placed along
the test section, and each manometer is relevant to a specific pressure tap. The diameters and
tapping locations along the test section are shown in the Figure 2.
Figure 2
A hand pump is also provided, see Figure 3, to control the pressure above all the manometer tubes if
required, in order to maintain all manometer readings within their measurement range. This has no
effect on the head differences between individual readings.
Experiment 3: Bernoulli’s Principle
Figure 3
2. Bernoulli’s Equation
The equation is on Page 25, Lecture 6 written as:
V 1
2
2
+
P1
ρ +g h1=
V 2
2
2
+
P2
ρ + g h2
where
V 1(m/s) : velocity of the fluid at the first point of interest
P1 (Pa) : gauge pressure of fluid at that point
ρ(kg /m) : density of the fluid
g(m/s
2
) :gravitational acceleration
h1(m) :the height of the point relative to a common reference
V 2(m/s ) : velocity of the fluid at the second point of interest
The above equation is the kinematic form. As you can see, each term has the dimension of
m
2
/s
2
Experiment 3: Bernoulli’s Principle
The head form of the equation can be obtained by dividing each term by the gravitational
acceleration g :
V 1
2
2 g
+
P1
ρ g
+h1=
V 2
2
2 g
+
P2
ρ g
+h2
Each term in the head form has the dimension of m
Since Bernoulli’s equation can also be understood as a version of conservation of energy with
assumptions made on the flow field, each term in the equation actually represents a type of energy.
V
2
2 g
represents the kinetic energy. It is associated with the velocity of the fluid.
P
ρ g
represents the pressure energy. It is associated with the ability of the fluid to do work on the
surroundings.
h represents the potential energy. It is associated with the vertical elevation of the fluid (ie the
energy associated with gravity acting on the fluid).
Certain terms in this equation have traditionally been grouped together:
V
2
2 g
+
P
ρ g
+h is known as the total head.
P
ρ g
+h is known as the piezometric or hydraulic head.
A plot of total head against pipe length is called the total energy line, as each of the terms represents
a type of energy. A plot of hydraulic head against pipe length is called the hydraulic grade line. The
water height in the manometers in the experiment is a measure of the hydraulic head along the
pipe. In our laboratory system, the test section is horizontal, so h1=h2 .
Experiment 3: Bernoulli’s Principle
3. Flow Rate Measurement
A Venturi meter is a simple way to measure the flow rate in a pipe. In a Venturi meter, the
interchange between pressure head and velocity head is utilised to determine the flow rate ( Q ). The
equation for the Venturi meter is:
Qreal=Cv Qideal=Cv (V T AT )=Cv AT √
[2 g⋅δ(
P
ρ g
+h)]
[1−(
DT
Dp
)
4
]
where V T is the velocity in the throat, DT is the throat diameter, DP is the original diameter
of the pipe and δ(
P
ρ g
+h) is the hydraulic head loss ( or velocity head gain ) at the Venturi
contraction. Note that mathematically, the loss from a to b is a minus b; the gain from a to b is b
minus a. CV is the dimensionaless Venturi discharge coefficient – it is essentially a calibration
coefficient. If Cv is known, and the pressure head loss is measured at the Venturi contraction in a
pipe, then the flow rate throught that pipe can be determined.
EXPERIMENTAL PROCEDURE
1. Level the test apparatus using the adjustable feet as well as possible.
2. Adjust the outlet control valve position such that the difference between the levels in the
manometers will be at their largest ensuring that the levels within each tube are within the 0300mm
measurement range. You must avoid any readings outside this measurement range to reduce errors.
3. Allow sufficient time for the manometer levels to stabilise, then record all readings.
4. Measure the flow rate using a stop watch by measuring the time taken to collect 10 Litres of
water in a bucket. Repeat 3 times for each flow rate.
5. Close the outlet control valve slowly ( flow rate should reduce ) and allow manometers to
stabilise. DO NOT close the control valve; otherwise pressure will build up at the inlet and the
clamp wont hold the hose tight.
6. Repeat steps 36 for five different flow rates.
Experiment 3: Bernoulli’s Principle
CALCULATIONS
For your calculation, you are required to provide:
a) A table showing the raw experimental results
b) Starting on the next page, answers to the following questions:
1. Plot the hydraulic grade lines for the five flow rates. What does this plot tell you about the
interchange of different types of energy as the water flows through the different sections of the
system?
2. Determine the flow velocity at the inlet, outlet and throat for each flow rate based on Bernoulli’s
equation.
3. For each flow rate, determine the discharge coefficient for the Venturi meter (Cv) using the
pressure drop between manometers A and E for δ(
P
ρ g
+h) . Is Cv a true constant, or does it vary
with Reynolds number?
4. Discuss reasons for the difference between the real flow rate (Qreal) and ideal flow rate
(Qideal) .
5. Identify any potential influences that were not measured or taken into account.
6. Provide three real world applications of Bernoulli’s equation with correct academic references.
Experiment 3: Bernoulli’s Principle
Record your results in the table below:
Run 1 Run 2 Run 3 Run 4 Run 5
Measuring
Bucket Volume
(L)
Discharge
Time (s)
Manometer A
Manometer B
Manometer C
Manometer D
Manometer E
Manometer F
__MACOSX/._MECH202 Lab 3.pdf
MECH202 Lab 4 Fluid Friction Loss – V22.pdf
MECH202 – Fluid Mechanics – 2015 Lab 4
Fluid Friction Loss
Introduction
In this experiment you will investigate the relationship between head loss due to fluid friction and
velocity for flow of water through both smooth and rough pipes. To do this you will:
1) Express the mathematical relationship between head loss and flow velocity
2) Compare measured and calculated head losses
3) Estimate unknown pipe roughness
Background
When a fluid is flowing through a pipe, it experiences some resistance due to shear stresses, which
converts some of its energy into unwanted heat. Energy loss through friction is referred to as “head
loss due to friction” and is a function of the; pipe length, pipe diameter, mean flow velocity,
properties of the fluid and roughness of the pipe (the later only being a factor for turbulent flows),
but is independent of pressure under with which the water flows. Mathematically, for a turbulent
flow, this can be expressed as:
hL=f
L
D
V
2
2 g
(Eq.1)
where
hL = Head loss due to friction (m)
f = Friction factor
L = Length of pipe (m)
V = Average flow velocity (m/s)
g = Gravitational acceleration (m/s^2)
Friction head losses in straight pipes of different sizes can be investigated over a wide range of
Reynolds’ numbers to cover the laminar, transitional, and turbulent flow regimes in smooth pipes. A
further test pipe is artificially roughened and, at the higher Reynolds’ numbers, shows a clear
departure from typical smooth bore pipe characteristics.
Experiment 4: Fluid Friction Loss
The head loss and flow velocity can also be expressed as:
1) hL∝V −whe n flow islaminar
2) hL∝V
n
−whe n flow isturbulent
where hL is the head loss due to friction and V is the fluid velocity. These two types of flow are
seperated by a trasition phase where no definite relationship between hL and V exist. Graphs
of hL −V and log (hL) − log (V ) are shown in Figure 1,
Figure 1. Relationship between hL ( expressed by h) and V ( expressed by u ) ;
as well as log (hL) and log ( V )
Experiment 4: Fluid Friction Loss
Experimental Apparatus
In Figure 2, the fluid friction apparatus is shown on the right while the Hydraulic bench that
supplies the water to the fluid friction apparatus is shown on the left. The flow rate that the
hydraulic bench provides can be measured by measuring the time required to collect a known
volume.
Figure 2. Experimental Apparatus
Experimental Procedure
1) Prime the pipe network with water by running the system until no air appears to be discharging
from the fluid friction apparatus.
2) Open and close the appropriate valves to obtain water flow through the required test pipe, the four
lowest pipes of the fluid friction apparatus will be used for this experiment. From the bottom to the
top, these are; the rough pipe with large diameter and then smooth pipes with three successively
smaller diameters.
3) Measure head loss between the tappings using the portable pressure meter for ten different flow
rates by altering the flow using the control valve on the hydraulics bench for each of the pipes
mentioned above. Measure the flow rates using the volumetric tank or, for small flow rates, use the
measuring cylinder.
4) Measure the internal diameter of each test pipe sample using a Vernier calliper using the pipe
samples.
Tables to record experimental raw data are provided at the end of this outline.
Experiment 4: Fluid Friction Loss
Calculations
For your calculations, you are required to provide:
a) Tables showing the raw experimental data
b) Answers to the questions that will be found below:
For the three smooth pipes
Q1) Plot log (hL) vs log ( V ) for the three smooth pipes and determine n
Q2) Estimate the Reynolds number range for transitional flow for each of the pipes and comment
what type of flow each of the flow rates is expected to create for each pipe.
Q3) Compare the values of head losses calculated using the friction factors obtained from the
Moody diagram and Eq.1 to those measured by the portable pressure meter.
For the rough pipe
Q4) Use the measured head losses and Eq.1 to determine the friction factor f of the pipe for each
flow rate. Also, calculate the Reynolds number in the pipe for each flow rate. Plot your values on a
Moody diagram and use them to obtain an estimate for the roughness (ε) of the pipe.
For all calculations, use water properties at 20 Celsius as provided in the Moody diagram attached.
Experiment 4: Fluid Friction Loss
Smooth Pipe 1 Smooth Pipe 2 Smooth Pipe 3 Rough Pipe
Diameter
Smooth Pipe 1
Run Measuring Tank
Volume
Measuring Time Head Loss
1
2
3
4
5
6
7
8
9
10
Smooth Pipe 2
Run Measuring Tank
Volume
Measuring Time Head Loss
1
2
3
4
5
6
7
8
9
10
Smooth Pipe 3
Run Measuring Tank
Volume
Measuring Time Head Loss
1
2
3
4
5
6
7
8
9
10
Rough Pipe
Run Measuring Tank
Volume
Measuring Time Head Loss
1
2
3
4
5
6
7
8
9
10
__MACOSX/._MECH202 Lab 4 Fluid Friction Loss – V22.pdf
Lab3Results.xlsx.xlsx
Sheet1
Run 1  Run 2  Run 3  Run 4  Run 5  deep  A throat  A at H  Sqrt Value  Q ideal  Cv  
Discharge Time 1  29.8  32.1  34.93  37.75  52.93  7.85E05  0.001963495408  Manometer A  2.363808868  2.23012569  1.991654386  1.90906252  1.390325475  Manometer A  1.86E04  1.86E04  1.86E04  1.86E04  1.86E04  Manometer A  1.11E+00  1.20E+00  1.31E+00  1.42E+00  1.98E+00  
Discharge Time 2  30.2  32.75  35.11  37.75  54.05  Manometer B  2.414282518  2.29769073  2.038094458  1.957611366  1.427135651  Manometer B  1.90E04  1.90E04  1.90E04  1.90E04  1.90E04  Manometer B  1.13E+00  1.23E+00  1.33E+00  1.45E+00  2.02E+00  
Discharge Time 3  29.78  32.32  35.4  39.44  52.76  Manometer C  2.135051628  2.022985672  1.800433617  1.719861798  1.257084361  Manometer C  1.68E04  1.68E04  1.68E04  1.68E04  1.68E04  Manometer C  1.00E+00  1.09E+00  1.18E+00  1.28E+00  1.79E+00  
Average Time  29.9267  32.3900  35.1467  38.3133  53.2467  Manometer D  1.575578213  1.494724736  1.31822331  1.349244573  0.9540599872  Manometer D  1.24E04  1.24E04  1.24E04  1.24E04  1.24E04  Manometer D  7.41E01  8.02E01  8.70E01  9.48E01  1.32E+00  
Q real  1.67E04  1.54E04  1.42E04  1.31E04  9.39E05  Manometer E  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  Manometer E  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  Manometer E  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  
Manometer F  1.464386336  1.361052186  1.178705769  1.135195997  0.7772155682  Manometer F  1.15E04  1.15E04  1.15E04  1.15E04  1.15E04  Manometer F  6.88E01  7.45E01  8.08E01  8.81E01  1.22E+00  
Manometer G  1.471245326  1.353634953  1.178705769  1.117317777  0.7772155682  Manometer G  1.16E04  1.16E04  1.16E04  1.16E04  1.16E04  Manometer G  6.92E01  7.49E01  8.12E01  8.85E01  1.23E+00  
Manometer A  0.3  0.295  0.278  0.292  0.29  0.025  Manometer H  2.363808868  2.252584722  2.011772617  1.914328909  1.397547993  Manometer H  1.86E04  1.86E04  1.86E04  1.86E04  1.86E04  Manometer H  1.11E+00  1.20E+00  1.31E+00  1.42E+00  1.98E+00  
Manometer B  0.24  0.245  0.236  0.254  0.27  0.0139  
Manometer C  0.135  0.149  0.161  0.184  0.233  0.0118  Cv Average  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  
Manometer D  0.0525  0.075  0.102  0.133  0.205  0.0107  Cv Ave AD  9.98E01  1.08E+00  1.17E+00  1.28E+00  1.77E+00  
Manometer E  0.0225  0.048  0.081  0.111  0.194  0.01  Cv Ave FH  8.30E01  8.99E01  9.75E01  1.06E+00  1.48E+00  
Manometer F  0.129  0.14  0.15  0.175  0.224  0.025  
Manometer G  0.13  0.139  0.15  0.173  0.224  0.025  
Manometer H  0.3  0.3  0.282  0.293  0.291  0.025  
Velocity at H  8.51E02  1.97E+00  1.81E+00  1.66E+00  1.20E+00  Re  Cv  
VA Bernoulli  0.08509063565  1.966754012  1.812427157  1.661915046  1.196023056  9.00E01  8.81E01  9.09E01  8.70E01  8.60E01  
0.2593075708  1.979424498  1.823977028  1.673308585  1.204355077  8.81E01  8.55E01  8.89E01  8.49E01  8.38E01  
0.4150185734  2.003527226  1.844421915  1.694096107  1.219619265  9.96E01  9.72E01  1.01E+00  9.66E01  9.51E01  
0.5047181553  2.02191032  1.860347333  1.709082099  1.23104474  1.35E+00  1.31E+00  1.37E+00  1.23E+00  1.25E+00  
VE Bernoulli  0.5336107348  2.028576186  1.865982904  1.715506229  1.235504412  5314.847956  20204.9421  18585.48709  17086.71543  12305.82083  0  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  #DIV/0!  
0.4221852867  2.005772007  1.847401472  1.696750312  1.223303377  1.45E+00  1.44E+00  1.54E+00  1.46E+00  1.54E+00  
VG Bernoulli  0.4209993067  2.006021272  1.847401472  1.697339572  1.223303377  1.45E+00  1.45E+00  1.54E+00  1.49E+00  1.54E+00  
0.08509063565  1.965482471  1.811323328  1.661614161  1.195604931  9.00E01  8.73E01  9.00E01  8.68E01  8.56E01  
Sheet2
pipe 1  D= 0.0076  
run  tank  time1  time2  time3  Average time  HL1  HL2  average HL  flow rate  friction 
1  5  12.3  16.8  13.56  1.42E+01  7.60E+01  7.58E+01  7.59E+01  2.84E+00  1.40E+00 
2  5  14.5  13.43  13.86  1.39E+01  7.52E+01  7.45E+01  7.49E+01  2.79E+00  1.44E+00 
3  5  14.05  12.08  13.76  1.33E+01  7.01E+01  7.22E+01  7.12E+01  2.66E+00  1.50E+00 
4  5  14.48  13.28  15.45  1.44E+01  6.59E+01  6.56E+01  6.58E+01  2.88E+00  1.18E+00 
5  5  17.3  15.1  17.28  1.66E+01  5.28E+01  5.24E+01  5.26E+01  3.31E+00  7.15E01 
6  5  17.78  17.25  19.41  1.81E+01  4.48E+01  4.41E+01  4.44E+01  3.63E+00  5.03E01 
7  3  12.35  12.85  9.31  1.15E+01  3.74E+01  3.66E+01  3.70E+01  3.83E+00  3.75E01 
8  3  15.63  14.73  14.93  1.51E+01  2.67E+01  2.62E+01  2.65E+01  5.03E+00  1.56E01 
9  2  12.45  13.13  12.43  1.27E+01  1.71E+01  1.68E+01  1.69E+01  6.34E+00  6.28E02 
10  2  11.01  12.3  11.07  1.15E+01  8.26E+00  8.69E+00  8.48E+00  5.73E+00  3.85E02 
pipe 2  d=0.01081  
run  tank  time1  time2  time3  average time  hl1  hl2  flow rate  flow rate  friction 
1  5  7.5  7.76  7.68  7.65E+00  30.88  30.48  3.07E+01  1.53E+00  2.78E+00 
2  5  8  7.4  8.39  7.93E+00  30.41  30.13  3.03E+01  1.59E+00  2.55E+00 
3  5  8.25  7.13  7.93  7.77E+00  29.38  29.05  2.92E+01  1.55E+00  2.57E+00 
4  5  9.35  9.66  9.51  9.51E+00  21.89  21.38  2.16E+01  1.90E+00  1.27E+00 
5  5  12.53  12.86  11.98  1.25E+01  14.07  13.58  1.38E+01  2.49E+00  4.72E01 
6  3  9.58  8.06  7.86  8.50E+00  10.62  10.14  1.04E+01  2.83E+00  2.74E01 
7  3  9.98  10.85  8.51  9.78E+00  8.14  7.33  7.74E+00  3.26E+00  1.54E01 
8  2  8.03  8.86  8.63  8.51E+00  5.42  5.06  5.24E+00  4.25E+00  6.14E02 
9  2  11.56  12  11.91  1.18E+01  3.28  2.95  3.12E+00  5.91E+00  1.89E02 
10  2  7.08  7.58  7.43  7.36E+00  1.28  1.5  1.39E+00  3.68E+00  2.17E02 
pipe 3  d=0.01708  
run  tank  time1  time2  time3  Average Time  hl1  hl2  flow rate  flow rate  friction 
1  5  5.56  5.31  5.23  5.37E+00  9.45  9.17  9.31E+00  1.07E+00  2.71E+00 
2  5  5.28  5.38  15.5  8.72E+00  9.22  8.13  8.68E+00  1.74E+00  9.56E01 
3  5  5.78  4.5  5.68  5.32E+00  8.64  8.36  8.50E+00  1.06E+00  2.52E+00 
4  5  7.51  7.53  7.68  7.57E+00  5.2  4.94  5.07E+00  1.51E+00  7.41E01 
5  5  11.6  11.28  7.86  1.02E+01  3.06  2.42  2.74E+00  2.05E+00  2.19E01 
6  3  8.43  7.33  7.15  7.64E+00  2.24  1.85  2.05E+00  2.55E+00  1.06E01 
7  3  8.96  9.08  7.88  8.64E+00  1.78  1.27  1.53E+00  2.88E+00  6.16E02 
8  2  8.56  8.43  8.76  8.58E+00  1.15  0.8  9.75E01  4.29E+00  1.77E02 
9  2  11.76  11.41  11.58  1.16E+01  0.69  0.51  6.00E01  5.79E+00  5.99E03 
10  2  8.56  8.41  8.33  8.43E+00  0.1  0.18  1.40E01  4.22E+00  2.64E03 
rough pipe  d=0.01708  
run  tank  time1  time2  time3  average time  hl1  hl2  flow rate  flow rate  friction 
1  5  7.85  7.86  7.86  7.86E+00  75.37  74.91  7.51E+01  1.57E+00  1.02E+01 
2  5  8.35  7.8  7.81  7.99E+00  74.61  75.99  7.53E+01  1.60E+00  9.89E+00 
3  5  7.83  8.11  7.63  7.86E+00  72  71.54  7.18E+01  1.57E+00  9.74E+00 
4  5  9.56  9.29  9.76  9.54E+00  50.84  50.8  5.08E+01  1.91E+00  4.68E+00 
5  5  11.5  11.15  12.96  1.19E+01  30.09  29.63  2.99E+01  2.37E+00  1.78E+00 
6  3  8.76  8.28  8  8.35E+00  21.87  21.33  2.16E+01  2.78E+00  9.35E01 
7  3  9.63  9.83  8.13  9.20E+00  17.23  16.32  1.68E+01  3.07E+00  5.98E01 
8  2  8.93  8.91  8.4  8.75E+00  10.2  9.75  9.98E+00  4.37E+00  1.75E01 
9  2  11.31  11.51  12.05  1.16E+01  3.64  3.41  3.53E+00  5.81E+00  3.50E02 
10  2  8.56  8.56  8.93  8.68E+00  0.8  1.1  9.50E01  4.34E+00  1.69E02 
Sheet3
corey results  
Smooth Pipe 1 (m)  Smooth Pipe 2 (m)  Smooth Pipe 3 (m)  Rough Pipe  
Diameter  0.0076  0.01041  0.01708  0.01708  
Smooth Pipe 1  
Run  Tank Volume  Time 1  Time 2  Time 3  Average time  Flow velocity  HL 1  HL 2  Average HL  friction  
1  5  12.36  16.8  13.56  14.19666667  49.15743306  76.04  75.82  75.93  0.004685410023  
2  5  14.5  13.43  13.86  13.33666667  46.17959372  75.21  74.51  74.86  0.005234343296  
3  5  14.05  12.08  13.76  13.13666667  45.48707295  75  74.76  74.88  0.005396379062  
4  5  14.84  13.28  15.45  14.40666667  49.88457987  65.92  65.64  65.78  0.003941611593  
5  5  17.3  15.1  17.28  16.55333333  57.3176362  52.82  52.38  52.6  0.002387381347  
6  5  17.78  17.26  19.41  15.96333333  55.27469991  44.8  44.06  44.43  0.002168383639  
7  3  12.35  12.85  9.31  13.31  76.81209603  37.42  36.55  36.985  0.0009347145132  
8  3  15.63  14.73  14.93  14.49666667  83.66035703  26.72  26.23  26.475  0.0005640390037  
9  2  12.45  13.13  12.43  8.526666667  73.81117267  17.08  16.75  16.915  0.0004629567143  
Smooth Pipe 2  
Run  Tank Volume  Time 1  Time 2  Time 3  Average time  Flow velocity  HL 1  HL 2  Average HL  friction  
1  5  7.5  7.76  7.68  7.553333333  13.94014167  30.88  30.48  30.68  0.03224561861  
2  5  8  7.4  8.39  7.51  13.86016734  30.41  30.13  30.27  0.03218290225  
3  5  8.25  7.13  7.93  8.346666667  15.40428718  29.38  29.05  29.215  0.0251462026  
4  5  9.35  9.66  9.51  10.62333333  19.60601567  21.89  21.38  21.635  0.011495502  
5  5  12.53  12.86  11.98  11.15  20.57801143  14.07  13.58  13.825  0.006668191514  
6  3  9.58  8.06  7.86  9.496666667  29.21113829  10.62  10.14  10.38  0.002484563635  
7  3  9.98  10.85  8.51  9.896666667  30.44151267  8.14  7.33  7.735  0.001704816313  
8  2  8.03  8.86  8.65  9.63  44.43189463  5.42  5.06  5.24  0.0005421149133  
9  2  11.56  12  11.91  7.853333333  36.23452535  3.28  2.95  3.115  0.0004845768139  
Smooth Pipe 3  
Run  Tank Volume  Time 1  Time 2  Time 3  Average time  Flow velocity  HL 1  HL 2  Average HL  friction  
1  5  5.36  5.31  5.23  5.35  3.667820259  9.45  9.17  9.31  0.2319105257  
2  5  5.28  5.38  5.5  5.053333333  3.464433341  9.22  8.13  8.675  0.2422099242  
3  5  5.78  4.5  5.68  5.936666667  4.070023602  8.64  8.36  8.5  0.1719538641  
4  5  7.51  7.53  7.86  8.773333333  6.014768175  5.2  4.94  5.07  0.0469631309  
5  5  11.66  11.28  11.16  10.09  6.917440451  3.06  2.42  2.74  0.0191887451  
6  3  8.43  7.33  7.13  8.28  9.460919547  2.24  1.85  2.045  0.007656203758  
7  3  8.96  9.08  7.88  8.823333333  10.08174478  1.78  1.27  1.525  0.005027884757  
8  2  8.56  8.43  8.76  9.466666667  16.2252485  1.15  0.8  0.975  0.001241105703  
9  2  11.76  11.41  11.58  7.723333333  13.237289  0.69  0.31  0.5  0.0009562220902  
Rough Pipe  
Run  Tank Volume  Time 1  Time 2  Time 3  Average time  Flow velocity  HL 1  HL 2  Average HL  friction  
1  5  7.85  7.86  7.86  7.836666667  5.372613974  75.37  74.91  75.14  0.8723420056  
2  5  8.35  7.8  7.81  8.086666667  5.544007444  74.61  45.99  60.3  0.6574406783  
3  5  7.83  8.11  7.63  8.41  5.765676332  72  71.54  71.77  0.7234846115  
4  5  9.56  9.29  9.76  10  6.855738802  50.84  50.4  50.62  0.3609113037  
5  5  11.5  11.15  12.96  10.31  7.068266705  30.09  29.63  29.86  0.2002861029  
6  3  8.76  8.28  8  8.956666667  10.23409453  21.97  21.33  21.65  0.06927011705  
7  3  9.63  9.83  8.13  9.456666667  10.8054061  17.23  16.32  16.775  0.04814677597  
8  2  8.93  8.91  8.4  9.783333333  16.76799449  10.2  9.75  9.975  0.01188878652  
9  2  11.31  11.51  13.05  7.606666667  13.03732995  5.64  5.41  5.525  0.01089285789 
__MACOSX/._Lab3Results.xlsx.xlsx
Labs Layout.pdf
MECH202 Fluid Mechanics, 2015, Week 6 Lab Reports Requirement
Due date:
Weighting: Combined 8% (or 4% each)
For the two reports below, please follow the suggested outline and formatting included in the
ENGG100 example report that has been provided on ilearn previously.
The specific requirements for each report, and what should be covered in each section are
outlined below. Please ensure that below the title of your report, you include your name and
student number. An assignment cover sheet should also be included.
It is expected that all reports will be typed including any equations that you wish to include.
Diagrams should be created using graphics software and are not to be hand drawn. Marks will be
awarded for appropriate formatting and presentation of your reports.
All work submitted should be the students own work and not be simply a duplicate of the
information provided. The intention of the two reports is for students to demonstrate that they
understand how the apparatus and the process connects with the theory presented in class.
Each lab report will be marked out of a total of 15 marks.
Week 7, Laboratory 3 – Bernoulli’s Principle Lab Report
I. ABSTRACT
This should be a concise summary of what was being investigated, what method was utilised and
the outcome of the experiments. Writing a concise abstract is challenging, but is necessary to
entice the reader to read the remaining report. This is expected to be no more than 4 or 5
sentences in length. (1 mark)
II. INTRODUCTION
Describe the problem being investigated in greater detail than that possible to provide in the
abstract. This should not be greater than one paragraph in length. (1 mark)
III. METHOD
Describe the process and the equipment that has been used to obtain the experimental utilising a
diagram as necessary. In total, this section should be no longer than 1 page in length. (1 marks)
IV. RESULTS AND DISCUSSIONS
This is where the results obtained in the lab, the analysis that has been conducted and the
observations made should be included. For this particular laboratory, these are expected to be:
1. Provide a table showing the raw experimental results that were obtained during the
tutorial.
2. Plot the hydraulic grade lines for the five flow rates. What does this plot tell you about
the interchange of different types of energy as the water flows through the different
sections of the system (2.5 marks)?
3. Determine the flow velocity at the inlet, outlet and throat for each flow rate based on
Bernoulli’s equation (2.5 mark).
4. For each flow rate, determine the discharge coefficient for the Venturi meter (Cv) using
the pressure drop between manometers A and E for (
+ ℎ). Is Cv a true constant, or
does it vary with Reynolds number? (2.5 marks)
5. Discuss reasons for the difference between the real flow rate ( ) and ideal flow rate
( ). (1 mark)
6. Identify any potential influences that were not measured or taken into account. (1
mark)
7. Provide three real world applications of Bernoulli’s equation with correct academic
references. (1.5 marks)
In total, this section should not exceed more than five pages in length.
V. CONCLUSION
This section should highlight the most significant outcome of the experiment. This should be no
more than one paragraph in length (1 mark).
Week 8, Laboratory 4 – Fluid Friction Loses Lab Report
I. ABSTRACT
This should be a concise summary of what was being investigated, what method was utilised and
the outcome of the experiments. Writing a concise abstract is challenging, but is necessary to
entice the reader to read the remaining report. This is expected to be no more than 4 or 5
sentences in length. (1 mark)
II. INTRODUCTION
Describe the problem being investigated in greater detail than that possible to provide in the
abstract. This should not be greater than one paragraph in length. (1 mark)
III. METHOD
Describe the process and the equipment that has been used to obtain the experimental utilising a
diagram as necessary. In total, this section should be no longer than 1 page in length. (1 marks)
IV. RESULTS AND DISCUSSIONS
This is where the results obtained in the lab, the analysis that has been conducted and the
observations made should be included. For this particular laboratory, these are expected to be:
1. Provide a table showing the raw experimental results that were obtained during the
tutorial.
For the three smooth pipe
1. Plot log(hL) vs log(V) for the three smooth pipes and determine n. (3 marks)
2. Estimate the Reynolds number range for transitional flow for each of the pipes and
comment what type of flow each of the flow rates is expected to create for each pipe
(3 marks).
3. Compare the values of head losses calculated using the friction factors obtained from
the Moody diagram and Eq.1 to those measured by the portable pressure meter. (3
marks)
For the three smooth pipe
4. Use the measured head losses and Eq.1 to determine the friction factor f of the pipe
for each flow rate. Also, calculate the Reynolds number in the pipe for each flow rate.
Plot your values on a Moody diagram and use them to obtain an estimate for the
roughness (ε) of the pipe. (3 marks)
For all calculations, use water properties at 20 Celsius as provided in the Moody diagram
attached.
In total, this section should not exceed more than five pages in length.
V. CONCLUSION
This section should highlight the most significant outcome of the experiment. This should be no
more than one paragraph in length (1 mark).
__MACOSX/._Labs Layout.pdf
Last semester friend report bit diffrent.docx
2
Introduction:
The Bernoulli’s principle states that the fluid speed is inversely proportional to the pressure or the potential energy for a nonconducting inviscid flow of fluid. Bernoulli Principle is named after the DutchSwiss mathematician Daniel Bernoulli. Bernuolli’s theorem usually relates to Bernuolli’s equation he expression of the Bernoulli’s equation is as follows:
Figure1
The experiment’s objective is to investigate the validity of Bernoulli’s Theorem as applied to the flow of water in tapering circular duct. Bernoulli’s theorem is based on the conservation of mass and energy in the fluid flow. The report first represents the literature review of the experiment. The report then explains the method and findings of this experiment. The values computed are then compared with the measured values to determine the validity of the Bernoulli’s principle.
In Bernoulli’s theorem, the fluid is considered incompressible and has no viscosity. The fluid is taken to be flowing through a pipe with a crosssectional area and pressure such that an element is moved a distance . The theorem states that the sum of pressure, the potential, and kinetic energy per unit volume is equal to fixed constant at any point (Giambattista, Richardson and Richardson, 2010).
Where p is the pressure, is the density of water in this case, g is gravitational acceleration, h is height, and v is the velocity. This is considered on one side of the pipe. After dividing this equation by the viscosity, .
Constant
Where is the pressure head, is the velocity head, and the whole equation is the piezometric head (Oertel, 2004).
Application of the Bernoulli’s principle to various fluid flow types results in what is referred to as the Bernoulli’s equation. The Bernoulli’s equation forms differ depending on the types of flow. The simple Bernoulli’s principle is applied to incompressible flows. For compressible flows at higher Mach numbers, more advanced forms of the Bernoulli equation are applied.
To understand Bernoulli’s Principle, the best way is through grasping the energy conservation principle. The energy conservation principle states that the aggregated energy would be the same for an ideal fluid or any cases where effects of viscosity are neglected. The energy conservation principle clearly simplifies Bernoulli’s equation, which then deliberates itself and states that all forms of energy in total would be the same. As a result, it could be validated through multiple calculations, which has been achieved by the fluid scientists. It is very important for the system to be a steady flow (Oertel, 2004).
The principle can also be directly derived from Newton’s second law. If a small fluid volume is flowing horizontally from a highpressure region to a lowpressure region then the pressure in front is will be less than behind. This gives the volume a net force, and there is acceleration along the streamline. Fluid particles are subject to only weight and pressure. If a fluid is horizontally flowing along a streamline section, the velocity will increase only when the fluid on that section moves from a higherpressure region to a lower pressure region (Mulley, 2004).
Bernoulli’s theory has many implementations in everyday uses; more specifically in pipes and infrastructure uses. The Bernoulli’s equation is applied when given velocities at two points of the streamline and pressure at one point. In such a case, Bernoulli’s Equation could be used to determine the unknown pressure. An example of such a case is the flow through the converging nozzle.
Several equipment are used in analyzing the Bernoulli’s equation that has been implemented in the real world. For instance, the pitot probe for the total pressure considered as the head hT of the fluid in a short distance upstream of the probe’s tip. Also, the valve needs to be controlled gradually to stabilize the dihydrogen monoxide level in the manometer (Mulley, 2004).
Methodology
The following apparatus are required to perform the experiment:
1. Hydraulic Bench: This allows flow by timed volume collection to be measured.
2. Bernoulli’s Apparatus Test Equipment.
3. A stopwatch for timing the flow measurement
The first step is ensuring that the Bernoulli apparatus on the hydraulics bench is leveled. The manometer is carefully filled with water to eliminate air pockets from within the pipes to ensure no obstruction that occurs in the resulting reading obtained. The inlet feed and control valves were adjusted prior to the start of the experiment for convenience and to obtain correct reading for the difference between highest and lowest manometer levels. Three readings were recorded to obtain an average discharge.
Equations used:
Velocity=discharge/area
Results and Discussion:
Table 1: Discharge (Flow rate)
Observation No 
Volume (L) 
Time (seconds) 
Flow rate (mm^3/sec) 
Average Discharge (mm^3/sec) 
1 
3 
30.37 
0.098 
99044 
2 
3 
30.37 
0.098 
99044 
3 
3 
30.13 
0.099 
99044 
Table 2: Manometer Readings
Obs. No. 
Tube No. 
Diameter (mm) 
Area of C/S (mm^2) 
Man.level (mm) 
Probe Level (mm) 
probe DST. (mm) 
1 
1 
25 
490.9 
205 
210 
141.34 
2 
2 
13.9 
151.7 
180 
210 
81.26 
3 
3 
11.8 
109.4 
155 
210 
72.86 
4 
4 
10.7 
89.9 
125 
207 
68.36 
5 
5 
10 
78.5 
85 
207 
60.46 
6 
6 
25 
490.9 
135 
150 
0 
Table 3: Results
Tube No 
Static Head (mm) 
Velocity (measured) (mm/sec) 
El.head (calculated) (mm) 
El.head (measured) (mm) 
Velocity (calculated) (mm/sec) 
Total Head (measured) (mm) 
Total Head (calculated) (mm) 
A 
205 
201.76 
2.07 
5 
313.21 
210 
210 
B 
180 
657.23 
22.02 
30 
767.2 
210 
209.99 
C 
155 
902.86 
41.55 
55 
1038.8 
210 
210 
D 
125 
1101.71 
61.86 
82 
1268.4 
207 
206.99 
E 
85 
1261.71 
81.14 
122 
1547.14 
207 
207 
F 
135 
201.76 
2.07 
15 
542.49 
150 
149.99 
Table 4: The Dimension of cross section
Tapping Position 
Manometer Height 
Diameter of crosssection (mm) 
A 
h1 
25 
B 
h2 
13.9 
C 
h3 
11.8 
D 
h4 
10.7 
E 
h5 
10 
F 
h5 
25 
The results obtained from the experiment are used to determine the validity of the Bernoulli’s principle. Comparison of the values of the measured and calculated head is used to verify the principle. The total head cannot be calculated directly without first finding the velocity and the static head. The velocity requires to be calculated from the crosssectional area and the discharge. The static head is obtained from the manometer reading.
Table 1 shows the results obtained in getting the average discharge by measuring the flow rate and the time. The average discharge was obtained as 9904mm3/sec.
Table 2 shows the readings from the manometer for each tube. The readings obtained include the tube diameter that is used to get the crosssectional area, the manometer level, the probe level and the probe distance. These values are used in the calculations in Table 3 to obtain the total heads.
From the given formulas, Table 3 was generated. The table shows the calculated and the measured values of the velocity and the head. Comparing the values of the calculated and measured total heads, it is clear that for all the tubes, the values are similar. There are only negligible disparities in some of the values, for example, in tube B the measured total head is 210mm while the calculated total head is 209.99mm. The values are used to determine the validity of the Bernoulli’s principle.
Table 4 shows the diameters of the tubes and their tapping points. The diameters are used to assist in obtaining the crosssectional area that is required in the calculation of the velocity.
The experiment’s purpose was to investigate the validity of Bernoulli’s Theorem. Comparisons were made with the theoretically calculated result against measured results to determine the validity of the Bernoulli’s equation. From Table 3, the values of the calculated, and the measured total head for all the tubes were identical. From these values, it can be concluded that the Bernoulli’s principle is valid. It is important to note that throughout the experiment there were various errors caused by human and experimental errors.
References
Brewster, H. (2009). Fluid mechanics. Jaipur, India: Oxford Book Co.
Chanson, H. (2004). Environmental hydraulics of open channel flows. Oxford: Elsevier ButterworthHeinemann.
Giambattista, A., Richardson, B. and Richardson, R. (2010). College physics. Boston: McGrawHill.
Enrique Zeleny, (2015), BernoullisTheorem [ONLINE]. Available at: http://demonstrations.wolfram.com/BernoullisTheorem/ [Accessed 12 May 15].
Mulley, R. (2004). Flow of industrial fluids. Boca Raton, Fla.: CRC Press.
Oertel, H. (2004). Prandtl’s essentials of fluid mechanics. New York: Springer.
__MACOSX/._Last semester friend report bit diffrent.docx
last semester friend report2.docx
Flow Measurement Report Fluid Mechanics
Table of Contents
Table of Contents 2
1 Abstract 3
2 Experimental Setup 3
2.1 Objective of Experiment 3
2.2 Apparatus 3
2.3 Risks 4
2.4 Method 4
2.5 Diagram of Setup and Photos 5
2.6 Theory (Formula) 6
2.6.1 Orifice Plate: 7
2.6.2 Flow Nozzle: 8
2.6.3 Venturi: 9
2.7 Results 10
3 Discussion 11
3.1 Explanation of each device 11
3.1.1 Geometry: 11
3.1.2 How they measure pressure: 12
3.1.3 Differences in Accuracy: 12
3.2 How our results fit with these: 13
3.3 Experimental Error 14
3.4 Relative energy costs (in terms of pressure drops across each device) 15
3.5 Relative Advantages and Disadvantages of each device 16
3.5.1 Orifice plate: 16
3.5.2 Flow nozzle: 16
3.5.3 Venturi: 16
3.6 Other methods that measure flow 17
4 Conclusion 17
5 References 18
6 Appendix 18
6.1 Appendix 1: 18
6.2 Appendix 2: 19
Abstract
This report outlines an experiment that was designed to determine the accuracy of three different devices when they measured the flow rate of a fluid through a cylindrical pipe. These three devices were the Orifice plate, Venturi and Flow nozzle.
As the fluid flowed from the source to a volumetric tank it was forced to go through the Venturi, Nozzle and Orifice. Through the use of a differential pressure transmitter, the individual pumps were able to change in pressure for the calibrated devices and hence calculate flow rates.
Upon applying the data recorded in the experiment, it was calculated that the orifice provided a flow rate of. The Venturi yielded a flow rate of while the nozzle had a flow rate of. These were compared to the measured flow rate of.
It was initially assumed that the Orifice would be the least accurate device, while the venture would be the most accurate. The presumption of the orifice plate being the least accurate of the three devices was correct. However the second presumption was disproved through the experiment as the nozzle unexpectedly had the most accurate flow rate.
However this result was due to the multitude of errors present within the experiment and hence it is suggested that the experiment is repeated once the faults have been corrected.
Experimental Setup
Objective of Experiment
This experiment aims to measure the flow rate of water through a circular pipe with the use of three different measuring techniques. Through an analysis of the measurement techniques, individuals will be able to determine the various advantages and disadvantages of each method.
Apparatus
· Water Supply
· Venturi
· Orifice
· Nozzle
· Flow regulating valve
· Onoff Valve
· Volumetric tank
· Drain
· Differential pressure transmitters
· Stopwatch
· Power supply
· Ammeters
Risks
This experiment presents a variety of risks to individuals either participating or observing.
The first is a leakage of water, which can happen through broken pipes, improper connections or a defective volumetric tank. These risks can result in slippage or damage to surrounding equipment. This can be prevented by testing all components prior to the experiment, and replacing all defective parts.
Rusting equipment is also a major risk within this experiment. Failure to appropriately maintain and manage equipment may result in rusting that can deem it unable to fulfil its use. Hence surrounding equipment can be waterproofed to prevent any damage. Furthermore getting rust into open wounds and eyes can be extremely harmful. Therefore individuals must wear gloves, lab coats and safety goggles to prevent harm.
Electrical safety is one of the most important considerations when undertaking this experiment. This experiment presents the potential for a water and electricity mix which can be extremely harmful and result in electrocution. Therefore individuals must dry their hands before dealing with electrical equipments and follow appropriate procedures.
Method
1. Before beginning the experiment it is important to calibrate each device as shown in the graphs in Appendix 1 to minimise errors in the experiment.
2. The experiment is set up as shown in the diagram below.
3. Then a Differential Pressure Transmitter in conjunction with a power supply and ammeter is connected to each the orifice, nozzle and venturi.
4. The water is supplied at a steady rate and simultaneously the stop watch is started
5. The volumetric tank is filled to 100 litres and the time is recorded.
6. Average the data in each column after every three trials
7. With the recorded data, gather the pressure drop, and calculate the flow rate.
8. The volumetric tank is emptied ready to repeat the experiment again at different flow rates for a total of three sets of flow rates.
9. Compare measured flow rates with the calculated flow rates to deduce the accuracy in each device.
10. Use the stopwatch as the control experiment, and have the differential pressure transmitter as the actual experiment.
Diagram of Setup and Photos
Figure 1: Third measuring device the venturi used in the experiment.
Figure 2: Nozzle flow device used in the experiment.
Figure 3: The orifice plate utilised during the experiment.
Figure 4: Experimental Setup and Arrangement for measuring pressure difference (Huynh 2008)
Theory (Formula)
The measured flow rate for the experiment can be found by using the equation below:
When:
V = volume of fluid (100 litres)
T = average time (49.33 seconds)
This is then compared with the calculated flow rate values of the orifice, nozzle and venturi to deduce the accuracy of the devices in measuring the flow rate of a fluid.
Orifice Plate:
All the Calculation shown in the appendix
· For all three devices finding the pressure is necessary in determining the flow rate as it is needed in the final equation which determines the Qcalculated value for the devices. This can be acquired by using the equation in the corresponding graph found in appendix 1.
Where:
mA = average milliamps recorded on multimeter (9.09)
P = Pressure
· The area is also needed to calculate the flow rate of the devices. For the orifice, only one area is needed.
Where:
A = area with respect to d.
r = radius (0.0125 meters)
· This ratio is needed in order to extract necessary information from the graph in appendix 2.
Where:
d = orifice diameter (25 millimeters)
D = pipe diameter (52.6 millimeters)
· Using the d/D value and assuming a high Reynolds number (Re) of 2 x 105, a coefficient can be found of Cv= 0.64 from graph in appendix 2.
· The flow can be calculated by using the equation:
Where:
Qcalculated = calculated flow rate
Cv = orifice coefficient (0.64)
A = area (4.91 x 104 m2)
ΔP = average pressure (14261.6 Pa)
Ρ = density of fluid (1000 kg/m3)
Flow Nozzle:
All the Calculation shown in the appendix
· Solving for the pressure by using the nozzle graph in appendix 1 yields. (Average P)
Where:
mA = average milliamps recorded on multimeter (10.546)
P= Pressure
· Calculating the area for both the pipe and nozzle diameter
Where:
A1 = area of the pipe
r = radius (0.0263 meters)
Where:
A2 = area of the nozzle
r = radius (0.01 meters)
· Calculating the diameter ratio gives.
Where:
d = nozzle diameter (20 millimetres)
D = pipe diameter (52.6 millimetres)
· Using the d/D value and assuming a high Reynolds number (Re) of 2 x 105, a coefficient can be found of Cv= 0.985 from the graph
· The flow can be calculated by using the equation:
Where:
Qcalculated = calculated flow rate
Cv = Nozzle coefficient (0.985)
A1 = area of pipe (2.17 x 103 m2)
A2 = area of nozzle (3.14 x 104 m2)
ΔP = average pressure (17690.7Pa)
ρ = density of fluid (1000 kg/m3)
Venturi:
All the Calculation shown in the appendix
· Solving for the pressure by using the Venturi graph in appendix 1 yields.
Where:
mA = average milliamps recorded on multimeter (10.186)
P= Pressure
· Calculating the area for both the pipe and venturi diameter
Where:
A1 = area of the pipe
r = radius (0.0263 meters)
Where:
A2 = area of the venturi
r = radius (0.0102 meters)
· Calculating the diameter ratio gives.
Where:
d = venturi diameter (20.35 millimetres)
D = pipe diameter (52.6 millimetres)
· Using the d/D value and assuming a high Reynolds number (Re) of 2 x 105, a coefficient can be found of Cv= 0.975 from the graph
· Likewise with the venturi the flow can be calculated by using the equation:
Where:
Qcalculated = calculated flow rate
Cv = Venturi coefficient (0.975)
A1 = area of pipe (2.17 x 103 m2)
A2 = area of nozzle (3.25 x 104 m2)
ΔP = average pressure (14682.4 Pa)
ρ = density of fluid (1000 kg/m3)
Results
Nozzle 
Orifice 
Venturi 

d (mm) 
20 
25 
20.35 
Area d (mm2) 
0.0003142 
0.0004909 
0.0003253 
D (mm) 
52.6 
52.6 
52.6 
Area D (mm2) 
0.002173 
0.002173 
0.002173 
d/D 
0.38 
0.48 
0.3868821 
d*D (mm2) 
1070.41 

Cv 
0.983 
0.640 
0.973 
Table 1: Dimensions for the flow devices used along with their corresponding coefficient values.
Table 2: Recorded multimeter readings for the devices after nine trials.
Table 3: Average recorded result from the experiment
Table 4: Error comparison of devices And Average Flow rate
Figure 5: Pressure drop across device vs. measured mass flow rate
Table 5: Orifice related calculation
Figure 6: Measured mass flow rate vs. calculated mass flow rate for Orifice
Table 6Venturi related calculation
Figure 7: Measured mass flow rate vs. calculated mass flow rate for Venturi Meter
Table 7 Nozzle related calculation
Figure 8: Measured mass flow rate vs. calculated mass flow rate for Nozzle
Figure 22
Table 8: Shows the measured and calculated flow rates for the devices along with their average pressures.
Discussion
Explanation of each device
Geometry:
Orifice Plate: The orifice plate consists of a main cylindrical pipe roughly 52.6mm in diameter along with two thin plates located about halfway through the pipe. The plates extended into the pipe from either side leaving an orifice in the centre of the pipe of about 25mm in diameter which is roughly half of the original diameter. The plates also consist of 45 degree bores which provide a sharper edge for the plates.
Figure 5: Orifice (Munson 2013)
Nozzle: This flow measuring device is made up of a funnel inlet that is designed to impede regular flow and measure pressure. This funnel inlet decreases in diameter from 52.6mm to 20mm to create less turbulence when the fluid exits the device.
Figure 6: Nozzle Munson 2013)
Venturi: Being the most complex out of the three devices the venture produces a contraction in the pipe which is shaped like an hour glass. The contraction leading to the centre of the venturi is not equal on both sides. In the experimental setup the venturi had a declined slope of 20 degrees on the entry side of the flow and a decline of 5 to 7 degrees on the exit side. The funnel decreases from a maximum of 52.6mm to 20.35mm.
Figure 7: Venturi (Munson 2013)
How they measure pressure:
Since the drop in pressure is used to measure the flow rate, it is important to have an understanding of Bernoulli’s equation.
Figure 8: Princeton 2008
Orifice:
As fluid begins to flow, the velocity around the orifice plate increases due to the restricted cross section. Through the formula we see that change in pressure is proportional to the square of the velocity. Hence the increase in final velocity results in a decrease in pressure. Two separate tubes on either side of the orifice are connected to a differential pressure meter to measure the change.
Nozzle:
As fluid begins to flow, the velocity increases due to the decreasing cross section and results in a drop in pressure due to the same formula applicable to orifice. Similar to the orifice, two separate tubes across the nozzle measure the change in pressure.
Venturi:
The venturi was built to further reduce turbulence within flow measurement. To do this it eliminates restrictions by the flow measurement device and simply has a slowly decreasing diameter, and again the pressure is determined through two tubes across the device which is connected to a differential pressure meter.
Differences in Accuracy:
Firstly from the designs developed for each device we can see the varying amounts of turbulence. The orifices design is built in such a way, that the fluid is required to quickly adapt to a changing diameter and hence there is a significant amount of turbulence after exiting the orifice. Therefore in theory the Orifice is very inaccurate.
Secondly the Nozzle is built to allow the water to adjust to the changing diameter. Despite this design, as the water exits the device there is turbulence, and hence a loss in pressure. However due to the inlet, there is less turbulence and hence less pressure loss in comparison to the orifice.
Lastly the Venturi is built in such a way that it alleviates turbulence extensively and allows pressure drops to mainly occur due to the changing diameter. However unlike the Nozzle, this is done as the water both enters and exits the device. Hence in theory the venturi should be the most accurate way of measuring the flow rate.
Expected results due to theory 

Device 
Accuracy Ranking (Most Accurate to Least Accurate) 
Venturi 
1 
Nozzle 
2 
Orifice 
3 
Table 9: Expected Results Due to theory
How our results fit with these:
Table 9: Results
Firstly, aligning with theory, the results indicate that the orifice is indeed the least accurate way of measuring flow rate. This is highlighted through 5.96%,3.3%, and 15.8% errors across the three flow rates and is clearly further away from the actual flow rate than both the nozzle and venturi. However observing these results alone cannot ensure their validity, and hence we must analyse both the nozzle and venturi.
In this section of the results both the venturi and nozzle do not seem to follow theory. Through an analysis of the results, it can be determined that across the board the nozzle seems to be significantly more accurate than the venturi. This is most clearly highlighted through the measured flow rate of 1.38, where the nozzle has 2.8% error in comparison to that of 27% for the venturi. This leads us to question the method and whether results have been skewed due to experimental error.
Results analysis 

Device 
Accuracy Ranking (Most Accurate to Least Accurate) 
Venturi 
2 
Nozzle 
1 
Orifice 
3 
Table 10: Results Analysis
Experimental Error
Through a careful analysis, one can determine a plethora of errors that litter the experimental method of this investigation.
Errors 

Error 
Reasoning 
Solution 
Parallax Error 
During the control experiment, we were required to observe the tub as it filled to one hundred litres and then stop their timing. However individuals observing the tub were required to have their eyes exactly in line with the limit when timing. This cannot be done accurately with human eyesight and hence this affected the result. 
Both these problems can be solved through the use of a digital timer. 
Reaction Times 
During the control experiment, participants were required to time the water exactly as it reached 100L. Due to the lack of digital timers in the investigation, individuals must take into account the potential for reaction time errors. 

Volume Measurement 
Prior to conducting the experiment, a volume measurement method was developed through the use of a ruler. However this was an extremely inaccurate method of measurement. 
Volume measurement can be solved through the use of telemetric measurement. 
Series connection of the devices 
Within the actual experiment, the devices were connected in series. Pressure drops from previous devices may result in inconsistencies with measurement. 
This can be solved by separating the testing of devices into individual categories. This would allow for less pressure drops and hence a more accurate result. 
Leaking pipes Table 11: Errors 
Leaking pipes within the experiment may result in lower than expected pressures. 
Prior to the experiment, pipes must be tested to eliminate leaks and hence unnecessary pressure drops. 
Flow measurement accuracy comparison
Figure 6,7,8 Shows in the result shows Graphical representation of the accuracy of the three devices.
Before we analyse this graph, individuals must understand the relationship between time and flow rate. As flow rate decreases, time increases due to the fluid travelling more quickly. Therefore individuals can determine that across a variety of different flow rates the Nozzle is consistently the most energy consuming device, yet this cannot solely be attributed to the design, but also could be caused by the fact that it has the largest diameter change. Furthermore the venturi has the second biggest diameter change while the orifice has the smallest and subsequently both have the second and third highest energy uses respectively. This is due to Bernoulli’s equation and the effect of decreasing diameter resulting in increased velocity. This in turn leads to a decrease in pressure, and hence we can determine that pressure change is proportional to the energy usage.
Relative Advantages and Disadvantages of each device
The measuring devices which were used in the experiment all provide a different way in which they measure flow, some being more accurate than others however at a cost of being more expensive to manufacture. The merits and flaws of each device can be distinguished from the tables below.
Orifice plate:
Advantages 
Disadvantages 
Does not consist of any moving components 
Can’t be used for highly viscous fluids and fluids with large solid content. 
Fairly cheap to produce, as cost does not rise much with changes in pipe size. 
Fails in terms of accuracy when measuring large flow rates 
Has relatively high accuracy when used in slower flow speeds and temperatures 
Generally lower overall accuracy compared to the nozzle and venturi. 
More prone to wear due to flow of fluid compared to other devices, resulting in a drop in accuracy 
Table 12: Orifice
Flow nozzle:
Advantages 
Disadvantages 
Able to tolerate roughly a 60% greater flow rate as opposed to the orifice. 
Not very good at measuring fluids with high viscosity content 
Can measure liquids that have suspended solid content. 
Cannot perform very well at low pressures 
Able to measure fluid at a variety of temperatures. 

Quite firm making it impervious to wear 
Table 12: Nozzle
Venturi:
Advantages 
Disadvantages 
Has relatively low maintenance and pumping costs 
Relatively high cost to manufacture regardless of pipe size due to high cost of parts 
Can measure high flow rates with ease at low pressure drops 
CNC machining needed to acquire a high accuracy 
Able to measure liquids with high viscosity and large solid content 

Has a low wear rate making able to maintain its high accuracy accurate for a greater amount of time. 
Other methods that measure flow
Other flow rate measuring devices which were also viable for the execution of this experiment include:
· Oval gear meter
This measuring device consists of a positive displacement meter which uses two or a greater amount of oval like gears that are designed to turn perpendicular to each other, forming a T shape. As fluid passes through the device compartments within the device are repeatedly filled and emptied with the liquid. The flow rate is measured based upon the amount of times these compartments are filled and emptied.
· Turbine flow meter
Turbine flow meters harness the mechanical energy generated via the flow of fluid as it passes through the device to rotate a “pinwheel” which is placed in the centre of the flow surge. Vanes on the rotor are angled to transfer energy from the flowing fluid into rotational energy. As the fluid flows faster, the rotor rotates proportionally faster. A transmitter measures the rotors rotational velocity via pulse signals to determine the flow rate of the fluid.
Conclusion
Through this analysis of the experiment, individuals can determine the capacity for the Venturi, Nozzle, and Orifice to measure flow rates. Through an analysis of the available results, individuals can see that the Nozzle is consistently the most accurate and reliable form of measurement among these device. In comparison both the Orifice seem to be lacking measurement capacity. However participants must take into consideration the plethora of errors present within this experiment and their potential to affect the results. The major flaw of this experiment was the fact that the devices were not setup appropriately as they were connected in series which did not conform to Australian standards. This severely diminished the reliability for the experiment hence it is recommended that the experiment is repeated several times once the errors have been corrected to ensure a much more accurate, valid and reliable result.
References
Emerson process management 2010, Fundamentals of orifice Measurement, viewed 6th September 2014, <http://www2.emersonprocess.com/siteadmincenter/pm%20daniel%20documents/fundamentalsoforificemeasurementtechwpaper.pdf>
Princeton 2008, Bernoulli’s Equation, viewed 4th September 2014, <https://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html>
Munson 2013, Fundamentals of Fluid Mechanics, 11th Edition, John Wiley & Sons, United States of America
Huynh, BP, 2008, Fluid Mechanics – Course Notes, UTS Engineering
Appendix
Appendix 1:
Figure 10: Calibration chart for the Differential Pressure Transmitter (DP Cell) for the Orifice “Huynh, BP, 2008 “Fluid Mechanics – Course Notes”, UTS Engineering”).
Figure 11: Calibration chart for the Differential Pressure Transmitter (DP Cell) for the Nozzle “Huynh, BP, 2008 “Fluid Mechanics – Course Notes”, UTS Engineering”).
Figure 12: Calibration chart for the Differential Pressure Transmitter (DP Cell) for the Venturi (“Huynh, BP, 2008 “Fluid Mechanics – Course Notes”, UTS Engineering”).
Appendix 2:
Figure 13: Correction coefficients for the Orifice (from street et al, 1996).
Figure 14: Correction coefficients for the Nozzle (from street et al, 1996)
Figure 15: Correction coefficients for the venturi (from street et al, 1996).
Figure19 Nozzle/Venturi Calculation Example
figure 20 Orifice Calculations
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__MACOSX/._last semester friend report2.docx
my half report this semester.docx
Bernoulli’s Principle
Jasem Alsabe (SID: 43365019)
Tutor name: Nicholas Tse
Abstract—The main aim of this lab report is to investigate and validate experimentally Bernoulli’s Principle by applying the Bernoulli’s equation to observe the fluid flow rate and pressure along Venturi meter. The flowing fluid used in this
experiment was water and we recorded 5 trials of varying flows.
Introduction
In this experiment we analyze the Bernoulli’s Principle by using the Bernoulli equation to calculate the fluid flow rate and explore the interchange of pressure and kinetic energy along Venturi flow meters. Venturi flow meters instrument are widely used to measure the flow of fluid in pipe and makes the use of Bernoulli effect. Through the experiment, we had to rely heavily on the Bernoulli equation, as it allows us to relate velocity, pressure and area of the flow. As a pipe narrows the flow increases and the pressure decreases. However, The experiment is important to conduct because it allows us to apply the Bernoulli principles to a real life situation. The experiment focuses on determining the interchange of pressure, kinetic energy and fluid flow rate, as well as using the Bernoulli equation to find the pressure at different locations along the pipe. This allows us to demonstrate our understanding of Bernoulli equation.
.
Methods
Appartus
The following apparatus were used for the experiment:
1 Venturi flow meter
2 Stop watch
3 Water
.
Experimental setup
The following procedure was followed to setup the apparatus and take the required measurements:
1. The pipe valve on the Venturi meter was loosed to let the water flow into it.
2. The water flow was adjusted to give the maximum difference between the monometer at the upstream
3. Location and at the Venturi throat.
4. Support the exit tube so that it does not detach from the apparatus.
5. Recording for the range 0300mm to minimize the error possibility.
6. Using stopwatch to measure the flow rate for 3 trails.
7. All the monometer readings were recorded.
Results
Conclusion
In conclusion, I would like to emphasize that this lab helped us expand our understanding of incompressible flow through a Venturi flow meter and Bernoulli’s Principle. Comparing the theoretical and actual values for velocities, flow rates, a slight difference was found. The difference in the readings can be attributed to the friction involved in the actual experiment reducing the kinetic energy. The actual readings can be improved by reducing the friction in the Venturi flow meter. For a given Laminar flow, the Reynolds number has to be less than 2100, but as per our results the number is a lot greater than it. The following error can be explained due as a result of human error due to hand adjustments on the outer surface flow and the manometer reading fluctuations due to the periodic change in diameter. Manometer readings play a vital role in conducting this experiment successfully, because of the fluctuations that were encountered we were unable to achieve the desired results for this experiment.
__MACOSX/._my half report this semester.docx
this semester friend report.pdf
Assignment Coversheet
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Mech202 Fluid Mechanics
Mitic Stefan
42462215
Lab report 3
09/10/2015
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Stefan Mitic
08/10/2015
Bernoulli’s Principle
Stefan Mitic (SID: 42462215)
Abstract— This report will thoroughly analyse the flow through a Venturi meter. Through
observation of the flow rate and pressure variation along the system analysis of the interchange of
pressure and kinetic energy will be made using Bernoulli’s equation.
I. INTRODUCTION
As can be seen in figure 1, water enters the test section from the inlet located to the left of A. It then flow
through a contraction (from A to D), a throat (located at point E) and an expansion (E to F), before exiting
through a control valve used to control the flow rate in this experiment. The length of the pipe with the
contraction and expansion is an example of a Venturi flow meter. There are various pressure tapings placed
along the test section, and each monometer is relevant to a specific pressure tap. The water flow rate was
altered and the time was measured in order to calculate the flow rate so that by using Bernoulli’s equation
we may plot the relation between each section.
Figure 1. Visual representation of the venturi flow meter.
Using Bernoulli’s equation, as can be seen below, we can calculate pressure at each point. Having already
known the density of water to be 1000kg/m^3 and obtaining the velocity of the fluid by measuring it
externally, as well as the obtained pressures, we can alternatively calculate the pressure inside the system.
(1)
In order to use Bernoulli’s equation we must assume that, this is an inviscid flow containing no shear
stresses as well as being a steady flow which flows along a streamline while having constant density and has
an inertial reference frame.
II. METHODS AND EQUIPEMENT
A. Equipement
Water at room temperature
Stop watch
Test apparatus (figure 2)
Figure 2 Test apparatus
B. Method
When conduction this experiment it is important NOT to close the control valves as the pressure will build
up at the inlet and the clamp won’t hold the hose tight.
1. Level the test apparatus using the adjustable feet as well as possible.
2. Support the exit tube so that it does not detach from the apparatus.
3. Adjust the outlet control valve position such that the difference between the levels in the manometers will
be at their largest ensuring that the levels within each tube are within the 0300mm measurement range. You
must avoid any readings outside this measurement range to reduce errors.
4. Allow sufficient time for the manometer levels to stabilise, or close to stabilising, then record all
readings.
5. Measure the flow rate using a stop watch or phone by measuring the time taken to collect 5 Litres of
water in a bucket. Or is the flow rate is too slow use 3 litters.
6. Get 3 readings for each flow rate from 3 different recorders and average the results in order to save time
7. Close the outlet control valve slowly (flow rate should reduce) and allow manometers to stabilise.
8. Repeat steps 36 for five different flow rates.
III. RESULTS AND DISCUSSION
The section below shows the results obtained and calculated during the experimentation phases.
Area at
throat
Area at
H
7.85E05 0.001963
Run 1 Run 2 Run 3 Run 4 Run 5
Time 1 29.8 32.1 34.93 37.75 52.93
Time 2 30.2 32.75 35.11 37.75 54.05
Time 3 29.78 32.32 35.4 39.44 52.76
Average
Time 29.9267 32.39 35.1467 38.3133 53.2467
Q real 1.67E04
1.54E
04
1.42E
04
1.31E
04
9.39E
05
Manometer
A 0.3 0.295 0.278 0.292 0.29 0.025
Manometer
B 0.24 0.245 0.236 0.254 0.27 0.0139
Manometer
C 0.135 0.149 0.161 0.184 0.233 0.0118
Manometer
D 0.0525 0.075 0.102 0.133 0.205 0.0107
Manometer
E 0.0225 0.048 0.081 0.111 0.194 0.01
Manometer
F 0.129 0.14 0.15 0.175 0.224 0.025
Manometer
G 0.13 0.139 0.15 0.173 0.224 0.025
Manometer
H 0.3 0.3 0.282 0.293 0.291 0.025
Table 1: results obtained from experiment
Bernoulli’s equation (in its kinematic form), as can be seen in equation 2, will be used to derive the head
form of the equation by dividing each term by the gravitational acceleration which can be seen by equation
3.
(2)
(3)
Each term now has a dimension with respect to distance. Since Bernoulli’s equation is a combination of
both the kinematic energy and pressure energy, we can use this information to obtain the hydraulic head.
Since the second term of the equation, P/pg, represents the pressure energy of the system which is
associated with the ability of the fluid to do work on surroundings and since the height, h, representing the
vertical elevation of the fluid and acting as potential energy, the hydraulic head can then be calculated. The
plot, as seen by figure 3, show the hydraulic grade line which was obtained from the above calculations.
This graph show the total head against the length of the pipe. The height was obtained from the experiment
and is a measure of hydraulic head along the pipe. However, since the testing apparatus was horizontal
h1=h2.
Figure 3: Hydraulic grade line between manometers
Figure 3 acts exactly as was expected from the experiment. The hydraulic gradient drops when it starts
entering the narrow regions hence restricting its flow as was expected. However, each hydraulic gradient
should exit at the same head height as it had entered in if the apparatus is completely horizontal. However,
since the horizontal measurement was calibrated relying completely on the human eye and inaccurate
equipment, such as can be seen by figure 4, errors have occurred. Regardless of these minor errors, the
results behaved as were expected with small errors.
Figure 4: level used obtain horizontal axis.
Using equation 2, it is now possible to determine the flow velocity at all points within the system. This data
can be seen in table 2 below. Once the flow velocities have been determined the discharge coefficient (Cv)
for the Venturi meter can be calculated using the pressure drop between manometers A and E and using
equation 3 seen below.
(3)
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
H
e
a
d
(
m
)
Distance Between Manometers m
Hydraulic Grade Line
Run 1 Run 2 Run 3 Run 4 Run 5
0
5000
10000
15000
20000
25000
0.800 0.900 1.000 1.100 1.200 1.300 1.400 1.500
R
e
Cv
Cv vs Re
run 1 run 2 run3 run 4 run 5
Run1 Run2 Run3 Run4 Run5
VA Bernoulli 0.085091 1.966754 1.812427 1.661915 1.196023
Vb 0.259308 25.735 24.62543 23.27774 18.87608
Vc 0.415019 26.44324 25.20482 23.84951 19.24966
Vd 0.504718 26.97648 25.6514 24.25761 19.52762
VE Bernoulli 0.533611 27.16844 25.80849 24.43154 19.63574
Vf 0.422185 26.50866 25.28868 23.92204 19.33944
VG Bernoulli 4.21E01 2.65E+01 2.53E+01 2.39E+01 1.93E+01
Velocity at H 8.51E02 1.97E+00 1.81E+00 1.66E+00 1.20E+00
Table 2: Flow velocity based on each manometer reading.
Once the velocities have been found using the venturi meter equation below, equation 4, we can the
discharge coefficient.
(4)
This equation measures the flow rate in a pipe and utilising the interchange between pressure head and
velocity head to obtain results. But since the flow rate has already been calculated, the formula can be
rearranged and the discharge coefficient can be found. The results are shown in table 3 below.
Cv Run 1 Run 2 Run 3 Run 4 Run 5
Manometer A 0.900 0.881 0.909 0.870 0.860
Manometer B 0.881 0.855 0.889 0.849 0.838
Manometer C 0.996 0.972 1.010 0.966 0.951
Manometer D 1.350 1.310 1.370 1.230 1.250
Manometer E 1.400 1.375 1.455 1.345 1.395
Manometer F 1.450 1.440 1.540 1.460 1.540
Manometer G 1.450 1.450 1.540 1.490 1.540
Manometer H 0.900 0.873 0.900 0.868 0.856
Re 5314.848 20204.94 18585.49 17086.72 12305.82
Table 3. Coefficient discharge
The results were compared to the Reynolds numbers after each run and from this information it can be seen
that although the discharge coefficient does act like a true constant it does vary slightly when compared to the
Reynolds numbers of the test. This can clearly be seen by figure 5 below.
Figure 5: Discharge coefficient compared to the Reynolds numbers
Furthermore, as can be seen by figure 5, the coefficient appears to be affect by the Reynolds number more
when the flow becomes slightly turbulent or is in the stage of transition to turbulent flow.
Q real 0.000167 0.000154 0.000142 0.000131 0.000094
Q Ideal 0.000186 0.000168 0.000152 0.000124 0.000115
Table 4: difference between real and ideal flow rate
The results shown in table 4 above compare the real flow rate as was calculated to the ideal flow rate which
is calculated using equation 4. Although similarities exist there are differences which are evident. These
differences could be caused by a variety of difference aspects. For instance the measured results were only
accurate to one decimal factor and have plenty of room for human error. These results where then used to
find the ideal flow rate, which hence altered the ideal flow rate value as the numbers used where not
accurate enough. Secondly while using equation 4 it was assumed that the apparatus was perfectly
horizontal, hence allowing h1 to equal to h2. This was shown not to be the case as stated before, hence two
calculation were conducted, one where the apparatus was assumed to be perfectly horizontal (Q real) and
one where those factors were taken into consideration (Q ideal) hence giving slightly different values
There were many potential influences which were not taken into consideration. One of these aspects was the
temperature of the water, which would alter the density and hence alter the ideal flow rate values and other
such calculations. Also, we assumed that the apparatus did not have any leaks. If the apparatus did have
holes and exits where pressure could escape this could also affect the readings and hence alter Bernoulli’s
equation calculations (equation 2). Other smaller factors that were not considered where the elevation of the
apparatus above sea level, which alter the pressure calculations and hence provide us with different values.
Bernoulli’s equation are constantly being used in real world applications. One of the most common is that of
water pipes which disperse water to each house. It is used to determine the pressure needed to real its target
as well as how fast the water needs to flow. It is also used when manufacturing cars, to calculate how much
fuel consumption is needed as well as the speed and pressure of both the exhaust and in the engine block.
Bernoulli’s equations are also more commonly used with pressurised systems such as aerosol cans. The
density of the liquid and the expected purpose of the product, spray paint or pray deodorant, is taken into
consideration in order to know what material and what dimensions of the container to use in order to contain
the pressure required for function.
IV. CONCLUSION
This report has thoroughly analysed the flow through a Venturi meter. Through observation of the flow rate
and pressure variation along the system analysis of the interchange of pressure and kinetic energy have been
made using Bernoulli’s equation.
ACKNOWLEDGMENT
We thank Dr Yu and Dr Kabir for their contribution to and discussion of the project.
__MACOSX/._this semester friend report.pdf
lab 4 requermenrt.pdf
MECH202 – Fluid Mechanics – 2015 Lab 4
Fluid Friction Loss
Introduction
In this experiment you will investigate the relationship between head loss due to fluid friction and
velocity for flow of water through both smooth and rough pipes. To do this you will:
1) Express the mathematical relationship between head loss and flow velocity
2) Compare measured and calculated head losses
3) Estimate unknown pipe roughness
Background
When a fluid is flowing through a pipe, it experiences some resistance due to shear stresses, which
converts some of its energy into unwanted heat. Energy loss through friction is referred to as “head
loss due to friction” and is a function of the; pipe length, pipe diameter, mean flow velocity,
properties of the fluid and roughness of the pipe (the later only being a factor for turbulent flows),
but is independent of pressure under with which the water flows. Mathematically, for a turbulent
flow, this can be expressed as:
hL=f
L
D
V
2
2 g
(Eq.1)
where
hL = Head loss due to friction (m)
f = Friction factor
L = Length of pipe (m)
V = Average flow velocity (m/s)
g = Gravitational acceleration (m/s^2)
Friction head losses in straight pipes of different sizes can be investigated over a wide range of
Reynolds’ numbers to cover the laminar, transitional, and turbulent flow regimes in smooth pipes. A
further test pipe is artificially roughened and, at the higher Reynolds’ numbers, shows a clear
departure from typical smooth bore pipe characteristics.
Experiment 4: Fluid Friction Loss
The head loss and flow velocity can also be expressed as:
1) hL∝V −whe n flow islaminar
2) hL∝V
n
−whe n flow isturbulent
where hL is the head loss due to friction and V is the fluid velocity. These two types of flow are
seperated by a trasition phase where no definite relationship between hL and V exist. Graphs
of hL −V and log (hL) − log (V ) are shown in Figure 1,
Figure 1. Relationship between hL ( expressed by h) and V ( expressed by u ) ;
as well as log (hL) and log ( V )
Experiment 4: Fluid Friction Loss
Experimental Apparatus
In Figure 2, the fluid friction apparatus is shown on the right while the Hydraulic bench that
supplies the water to the fluid friction apparatus is shown on the left. The flow rate that the
hydraulic bench provides can be measured by measuring the time required to collect a known
volume.
Figure 2. Experimental Apparatus
Experimental Procedure
1) Prime the pipe network with water by running the system until no air appears to be discharging
from the fluid friction apparatus.
2) Open and close the appropriate valves to obtain water flow through the required test pipe, the four
lowest pipes of the fluid friction apparatus will be used for this experiment. From the bottom to the
top, these are; the rough pipe with large diameter and then smooth pipes with three successively
smaller diameters.
3) Measure head loss between the tappings using the portable pressure meter for ten different flow
rates by altering the flow using the control valve on the hydraulics bench for each of the pipes
mentioned above. Measure the flow rates using the volumetric tank or, for small flow rates, use the
measuring cylinder.
4) Measure the internal diameter of each test pipe sample using a Vernier calliper using the pipe
samples.
Tables to record experimental raw data are provided at the end of this outline.
Experiment 4: Fluid Friction Loss
Calculations
For your calculations, you are required to provide:
a) Tables showing the raw experimental data
b) Answers to the questions that will be found below:
For the three smooth pipes
Q1) Plot log (hL) vs log ( V ) for the three smooth pipes and determine n
Q2) Estimate the Reynolds number range for transitional flow for each of the pipes and comment
what type of flow each of the flow rates is expected to create for each pipe.
Q3) Compare the values of head losses calculated using the friction factors obtained from the
Moody diagram and Eq.1 to those measured by the portable pressure meter.
For the rough pipe
Q4) Use the measured head losses and Eq.1 to determine the friction factor f of the pipe for each
flow rate. Also, calculate the Reynolds number in the pipe for each flow rate. Plot your values on a
Moody diagram and use them to obtain an estimate for the roughness (ε) of the pipe.
For all calculations, use water properties at 20 Celsius as provided in the Moody diagram attached.
Experiment 4: Fluid Friction Loss
Smooth Pipe 1 Smooth Pipe 2 Smooth Pipe 3 Rough Pipe
Diameter
Smooth Pipe 1
Run Measuring Tank
Volume
Measuring Time Head Loss
1
2
3
4
5
6
7
8
9
10
Smooth Pipe 2
Run Measuring Tank
Volume
Measuring Time Head Loss
1
2
3
4
5
6
7
8
9
10
Smooth Pipe 3
Run Measuring Tank
Volume
Measuring Time Head Loss
1
2
3
4
5
6
7
8
9
10
Rough Pipe
Run Measuring Tank
Volume
Measuring Time Head Loss
1
2
3
4
5
6
7
8
9
10
__MACOSX/._lab 4 requermenrt.pdf
last semester friend similar lab.docx
INTRODUCTION
The purpose of this report is to detail the process and outcomes of Fluid Friction Experiment. The experiment was conducted to make students able to better familiarise themselves with the concept of the head loss due to fluid friction and velocity for flow of water through smooth bore pipes.
There are three different types of visual flow that will be shown, laminar, transition and turbulent flow. Laminar flow is considered a smooth flow where particles move in parallel straight line. This kind of flow occurs at a very slow velocity. On the other hand, in turbulent flow particles flow in an erratic path. This flow occurs at higher velocities. The transition flow is when there is a significant disturbance in the velocity. This experiment is done to determine the Reynolds number and that there is to types of flow may exist in a pipe.
Literature Review:
A weighting function model of transient friction is developed for flows in smooth pipes by assuming the turbulent viscosity to vary linearly within a thick shear layer surrounding a core of uniform velocity and is thus applicable to flows at high Reynolds number. In the case of low Reynolds number turbulent flows and short time intervals, the predicted skin friction is identical to an earlier model developed by Vardy et al (1993). In the case of laminar flows, it gives results equivalent to those of Zielke (1966, 1968). The predictions are compared with analytical results for the special case of flows with uniform acceleration. It is this case that enables clarifying comparisons to be drawn with “instantaneous” methods of representing transient skin friction. (Alan E. Vardy & Jim M.B. Brown, 1995)
Transient conditions in closed conduits have traditionally been modeled as 1D flows with the implicit assumption that velocity profile and friction losses can be accurately predicted using equivalent 1D velocities. Although more complex fluid models have been suggested, there has been little direct experimental basis for selecting one model over another. This paper briefly reviews the significance of the 1D assumption and the historical approaches proposed for improving the numerical modeling of transient events. To address the critical need for better data, an experimental apparatus is described, and preliminary measurements of velocity profiles during two transient events caused by valve operation are presented. The velocity profiles recorded during these transient events clearly show regions of flow recirculation, flow reversal, and an increased intensity of fluid turbulence. The experimental pressures are compared to a water hammer model using a conventional quasisteady representation of head loss and one with an improved unsteady loss model, with the unsteady model demonstrating a superior ability to track the decay in pressure peak after the first cycle. However, a number of details of the experimental pressure response are still not accurately reproduced by the unsteady friction model. (Brunone, B., Karney, B., Mecarelli, M., and Ferrante, M., 2000)
A new model for the computation of unsteady friction losses in transient flow is developed and verified in this study. The energy dissipation in transient flow is estimated from the instantaneous velocity profiles. The ratio of the energy dissipation at any instant and the energy dissipation obtained by assuming quasisteady conditions defines the energy dissipation factor. This is a nondimensional, timevarying parameter that modifies the friction term in the transient flow governing equations. The model was verified for laminar and turbulent flows and the comparison of measured and computed pressure heads shows excellent agreement. This model can be adapted to an existing transient program that uses the wellknown method of characteristics for the solution of the continuity and momentum equations. (SilvaAraya, W. and Chaudhry, M., 1997)
An efficient procedure is developed for simulating frequencydependent friction in transient laminar liquid flow by the method of characteristics. The procedure consists of determining an approximate expression for frequencydependent friction such that the use of this expression requires much less computer storage or computation time than the use of the exact expression. The derived expression for frequencydependent friction approximates the exact expression very well in both time and frequency domains. Calculated results for a test system are compared with the experimental results so show that the approximate expression predicts accurately the surge pressures, pressure wave distortion as well as pressure attenuation in a liquid line. (A. K. Trikha, 1995)
From these correlations, a series of more general equations has been developed making possible a very accurate estimation of the friction factor without carrying out iterative calculus. The calculation of the parameters of the new equations has been done through nonlinear multivariable regression. The better predictions are achieved with those equations obtained from two or three internal iterations of the Colebrook–White equation. Of these, the best results are obtained with the following equation:
(Eva Romeo, Carlos Royo, Antonio Monzón, 2002)
· Methodology:
Equipment used:
1. Stop watch
2. Head loss meter
First water was added to the apparatus to initiate the experiment. The head loss meter was attached to the 10mm pipe discharge. Then 8 readings were recorded. The time was started as the water level on the reading apparatus got to 0 litres and time was then stopped at 2 litre water level. An average flow was recorded. The same procedure was executed for the second set of 8 readings but the pipe diameter was increased to 17.5mm. Time again was started at the 0 litre mark and stopped at the 5 litre mark. In between each reading the flow from the water source was decreased by closing the valve each time. After the readings were taken flow rate was calculated and then velocity was calculated.
Formulas used:
This equation was used to calculate flow rate Q, V is the volume and T was the time that was recorded.
This equation was used to calculated velocity from Q which was calculated previously and d is the diameter of the pipe that was being used
Velocity
Flow rate
These equations are the same and are used to calculate the upper and lower critical velocities.
ρ is the density, u1 and u2 are the upper and lower critical velocities, µ is the molecular viscosity
Results:
The reading abstained from this experiment were tabulated and further calculations were solved using the following readings.
Figure 2.0
Volume (V) Litres 
Time (T) secs 
Flow rate (Q) m^3/s 
Pipe Dia (dm) 
Velocity (u) m/s 
Head Loss 
Log u 
Logh 
2 
7.97 
2.51×10^4 
10mm 
3.2 
310 
0.50515 
2.49 
2 
9.28 
2.16×10^4 
10mm 
2.75 
293 
0.439333 
2.47 
2 
9.68 
2.07×10^4 
10mm 
2.64 
260 
0.421604 
2.41 
2 
11.34 
1.76×10^4 
10mm 
2.24 
205 
0.350248 
2.31 
2 
13.32 
1.50×10^4 
10mm 
1.91 
129 
0.281033 
2.11 
2 
19.09 
1.05×10^4 
10mm 
1.34 
90 
0.127105 
1.95 
2 
24.13 
8.29×10^5 
10mm 
1.06 
61 
0.025306 
1.79 
2 
44.59 
4.49×10^5 
10mm 
0.57 
22 
0.24413 
1.34 
5 
5.25 
9.5×10^4 
17.5mm 
3.95 
59.6 
0.596597 
1.78 
5 
5.91 
8.5×10^4 
17.5mm 
3.53 
50 
0.547775 
1.7 
5 
6.78 
7.4×10^4 
17.5mm 
3.08 
39 
0.488551 
1.59 
5 
7.41 
6.7×10^4 
17.5mm 
2.79 
32 
0.445604 
1.51 
5 
8.47 
5.9×10^4 
17.5mm 
2.45 
26 
0.389166 
1.41 
5 
11.63 
4.3×10^4 
17.5mm 
1.79 
15 
0.252853 
1.18 
5 
13.75 
3.6×10^4 
17.5mm 
1.5 
11.9 
0.176091 
1.08 
5 
20.07 
2.5×10^4 
17.5mm 
1.04 
6 
0.017033 
0.78 
The first set of 8 readings was taken using the 10mm pipe and the volume of water was 2 litres. The second set of 8 readings was taken using a 17.5mm pipe and a volume of 5 litres of water. In both findings the same process was used to calculate the flow rate, velocity, Log u, and Log h. As the experiment started the first finding we obtained was the time and head loss, time was then used to calculate flow rate (Q) also using volume, the relationship that is seen and is evident through our results in figure 2.0 is that as time increases flow rate decreases. We were then able to calculate the velocity as we had the flow rate and we knew what the diameter of the pipe was, these equations are shown in the methodology. A total of four graphs were made from the results two for each set of results these helped determine Reynolds number (Re) and nvalues.
Figure 2.1
Laminar flow
Transition
U2
U1
turbulent flow
Figure 2.2
U2
U1
Transition
turbulent flow
Laminar flow
Figure 2.1 and 2.2 show the three zones laminar, transition, and turbulent. Through this we can determine Re1 and Re2 using u1 and u2 from the graph, ρ density is a constant also µ viscosity is a constant.
Calculating Re values using figure 2.1
Re1 will have 2 values using u1 and u2
The same proses is used for figure 2.2 to calculate Re2
Figure 2.3
Laminar
Turbulent
Figure 2.4
Turbulent
Laminar
From figures 2.3 and 2.4 we got the n values. This was done using the turbulent section labelled in the graph.
From figure 2.3 the n value that is the gradient at the turbulent section was found to be
The same procces was repeated in figure 2.4
Discussion
REFRINSE LIST
A. K. Trikha. (1997). An Efficient Method for Simulating FrequencyDependent Friction in Transient Liquid Flow. Available: http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=1422535. Last accessed 20th May 2015
Alan E. Vardy & Jim M.B. Brown. (2010). Transient, turbulent, smooth pipe friction. Available: http://www.tandfonline.com/doi/abs/10.1080/00221689509498654. Last accessed 20th May 2015.
Brunone, B., Karney, B., Mecarelli, M., and Ferrante, M.. (2000). Velocity Profiles and Unsteady Pipe Friction in Transient Flow. Available: http://ascelibrary.org/doi/abs/10.1061/(ASCE)07339496(2000)126%3A4(236). Last accessed 20th May 2015.
Eva Romeo, Carlos Royo, Antonio Monzón. (2002). Improved explicit equations for estimation of the friction factor in rough and smooth pipes. Available: http://www.sciencedirect.com/science/article/pii/S1385894701002546. Last accessed 20th May 2015.
SilvaAraya, W. and Chaudhry, M.. (1997). Computation of Energy Dissipation in Transient Flow. Available: http://ascelibrary.org/doi/abs/10.1061/(ASCE)07339429(1997)123:2(108). Last accessed 20th May 2015.
Head loss/ Velocity 2L
0.57 1.06 1.34 1.91 2.24 2.64 2.75 3.2 22.0 61.0 90.0 129.0 205.0 260.0 293.0 310.0
head loss
Head loss / Velocity 5L
1.04 1.5 1.79 2.45 2.79 3.08 3.53 3.95 6.0 11.9 15.0 26.0 32.0 39.0 50.0 59.6
velocity m^3/s
head loss
logh/logu 2L
0.24 0.03 0.13 0.28 0.35 0.42 0.44 0.51 1.34 1.79 1.95 2.11 2.31 2.41 2.47 2.49
log u
log h
logh/logu 5L
0.02 0.18 0.25 0.39 0.45 0.49 0.55 0.6 0.78 1.08 1.18 1.41 1.51 1.59 1.7 1.78
log u
log h
__MACOSX/._last semester friend similar lab.docx
Last semester friend work similar.docx
Open Channel Flow Report Fluid Mechanics
Table of Contents
1 Abstract 2
2 Experimental Setup 3
2.1 Objectives 3
2.2 Apparatus 3
2.3 Safety Risks 3
2.4 Method 4
3 Calculations 5
3.1 Calculating the ‘Measured’ Flow Rate 5
3.2 Calculating the ‘Calculated’ Flow Rate 5
3.3 Measured Head Loss (Between Y1 and Y4): 8
3.4 Calculated Head Loss (Between Y1 and Y4): 8
4 Results 9
4.1 Raw Experimental Measurements 9
4.2 Calculated Friction, Velocity and Flow Rates 10
4.3 Calculated Vs Measured Head Loss (Between Y1 and Y4) 11
5 Discussion 12
5.1 Accuracy 12
5.2 Theory and Experiment 12
5.3 Improvements 12
5.4 Alternative Experiments 13
5.4.1 Pipe friction loss in a smooth pipe 13
5.4.2 Procedure for experimentation 14
6 Conclusion 14
7 References 15
8 Appendix 16
1
Abstract
The purpose of this report is to detail the process and outcomes of our Pipe Friction Experiment. The experiment was conducted as a means of students being able to better familiarise themselves with the concepts of energy losses due to friction in a practical setting. During the experiment we calculated the head loss due to friction caused by water flowing through a smooth pipe. We then compared these results to the physical head loss values we measured using piezometers.
We found that there was an average difference of about 6% between our measured and calculated values, which we concluded was an acceptable error most likely caused by failing in the experimental setup. We would recommend the experiment be repeated, and the improvements mentioned in the discussion be implemented to help obtain more accurate results.
2
Experimental Setup
2.1
Objectives
The aim of this experiment is to calculate the energy losses caused by water flowing through a pipe, and to assess their accuracy through the use of Bernoulli’s equation.
2.2
Apparatus
· Elevated water tank
· Water supply
· Pipe (Length: 13.3m, Diameter : 0.019m)
· Mass Scale
· Stop Watch
· Bucket
· Measuring tape (with millimetre increments)
· Five piezometric tubes
· Excess water drainage basin
2.3
Safety Risks
· Slipping on the wet ground surrounding the experimentation area
· Receiving open wounds from sharp edges if equipment was mishandled
· Falling from ladder due to instability
2.4
Method
1) Set up equipment as shown in diagram:
Figure 1 – Experimental Setup
2) Adjust the height of the exit tube (Ze) to the appropriate level (First instance was at 1300mm from ground).
3) Record the height of water level in each of the piezometric tubes, as well as the exit tube height.
4) Place bucket under water output and allow it to fill for exactly 20 seconds.
5) Measure the mass of the water in bucket and record results.
6) Repeat steps 3 to 5, adjusting the exit tube height (Ze) to 1600mm, 1900mm, 2200mm and 2500mm each time.
7) Calculate the ‘measured’ flow rate by using the recorded mass and time values. Also the ‘calculated’ flow rate can be obtained by using changes in height of the exit tube and Bernoulli’s equation.
3
Calculations
3.1
Calculating the ‘Measured’ Flow Rate
The control flow rate was calculating by directly measuring the volume of water flowing through the system over time:
m3/s
Where is the direct measurement of the flow rate.
Example:
m3/s
3.2
Calculating the ‘Calculated’ Flow Rate
The ‘calculated’ flow rate was measured by deducing the velocity of the flow and multiplying it by the cross sectional area of the tube:
m3/s
Where is calculated using Bernoulli’s equation:
Bernoulli’s equation:
This can be rearranged to:
Assumptions:
1) Pentrace = Pexit= 0 (gauge pressure)
2) VEntance= 0
3) ZEntrance– ZExit= H
4) Ve= VPipe (i.e. V is constant throughout pipe)
5) hLoss= hEntrance + hFriction
a. Where
i. K: Loss coefficient
Reentrant entrance; K assumed to be 0.5
b. And
Example:
If fassumed is originally assumed to be 0.015, then:
Finding the Re based on the estimated velocity:
Finding V using the new value for Re,
Re Calculated:
Therefore, V Final:
Re final:
From these results, we were able to calculate the head loss, and compare theoretical values to the measured results.
3.3
Measured Head Loss (Between Y1 and Y4):
The measured head can be calculated directed by subtracting the H values at Y4 from Y1.
H at Y1 = 415mm
H at Y2 = 1260mm
Head Loss = 845mm or 0.845m
3.4
Calculated Head Loss (Between Y1 and Y4):
Where:
Distance between Y1 and Y4 = 1960 + 1920 + 2020
= 5900mm
= 5.9m
4
Results
4.1
Raw Experimental Measurements
Refer to diagram for meaning of variable:
Figure 2 – Experimental Setup
Collection Tank
Piezometer Tubes
Water from Supply
Large Tank
H
Data Set 
Ze (mm) 
Y1 (mm) 
Y2 (mm) 
Y3 (mm) 
Y4 (mm) 
Y5 (mm) 
Mass (kg) 
Time (s) 
1 
1300 
415 
675 
955 
1260 
1515 
8.77 
20 
2 
1600 
375 
590 
825 
1115 
1295 
7.85 
20 
3 
1900 
335 
510 
700 
945 
1055 
6.81 
20 
4 
2200 
300 
435 
575 
780 
875 
5.79 
20 
5 
2500 
265 
355 
460 
625 
675 
4.7 
20 
4.2
Calculated Friction, Velocity and Flow Rates
Data Set 
H (mm) 
Friction (f) 
Velocity (m/s) 
Re 
Q Measured (m3/s) 
Q Calculated (m3/s) 
Error (%) 
1 
1945 
0.024 
1.444791 
27396.23 
0.0004385 
0.00040964 
6.6% 
2 
1645 
0.025 
1.303998 
24726.51 
0.0003925 
0.000369721 
5.8% 
3 
1345 
0.025 
1.179112 
22358.41 
0.0003405 
0.000334312 
1.8% 
4 
1045 
0.026 
1.020694 
19354.49 
0.0002895 
0.000289396 
0.0% 
5 
745 
0.027 
0.846903 
16059.04 
0.000235 
0.000240121 
2.2% 
4.3
Calculated Vs Measured Head Loss (Between Y1 and Y4)
Data Set 
H Loss (Measured) 
H Loss (Calculated) 
Error (%) 
1 
0.845 
0.952 
12.7% 
2 
0.74 
0.802 
8.4% 
3 
0.61 
0.656 
7.5% 
4 
0.48 
0.508 
5.8% 
5 
0.36 
0.361 
0.3% 
5
Discussion
The purpose of this experiment was to highlight friction loss with respect to flow through pipes. Comparisons were made on theoretical calculated results against measured results to determine the validity of the calculated results.
5.1
Accuracy
It is important to note that throughout the experiment there were multiple faults in accuracy due to human error and experimental equipment error. An example of human error would be the unsynchronised and noninstantaneous reactions from the individual timing of water flow, and the second individual holding the bucket under the water output.
A second human error factor would be determining Reynolds number after obtaining the friction. This was done visually on a Moody diagram which was not easy to read, and was additionally limited by its accuracy, which was only to three decimal places.
Experiential equipment error would be related to how accurate the mass scale that was being used, the pressure of the input water supply, the stopwatch accuracy and the measurements of the equipment such as the height of elevated components.
Data Set 
H Loss (Measured) 
H Loss (Calculated) 
Error (%) 
1 
0.845 
0.952 
12.7% 
2 
0.74 
0.802 
8.4% 
3 
0.61 
0.656 
7.5% 
4 
0.48 
0.508 
5.8% 
5 
0.36 
0.361 
0.3% 
As seen in from the table above, the error was on average around 6.9%. We believe this was caused by some of the experimental errors mentioned above and not due to the theoretical calculations being invalid.
5.2
Theory and Experiment
The aim of this experiment is to determine the friction experienced by water flowing through a pipe when the entrance and exit height of the flow were altered. It was assumed that the velocity is constant throughout the elevation in the pipe however in the experiment and reality it is known that the water will travel more slowly due to friction.
The usefulness of the experiment was shown by the similarity of Qmeasured and Qcalculated. The error margin was small enough for us to consider the method to be consistent with the theory, however improving the accuracy of the experiment is still highly recommended.
5.3
Improvements
Some improvements that can be for the experiment giving a learning and accuracy advantage would be;
1. Digitally calibrated measuring devices to give accurate readings by removing human error yielding precise results.
2. Synchronised timer and bucket system to obtain a more precise measurement once again removing human error and making results and measurements more accurate.
3. See through equipment to obtain a better understanding of the experiment and how the flow rate interacts with friction.
4. Repeating the experiment multiple times at the same height allowing to obtain more insight into the accuracy of each attempt which can show more stable and reliable measurements, this also can be applied to the end result.
5.4
Alternative Experiments
Figure 3 – Armfield C6MKII10 (Faculty UOH n.d.)
5.4.1
Pipe friction loss in a smooth pipe
The apparatus used, as seen above, is the Armfield C6MKII10 Fluid Friction Apparatus which is used to study fluid friction head losses which occurs when an incompressible fluid flows through pipes, bends, valves and pipe flow metering device.
Water is fed from the hydraulics bench via the barbed connector (1), as the water flows through the pipes and fittings it is then fed back into the volumetric tank via the exit tube (23).
The pipes are arranged to provide facilities for testing the following pipe types (Faculty UOHn.d.):
· An inline strainer (2)
· An artificially roughened pipe (7)
· Smooth bore pipes of 4 different diameters (8), (9), (10) and (11)
· A long radius 90° bend (6)
· A short radius 90° bend(15)
· A 45° “Y”(4)
· A 45° elbow(5)
· A 90° “T” (13)
· A 90° mitre (14)
· A 90° elbow (22)
· A sudden contraction(3)
· A sudden enlargement (16)
· A pipe section made of clear acrylic with a Pitot static tube (17)
· A Venturi meter made of clear acrylic (18)
· An orifice meter made of clear acrylic (19)
· A ball valve (12)
· A globe valve(20)
· A gate valve (21)
5.4.2
Procedure for experimentation
1. Fill the network of pipes with water while closing and opening the appropriate valves to obtain a flow of water through the desired test pipe.
2. Obtain readings at different flow rates by altering the flow using the control valve on the apparatus.
3. Measure the flow rates using the volumetric tank and measure head loss between the tapings using a pressurized water manometer.
4. Repeat experiment for a suitable sample size.
6
Conclusion
Our experiment allowed us to find the friction of the flow in the pipes using Bernoulli’s equation and the theory of energy conservation. However, the errors present in our method created some inaccuracies and hence the experiment was not completed to its full potential. To improve the outcome of this experiment we would recommend implementing the improvements mentioned in the discussion.
7
References
ADVDELPhysicsn.d., Moody Chart Calculator, Accessed 1 October 2014 <www.advdelphisys.com/michael_maley/Moody_chart/>
Faculty UOHn.d., Pipe friction loss in a smooth pipe, Accessed 28 September 2014 <http://faculty.uoh.edu.sa/m.mousa/Courses/ThermoLab%20ME%20316/ME%20316_2nd_semester%201213/ME3162nd1213%20Exps/Exp6Pipe%20friction%20loss.pdf>
Huynh, BP, 2008 “Fluid Mechanics – Course Notes”, UTS Engineering
Neutrium, 2012, Pressure Loss in Pipe, Accessed 20 August 2014, https://neutrium.net/fluid_flow/pressurelossinpipe/
The Engineering Toolbox n.d.Water – Dynamic and Kinematic Viscosity, Accessed 29 September 2014 <http://www.engineeringtoolbox.com/waterdynamickinematicviscosityd_596.html>
8
Appendix
Figure 4 Moody Diagram (Neutrium 2012)
Figure 5 Large Elevated Tank
Figure 6 – Piezometers
Figure 7 – Bucket being weighed on scales
Figure 8 – Water Output
Flow Rate (Measured Vs Calculated)
Q (Measured) Data Set 1 2 3 4 5 0.0004385 0.0003925 0.0003405 0.0002895 0.000235 Q(Calculated) 1.0 2.0 3.0 4.0 5.0 0.000409639741078858 0.000369720877958275 0.000334312154714795 0.000289396221955291 0.000240121406006494
Data Set
Head Loss (m)
Head Loss Between Two Points (Y1 and Y4)
H Loss (Measured) Data Set 1 2 3 4 5 0.845 0.74 0.61 0.48 0.36 H Loss (Calculated) 1.0 2.0 3.0 4.0 5.0 0.952492816490015 0.802811987315787 0.656402506346342 0.508360318125605 0.361335450967768
Data Set
Head Loss (m)
Page  5
__MACOSX/._Last semester friend work similar.docx
results_lab4V1.xlsx
Sheet1
Here are the times in seconds for all the pipes for every 5 litres unless specified  So the first 4 runs are 5 L  0.005  0.003  0.002  0.001  0.0001  kinematic viscosity  
SP 1 area m2  0.000001004  
0.0000453646  
Smooth pipe 1  D=7.60mm  0.0076  Flow rate m3/s  
Run 1  Run 2  Run 3  Run 4  Run 5 (3L)  Run 6 (2L)  Run 7 (1L)  Run 8 (100mL)  Run 9 (100mL)  Run 1  Run 2  Run 3  Run 4  Run 5 (3L)  Run 6 (2L)  Run 7 (1L)  Run 8 (100mL)  Run 9 (100mL)  
11.75  11.77  13.66  17.75  11.78  17.14  13.56  1.65  4.07  0.0003856537  0.0003709657  0.0003440367  0.0002830055  0.0002761583  0.0001251408  0.0000849257  0.0000611621  0.0000251099  
11.5  11.88  13.11  17.72  10.11  12.87  11.6  1.6  4.06  Velocity m/s  
13.3  14.41  14.36  17.14  12.98  17.76  11.93  1.73  3.83  8.501203597  8.177428315  7.583814539  6.238466372  6.087529559  2.758555991  1.872069718  1.348233696  0.5535121388  
12.74  14.41  14.12  18.06  11.89  12.16  1.56  3.97  Reynolds number  
14.27  14.15  15.81  9.37  16.18  9.73  64351.74038  61900.85178  57407.36105  47223.45063  46080.90105  20881.49954  14171.04567  10205.75308  4189.932525  
14.23  14.25  16.14  9.05  15.96  11.67  Log(V)  2.140207753  2.101377714  2.02601631  1.830734379  1.806242344  1.014707351  0.6270446198  0.2987953623  0.5914715961  
Head loss h_L  
Head Loss  76.765  74.125  66.125  42.39  20.515  9.765  7.12  3.825  1.68  
min  76.53  74.04  65.97  41.98  19.97  9.44  6.83  3.35  1.12  Log(h_L)  4.340748807  4.305752857  4.19154689  3.746912485  3.021156326  2.278804564  1.962907725  1.341558467  0.5187937934  
max  77  74.21  66.28  42.8  21.06  10.09  7.41  4.3  2.24  Friction  
0.1583853523  0.165288946  0.1714363346  0.1624128304  0.0825471247  0.1913468143  0.3029343718  0.3137716349  0.8176502575  
Smooth pipe 2  D=10.81mm  0.01081  SP 2 area m2  
Run 1  Run 2  Run 3  Run 4  Run 5 (3L)  Run 6 (2L)  Run 7 (1L)  Run 8 (100mL)  Run 9 (100mL)  0.0000917786  
6.35  7.63  8.18  13  11.08  17.21  11.98  1.51  4.08  Flow rate m3/s  
6.58  7.54  8.18  13.31  10.27  15.68  11.02  1.54  4.05  Run 1  Run 2  Run 3  Run 4  Run 5 (3L)  Run 6 (2L)  Run 7 (1L)  Run 8 (100mL)  Run 9 (100mL)  
7.41  8  9.1  15.06  10.51  16.76  13.06  1.71  3.83  0.0006802721  0.0006311803  0.0005617978  0.0003375338  0.0002906977  0.0001210776  0.0000843289  0.0000641026  0.0000250836  
7.31  7.61  9.27  14.87  10.03  17.67  11.44  1.48  Velocity m/s  
7.83  8.13  9.21  16.46  9.8  14.92  11.3  7.412102151  6.877208181  6.121230428  3.677696949  3.167380861  1.31923602  0.9188298099  0.6984480873  0.2733057733  
8.62  8.62  9.46  16.18  10.23  16.87  12.35  Reynolds number  
79805.60184  74046.4347  65906.87343  39597.51397  34102.97521  14204.12488  9892.978331  7520.143251  2942.66475  
Head Loss  Log(V)  2.00311409  1.928212782  1.811763127  1.302286727  1.15290502  0.2770527963  0.0846543644  0.3588944233  1.297164062  
min  30.92  28.73  21.85  9.81  4.23  2.05  1.76  1.02  0.49  Head loss h_L  
max  31.36  29.1  22.23  10.31  4.67  2.57  2.22  1.65  1.31  31.14  28.915  22.04  10.06  4.45  2.31  1.99  1.335  0.9  
Log(h_L)  3.438493166  3.364360492  3.092858984  2.308567165  1.492904096  0.8372475245  0.6881346387  0.2889312919  0.1053605157  
Friction  
0.1202155128  0.129665235  0.1247552499  0.1577505197  0.0940771455  0.2815086056  0.4999281826  0.5804137575  2.555462986  
Smooth pipe 3  D=17.08mm  0.01708  
Run 1  Run 2  Run 3  Run 4  Run 5 (2L)  Run 6 (2L)  Run 7 (1L)  Run 8 (100mL)  Run 9 (100mL)  SP 3 area m2  
6.04  6.26  8.08  13.9  15.71  19.43  10.96  1.7  3.88  0.0002291214  
6.04  6.78  8.36  13.28  14.36  15.61  12.52  1.64  4.03  Flow rate m3/s  
7.23  7.83  7.73  13.76  14.1  16.51  11.73  1.5  3.91  Run 1  Run 2  Run 3  Run 4  Run 5 (2L)  Run 6 (2L)  Run 7 (1L)  Run 8 (100mL)  Run 9 (100mL)  
7.37  7.69  8.66  14.53  14.36  18.67  9.09  1.41  0.0007019186  0.0006587615  0.0005542213  0.0003581662  0.0001323919  0.0001162115  0.000088054  0.000064  0.0000253807  
8.06  8.49  10.96  14.2  15.56  15.35  12.01  Velocity m/s  
8  8.49  10.34  14.09  16.55  17.69  11.83  3.063522842  2.87516395  2.418898324  1.56321593  0.5778242112  0.5072049826  0.3843116122  0.279327928  0.1107740831  
Reynolds number  
Head Loss  52116.50412  48912.15165  41150.18264  26593.35466  9829.917856  8628.546915  6537.890773  4751.913357  1884.483406  
min  9.74  8.45  5.24  2.13  1.29  0.84  0.79  0.63  0.55  log(V)  1.119565509  1.056109699  0.8833121984  0.4467451926  0.5484855894  0.6788400521  0.9563015655  1.275368818  2.200262439  
max  9.94  8.7  5.67  2.58  1.49  1.19  1.09  1.06  0.98  Head loss h_L  
9.84  8.575  5.455  2.355  1.39  1.015  0.94  0.845  0.765  
Log(h_L)  2.286455711  2.148850993  1.696532619  0.8565407275  0.3293037471  0.0148886125  0.0618754037  0.1684186516  0.2678794452  
Friction  0.3513498093  0.3476128076  0.3124254451  0.322953382  1.395115614  1.322165708  2.1327881  3.629233061  20.8916132  
Rough pipe  D=17.08mm  0.01708  
Run 1  Run 2  Run 3  Run 4  Run 5 (3L)  Run 6 (2L)  Run 7 (1L)  Run 8 (100mL)  Run 9 (100mL)  RP area m2  
6.04  6.26  8.08  14.05  14.18  15.35  8.16  1.61  3.91  0.0002291214  
6.04  6.78  8.36  14.18  13.81  19.81  8.55  1.61  4.01  Flow rate m3/s  
7.23  7.83  7.73  14.13  16.4  24.46  13.48  1.57  3.8  Run 1  Run 2  Run 3  Run 4  Run 5 (3L)  Run 6 (2L)  Run 7 (1L)  Run 8 (100mL)  Run 9 (100mL)  
7.37  7.69  8.66  15.04  14.32  18.07  12.73  1.56  3.9  0.0007019186  0.0006587615  0.0005542213  0.0003449069  0.0001947841  0.0001069709  0.000093882  0.0000629921  0.0000256082  
8.06  8.49  10.96  15.2  16.78  16.1  10.68  Velocity m/s  
8  8.49  10.34  14.38  16.92  18.39  10.31  3.063522842  2.87516395  2.418898324  1.505345669  0.8501350477  0.4668745454  0.4097479777  0.274929063  0.1117669366  
Reynolds number  
Head Loss  52116.50412  48912.15165  41150.18264  25608.86855  14462.45679  7942.447446  6970.613007  4677.080076  1901.373783  
min  75.34  69.03  50.15  19.67  7.22  3.05  2.29  1.15  0.64  log(V)  1.119565509  1.056109699  0.8833121984  0.409022552  0.1623600625  0.7616946968  0.8922129969  1.291242167  2.191339499  
max  76.13  69.7  50.75  20.2  7.77  3.59  2.78  1.82  1.35  Head loss h_L  
75.735  69.365  50.45  19.935  7.495  3.32  2.535  1.485  0.995  
Log(h_L)  4.327240405  4.239382418  3.920982747  2.992476981  2.014236132  1.199964783  0.930193637  0.3954147723  0.0050125418  
Friction  2.704215225  2.811913982  2.889434226  2.94802142  3.475222897  5.1041633  5.059774891  6.583730107  26.69213144  
Calculated H_L  
Run 1  Run 2  Run 3  Run 4  Run 5  Run 6  Run 7  Run 8  Run 9  
SP1  0.158  0.165  0.171  0.162  0.083  0.191  0.303  0.314  0.818  
SP2  0.120  0.130  0.125  0.158  0.094  0.282  0.500  0.580  2.555  
SP3  0.351  0.348  0.312  0.323  1.395  1.322  2.133  3.629  20.892  
RP  2.704  2.812  2.889  2.948  3.475  5.104  5.060  6.584  26.692 
&A
Page &P
Smooth pipe 2 3.43849316640585 3.36436049161018 3.09285898428471 2.30856716467159 1.49290409617815 0.837247524533702 0.688134638736401 0.288931291852213 0.105360515657826 Smooth pipe 1 2.14020775311153 2.10137771422248 2.02601631041528 1.83073437851928 1.80624234415481 1.01470735127573 0.627044619765575 0.298795362324794 0.591471596128055 4.34074880711086 4.30575285731789 4.19154689017846 3.74691248536455 3.02115632589415 2.27880456432864 1.96290772542388 1.3415584672785 0.518793793415168 Smooth pipe 3 1.11956550930293 1.05610969855834 0.883312198385049 0.446745192631654 0.548485589399971 0.678840052131722 0.956301 565472985 1.27536881809069 2.20026243877211 2.28645571106416 2.148850993052 1.69653261928503 0.856540727468381 0.3293037471426 0.0148886124937506 0.0618754037180874 0.168418651624963 0.267879445155601 Rough pipe 1.11956550930293 1.05610969855834 0.883312198385049 0.409022552024443 0.162360062472004 0.76169469676041 0.892212996902356 1.29124216724698 2.19133949875391 4.32724040497899 4.23938241753269 3.92098274679962 2.99247698083332 2.01423613155456 1.1999647829284 0.930193637043146 0.395414772254663 0.00501254182354418
Log (Velocity)
Log (Head Loss)
Smooth pipe 1 Smooth pipe 2 79805.6018442396 74046.4347008408 65906.8734331641 39597.51396637 34102.9752066954 14204.1248767267 9892.97833121846 7520.14325070719 2942.66475027673 Smooth pipe 3 52116.5041232754 48912.1516519278 41150.1826386254 26593.354658892 9829.91785626121 8628.54691547081 6537.89077261165 4751.91335728808 1884.48340628493 Rough pipe 52116.5041232754 48912.1516519278 41150.1826386254 25608.8685471234 14462.4567875476 7942.44744599319 6970.61300650537 4677.08007607095 1901.37378252564
Run
Reynolds
Smooth pipe 1 76.765 74.125 66.125 42.39 20.515 9.765 7.12 3.825 1.68 Smooth pipe 2 7.41210215093585 6.87720818128069 6.12123042802006 3.67769694932798 3.16738086101038 1.31923602000311 0.918829809855997 0.698448087299724 0.273305773291196 31.14 28.915 22.04 10.06 4.45 2.31 1.99 1.335 0.9 Smooth pipe 3 3.06352284190682 2.87516394956297 2.41889832372247 1.56321592959763 0.577824211222849 0.50720498261901 0.384311612160544 0.279327928027941 0.110774083132908 9.84 8.575 5.455 2.355 1.39 1.015 0.94 0.845 0.765 Rough pipe 3.06352284190682 2.87516394956297 2.41889832372247 1.50534566869507 0.850135047698934 0.466874545420209 0.409747977665772 0.274929063019627 0.111766936630898 75.735 69.365 50.45 19.935 7.495 3.32 2.535 1.485 0.995
Velocity (m/s)
Head Loss(m)
Sheet2
&”Times New Roman,Regular”&12&A
&”Times New Roman,Regular”&12Page &P
__MACOSX/._results_lab4V1.xlsx
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