Fluidmechanics-2labs /civil or mechanical engg

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

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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

Experiment 3: Bernoulli’s Principle

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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

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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

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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 0-300mm

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 3-6 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

MECH202 Lab 4 Fluid Friction Loss – V2-2.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

1

2

3

4

5

6

7

8

9

10

Smooth Pipe 2

Run Measuring Tank
Volume

1

2

3

4

5

6

7

8

9

10

Smooth Pipe 3

Run Measuring Tank
Volume

1

2

3

4

5

6

7

8

9

10

Rough Pipe

Run Measuring Tank
Volume

1

2

3

4

5

6

7

8

9

10

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 7.85E-05 0.001963495408 Manometer A 2.363808868 2.23012569 1.991654386 1.90906252 1.390325475 Manometer A 1.86E-04 1.86E-04 1.86E-04 1.86E-04 1.86E-04 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 1.90E-04 1.90E-04 1.90E-04 1.90E-04 1.90E-04 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 1.68E-04 1.68E-04 1.68E-04 1.68E-04 1.68E-04 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 1.24E-04 1.24E-04 1.24E-04 1.24E-04 1.24E-04 Manometer D 7.41E-01 8.02E-01 8.70E-01 9.48E-01 1.32E+00 Q real 1.67E-04 1.54E-04 1.42E-04 1.31E-04 9.39E-05 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 1.15E-04 1.15E-04 1.15E-04 1.15E-04 1.15E-04 Manometer F 6.88E-01 7.45E-01 8.08E-01 8.81E-01 1.22E+00 Manometer G 1.471245326 1.353634953 1.178705769 1.117317777 0.7772155682 Manometer G 1.16E-04 1.16E-04 1.16E-04 1.16E-04 1.16E-04 Manometer G 6.92E-01 7.49E-01 8.12E-01 8.85E-01 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 1.86E-04 1.86E-04 1.86E-04 1.86E-04 1.86E-04 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 A-D 9.98E-01 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 F-H 8.30E-01 8.99E-01 9.75E-01 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 8.51E-02 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 9.00E-01 8.81E-01 9.09E-01 8.70E-01 8.60E-01 0.2593075708 1.979424498 1.823977028 1.673308585 1.204355077 8.81E-01 8.55E-01 8.89E-01 8.49E-01 8.38E-01 0.4150185734 2.003527226 1.844421915 1.694096107 1.219619265 9.96E-01 9.72E-01 1.01E+00 9.66E-01 9.51E-01 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 9.00E-01 8.73E-01 9.00E-01 8.68E-01 8.56E-01

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 7.15E-01 6 5 17.78 17.25 19.41 1.81E+01 4.48E+01 4.41E+01 4.44E+01 3.63E+00 5.03E-01 7 3 12.35 12.85 9.31 1.15E+01 3.74E+01 3.66E+01 3.70E+01 3.83E+00 3.75E-01 8 3 15.63 14.73 14.93 1.51E+01 2.67E+01 2.62E+01 2.65E+01 5.03E+00 1.56E-01 9 2 12.45 13.13 12.43 1.27E+01 1.71E+01 1.68E+01 1.69E+01 6.34E+00 6.28E-02 10 2 11.01 12.3 11.07 1.15E+01 8.26E+00 8.69E+00 8.48E+00 5.73E+00 3.85E-02 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 4.72E-01 6 3 9.58 8.06 7.86 8.50E+00 10.62 10.14 1.04E+01 2.83E+00 2.74E-01 7 3 9.98 10.85 8.51 9.78E+00 8.14 7.33 7.74E+00 3.26E+00 1.54E-01 8 2 8.03 8.86 8.63 8.51E+00 5.42 5.06 5.24E+00 4.25E+00 6.14E-02 9 2 11.56 12 11.91 1.18E+01 3.28 2.95 3.12E+00 5.91E+00 1.89E-02 10 2 7.08 7.58 7.43 7.36E+00 1.28 1.5 1.39E+00 3.68E+00 2.17E-02 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 9.56E-01 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 7.41E-01 5 5 11.6 11.28 7.86 1.02E+01 3.06 2.42 2.74E+00 2.05E+00 2.19E-01 6 3 8.43 7.33 7.15 7.64E+00 2.24 1.85 2.05E+00 2.55E+00 1.06E-01 7 3 8.96 9.08 7.88 8.64E+00 1.78 1.27 1.53E+00 2.88E+00 6.16E-02 8 2 8.56 8.43 8.76 8.58E+00 1.15 0.8 9.75E-01 4.29E+00 1.77E-02 9 2 11.76 11.41 11.58 1.16E+01 0.69 0.51 6.00E-01 5.79E+00 5.99E-03 10 2 8.56 8.41 8.33 8.43E+00 0.1 0.18 1.40E-01 4.22E+00 2.64E-03 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 9.35E-01 7 3 9.63 9.83 8.13 9.20E+00 17.23 16.32 1.68E+01 3.07E+00 5.98E-01 8 2 8.93 8.91 8.4 8.75E+00 10.2 9.75 9.98E+00 4.37E+00 1.75E-01 9 2 11.31 11.51 12.05 1.16E+01 3.64 3.41 3.53E+00 5.81E+00 3.50E-02 10 2 8.56 8.56 8.93 8.68E+00 0.8 1.1 9.50E-01 4.34E+00 1.69E-02

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

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

1

2

3

4

5

6

7

8

9

10

Smooth Pipe 2

Run Measuring Tank
Volume

1

2

3

4

5

6

7

8

9

10

Smooth Pipe 3

Run Measuring Tank
Volume

1

2

3

4

5

6

7

8

9

10

Rough Pipe

Run Measuring Tank
Volume

1

2

3

4

5

6

7

8

9

10

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 quasi-steady 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 quasi-steady conditions defines the energy dissipation factor. This is a nondimensional, time-varying 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 well-known method of characteristics for the solution of the continuity and momentum equations. (Silva-Araya, W. and Chaudhry, M., 1997)

An efficient procedure is developed for simulating frequency-dependent friction in transient laminar liquid flow by the method of characteristics. The procedure consists of determining an approximate expression for frequency-dependent 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 frequency-dependent 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 non-linear 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

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 n-values.

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 Frequency-Dependent 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)0733-9496(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.

Silva-Araya, W. and Chaudhry, M.. (1997). Computation of Energy Dissipation in Transient Flow. Available: http://ascelibrary.org/doi/abs/10.1061/(ASCE)0733-9429(1997)123:2(108). Last accessed 20th May 2015.

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

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

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