Abstract:

The experiment concentrates on various methods of measuring flow rates using a Venturi meter,

Orifice meter, Turbine meter, Rota meter and actual flow rate using difference of weight of a

tank. The main objectives of this lab are to study flow pattern analysis, Flow velocity profile

measurement with Pitot tube. System Uncertainty Analysis of Flow rate (Orifice Plate). A

velocity profile of air jet will be sketched using measurements from the Pitot tube. Furthermore,

a velocity profile and turbulent flow across a cylinder will be studied using a laser Doppler

Velocimetry and a vortices counter experiment. With the help of results, orifice meter and

turbine meter will be calibrated using plots.

1

Table of Content:

Topic Page No.

Introduction 2

Theoretical Principles 3

Experimental System 9

Results and Discussions with Sample calculations 12

Conclusions 27

References 28

Nomenclature 29

Appendix

Data Sets 30

2

Introduction:

The experiments performed in this Lab gives an overview of flow measurement. The

flow measurement was calculated using different flow measuring devices such as a Venturi

meter, Orifice plate, Turbine and Rota meter. An air jet velocity was calculated and its profile

was studied using a Pitot tube. A velocity profile of a turbulent and laminar flow was studied

using a Laser Doppler Velociemetry.

The flow measurement using a Venturi, Orifice and a Turbine is an important

method. The flow measurement using a venture is the most precise method. This is because the

pipe loss due to turbulent flow is minimum in the Venturi. However, it is the most expensive

method of measuring flow rate because it is very expensive to manufacture a venture (its inner

surface needs a certain quality of surface roughness/ smoothness).

Moreover, a flow measurement using an orifice is relatively cheap method but, the

loss due to turbulent flow and disturbances in flow causes error in measuring a flow rate. A

calibration is required to measure the exact value of flow through the orifice. This technique is

important to use where the accuracy of flow measurement is not an important factor. This

method gives an approximate estimate of the flow rate.

Furthermore, a flow measurement using a turbine is another important flow

measurement method. In this method a turbine rotates with rotational speed ω, as the fluid flows

into the turbine. It can be shown that the rotational speed is proportional to the flow rate. The

relation between rotational speed and flow rate can be calibrated to find the flow rate for

consecutive flow rates.

A pitot tube is a common method of measuring an air jet velocity. It is often used to

measure the velocity of an air plane. This method takes into account the use of Bernoulli’s

equation and compares two points. One at a point far away from the pitot tube and other at the

position of the pitot tube (Stagnation pressure).

A flow past a cylinder can be studied using a water tunnel. A pattern of turbulence/

Vortex can be studied by injecting ink into the tunnel. This will give a good estimate of the flow

visualization. A laser Doppler Velocimetry can also be used to determine the velocity profile

across a cylinder.

In general, all the methods of flow measurements have different application. The

design (quality) and usage of flow measuring device depends on the required accuracy of the

application.

3

Theoretical Principles:

The Flow measurement can be calculated using different methods as mentioned

previously. The theoretical principles used to derive equation of flow rate are mentioned in this

section. Reynolds’s number and Bernoulli’s Equation are important criterion to study the flow

rate. They are described as follows:

Bernoulli’s Equation:

Bernoulli’s equation states that he sum of pressure, Kinetic energy and potential energy across

any two arbitrary points across a stream line is constant. This is shown in equation form as

follows:

𝑃1 + 𝜌𝑣1

2

2+ 𝑔𝑧1 = 𝑃2 +

𝜌𝑣22

2+ 𝑔𝑧2

Often, in many cases the potential energy change is negligible in flow measurement using these

devices. Thus, the equation reduces to the following:

𝑃1 + 𝜌𝑣1

2

2= 𝑃2 +

𝜌𝑣22

2

Reynolds’s Number:

The Reynolds’s number is described as the ratio of inertial force to the frictional/ viscous force.

This is defined in equation form as follows;

𝑅𝑒 = 𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝐹𝑜𝑟𝑐𝑒

𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑐𝑒=

𝜌𝑣𝐷

𝜇=

𝑣𝐷

𝜗

Where

µ = dynamic viscosity

𝜗 = the kinematic viscosity

D = Diameter of pipe

v = velocity of the fluid

When,

𝑅𝑒 ≫ 1, inertial force is dominant

𝑅𝑒 << 1, viscous force is dominant

4

Venturi Meter:

A schematic of a venturi meter is shown as follows:

1

From the schematic, it is apparent that the change in potential energy across the flow is almost

negligible (0). Thus, the modified version of Bernoulli’s equation can be applied to ventuari as

follows:

𝑃1 + 𝜌𝑣1

2

2= 𝑃2 +

𝜌𝑣22

2

From equation of continuity, we equate the flow rate at the point in stream line at point 1 and at

that of point 2. Then, the Bernoulli’s equation can be manipulated using these two equations.

Thus, the equation of continuity becomes:

A1v1 = A2v2

𝑣1 = 𝐴2

𝐴1𝑣2

𝑃1 + 𝜌(

𝐴2

𝐴1𝑣2)2

2= 𝑃2 +

𝜌𝑣22

2

𝑣2 = √2(𝑃1 − 𝑃2)

𝜌(1 − (𝐴2

𝐴1)2)

Thus, Flow rate becomes:𝑄2 = 𝐴2𝑣2 = 𝐴2√2(𝑃1−𝑃2)

𝜌(1−(𝐴2𝐴1

)2)

1 www.ustudy.in

5

Orifice Meter:

The schematic of an Orifice meter is shown as follows:

2

From the schematic, it is apparent that the change in potential energy across the flow is almost

negligible (0). Thus, the modified version of Bernoulli’s equation can be applied to Orifice

similarly as in venturi case. From equation of continuity, we equate the flow rate at the point in

stream line at point 1 and at that of point 2. Then, the Bernoulli’s equation can be manipulated

using these two equations. The equation obtained for an orifice is similar to that of the venturi

meter. The only difference is that the equation of flow rate for orifice is calibrated by a factor c.

𝑣2 = 𝑐 √2(𝑃1 − 𝑃2)

𝜌(1 − (𝐴2

𝐴1)2)

Thus, Flow rate becomes:𝑄2 = 𝑐𝐴2√2(𝑃1−𝑃2)

𝜌(1−(𝐴2𝐴1

)2)

Where, 𝑐 = 𝑄𝐴𝑐𝑡𝑢𝑎𝑙

𝑄𝐼𝑑𝑒𝑎𝑙

The values of c are summarized in the following table:

Meter c

Venturi meter 0.95<c<0.98 ~1

Orifice meter 0.6<c<0.7

A plot of flow rate and Reynolds number can be made to find calibration.

2 www.engineeringexcelspreadsheets.com

6

Turbine Meter:

A turbine rotates as the fluid flows into the turbine. Ideally, the rotational speed of the turbine is

proportional to that of the flow rate through the turbine. The schematic of a turbine meter is

shown as follows:

The Roto meter frequency can be measured and a relation between the flow rate and rotational

speed can be measured.

𝜔 ∝ 𝑄

The loss due to friction is calculated as shown: 𝑄 = −2𝜋

16

𝑎4

𝜇

𝑑𝑃

𝑑𝑥

Actual flow rate measurement:

An actual flow rate measurement in the experiment can be done using a weight measurement.

The weight of fluid entering a tank can be measured for a given time. The difference between

initial and final weight can be calculated. Tis difference can be divided by time. This will yield

the actual flow rate.The equation for this measurement is as follows:

𝑄 = 𝑊2 − 𝑊1

𝜌𝑡

Where

W1 = initial mass

W2 = final mass

t = time taken during mass change

𝜌 = density of the fluid

Thus, actual flow rate can be calculated using this method.

7

Pitot Tube:

A Pitot tube again works on the principle of Bernoulli’s equation. The schematic of a Pitot tube

is shown as follows:

The equation of velocity using a Pitot tube can be derived with the help of modified Bernoulli’s

equation. In this case, the velocity at point 1 is zero because of stagnation pressure. Velocity at

point 2 is assumed to be velocity of the air jet.

𝑃0 + 𝜌(0)2

2= 𝑃1 +

𝜌𝑈2

2

𝑈 = √2(𝑃0 − 𝑃1

𝜌= √

2𝜌𝑙ℎ𝑔

𝜌

𝑈 = √4𝜌𝑙𝑔ℎ

𝜌

Where,

U = Velocity of Air Jet

h = difference in height in manometer

𝜌𝑙 = density of liquid

𝜌 = density of air

Note: A factor of 4 is introduced in the equation. This is because the experiment was set up in

such a way that the height of the manometer column was supposed to be multiplied by 2.

8

Laser Doppler Velocimetry:

Laser Doppler Velocimetry (LDV) is also known as Laser Doppler Anemometry (LDA). Flow

past a cylinder can be studied using this method. The observations on stream lines, Reynolds

number computation and vortex shedding can be studied using a flow tunnel.

A velocity along a vertical line can be measured using LDV.

Strouhal number can be calculated as:

𝑠𝑡 = 𝑓𝑑

𝑈~0.2

9

Experimental System:

The instruments and equipment used in this experiment are shown as follows:

Instruments: Venturi Meter, Orifice Meter, Turbine meter, Rota meter, Weighing machine, Pitot

tube, Laser Doppler Velocimetry, Water Tunnel.

The first part of the lab was calibration of flow meters. For this a reading of pressure difference

(in Inches) across two stream line points in various meters were taken. Later, Pressure difference

was calculated and flow rate was calculated respectively. The schematic of the Experimental set

up is as shown below:

10

Basic Procedure for calibration:

Calibration of Flow-meters

First set the flow rate on the rotameter with the inlet hand valve to a value of

5.Record the pressure drop ΔPL through the rotameter on the differential pressure gage by

opening valves Q and R.

Record the pressure drop ΔPL through the Turbine flow meter on the differential

pressure gage by opening valves A and B. Record the digital output from the counter of Turbine

flow meter.

Furthermore, record the pressure drop ΔPM through the Venturi on the differential

pressure gage by opening valves E and D. Then record the pressure drop ΔPL through the

Venturi on the differential pressure gage by opening valves C and F.

Record the pressure drop ΔPM through the orifice on the differential pressure gage

by opening valves M and L. Then record the pressure drop ΔPL through the orifice on the

differential pressure gage by opening valves N and K. Repeat the above mentioned steps for

rotameter settings of 4.5, 4, 3, 2, and 1.5.

Measurement of Air Jet Velocity

First adjust the horizontal balance of a fan. Set the Pitot tube in an alignment with

the centerline of the jet exit from the fan and record the axial distance from the jet exit.

Remove the cap from the vertical manometer which is connected to the Pitot tube.

Record the initial reading of manometer.

Turn on the power of fan and set the power to maximum. Record the manometer

reading. If the variation of manometer readings is within the range of inclined manometer

measurement, then repeat steps shown above to use the inclined manometer instead of the

vertical manometer.

Recording the manometer reading in both traverse directions for at least 6 points on

each side or until the change in manometer reading becomes insignificant. Repeat steps different

axial distances such as x= 4.5, 6.5 and 8.5.

11

Measurement using Laser Doppler Velocimetry (LDV) and Water tunnel flow visualization

This part of the experiment uses Laser Generator and Processor. Open this program in computer,

wait until the “Ready” light on Processor turn to Green. Then follow procedure to set up a new

file.

Precisely adjust the laser focus point to the measurement location, using the traversing stage.

Move stage up/down and left/right to let laser beam focus at center of cylinder. Move left/right to

let focus at right edge of cylinder. Move 5 cycles of stage further to let the focus reach to first

measuring location. In this part, a velocity profile in the wake of a cylinder needs to be obtained

with at least 6 points at different locations.

Flow visualization:

Modify/ change the flow rate of water in the water tunnel. Inject red ink through the water

tunnel. Count the number of vortices formed in each case. Record your observations.

3

3 www.youtube.com

Flow visualization across a cylinder. The ink forms vortex. The number of vortex formed is

directly proportional to the velocity/ flow rate of water across the cylinder.

12

Results and Discussion with Sample Calculations:

Note: All calculations are performed in SI (Metric) units unless and otherwise specified.

Actual flow rate measurements:

The data obtained for change in weight of tank for given time period is summarized as follows:

Sr. No. Flow rate

Flow Rate

Weight (mass)

W1

Weight (mass)

W2

Difference in mass

Time mass/time Flow rate

Units Gallons

Per Minute

m3/s kg kg kg sec kg/s m3/s

1 5 0.000315 30 35 5 15 0.333333 0.000333

2 4.5 0.000284 30 34.5 4.5 15 0.3 0.0003

3 4 0.000252 29 36.5 7.5 30 0.25 0.00025

4 3 0.000189 28 33.5 5.5 30 0.183333 0.000183

5 2 0.000126 26.5 30 3.5 30 0.116667 0.000117

6 1.5 9.46E-05 26 28.5 2.5 30 0.083333 8.33E-05

It can be observed that the measured flow rate is approximately identical to the flow

rate as shown in the third column. The calculations are shown below:

𝑄 = 𝑊2 − 𝑊1

𝜌𝑡=

(35 − 30)𝑘𝑔

1000𝑘𝑔𝑚 (15s)

= 5𝑘𝑔

15000𝑘𝑔𝑠/𝑚3= 0.000333 𝑚3/𝑠

This calculated flow rate is identical to the flow rate in third column 0.000315𝑚3

𝑠.

Note: density of water here was used as 𝜌 = 1000𝑘𝑔/𝑚3

Similarly the flow rate calculations for the other cases can be performed. It can be

shown that the actual flow rate is almost identical of the prescribed flow rate as shown in the

table. Thus, the experimental data are consistent with the prescribed values of flow rate.

This data of actual flow rate will be used to calibrate the Ventuari meter, Orifice

meter and turbine meter. The value of calibration constant c will be found using the actual flow

rate found from this section.

Venturi Meter:

13

From the theory, the equation governing the flow rate through a venture meter is shown as

follows:

𝑄2 = 𝐴2𝑣2 = 𝐴2√2(𝑃1 − 𝑃2)

𝜌(1 − (𝐴2

𝐴1)2)

The data obtained for venturi meter from the experiment is summarized as follows:

Sr. No.

Flow rate

(gpm)

∆P: E-D

∆P: C-F

∆P = P1-P2

∆P = P1-P2

∆P = P1-P2

velocity flow rate Reynolds number

Flow rate

c

units Gallons

per minute

in in in m Pa m/s Qven m3/s

Re Q

m3/s

𝑄𝑣𝑒𝑛

𝑄𝑎𝑐𝑡

1 5 85 20 65 1.651 16191.357 6.696441 0.000328188 52680.9 0.000333 0.984563

2 4.5 70 15 55 1.397 13700.379 6.15983 0.000301889 48459.38 0.0003 0.993740

3 4 55 10 45 1.143 11209.401 5.571776 0.000273069 43833.16 0.00025 0.915521

4 3 32 7 25 0.635 6227.445 4.152956 0.000203533 32671.31 0.000183 0.900754

5 2 14 4 10 0.254 2490.978 2.62656 0.000128726 20663.15 0.000117 0.906320

6 1.5 5 0 5 0.127 1245.489 1.857259 9.10228E-05 14611.05 8.33E-05 0.915521

Sample Calculations:

Inner diameter of the tube = 0.590 in = 0.014986 m.

Venturi Bore = 0.311 in = 0.0078994m. 𝐴2 = 𝜋𝐷2

2

4=

𝜋(0.0078994𝑚)2

4= 49.00925 × 10−6𝑚2

(𝐴2

𝐴1) = (

𝐷2

𝐷1)2 = (

0.0078994𝑚

0.014986𝑚)2 = 0.0.277854

Then,

𝑣2 = √2(𝑃1 − 𝑃2)

𝜌(1 − (𝐴2

𝐴1)2)

= √2(16191.357)𝑘𝑔𝑚/𝑠2

1000𝑘𝑔/𝑚3(1 − (0.277854)2)= 6.696441 𝑚/𝑠

𝑄2 = 𝐴2𝑣2 = 𝐴2√2(𝑃1 − 𝑃2)

𝜌(1 − (𝐴2

𝐴1)2)

= (6.696441𝑚

𝑠) (49.00925 × 10−6𝑚2) = 0.00032818 𝑚3/𝑠

The Reynolds number is found as follows:

14

𝑅𝑒 = 𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝐹𝑜𝑟𝑐𝑒

𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑐𝑒=

𝜌𝑣𝐷

𝜇=

𝑣𝐷

𝜗=

(6.696𝑚

𝑠)(0.0078994𝑚)

(1.004×10−6)= 52680.9 ≫ 1

The Reynolds number is found to be much greater than 1. Thus I n this case the inertial force will

dominate the viscous force.

The calibration constant for case 2 is found as follows:

𝑐 =𝑄

𝑄𝑎𝑐𝑡=

0.0003

0.00301889= 0.993740

The calibration constant is close to 1. This shows that the venturi meter measures most accurate reading

for the flow rate.

In some cases, the calibration constant was found to be more than 1. This may be due to experimental

errors. There may be error in taking the reading. This was because the precision of the pressure gage was

not too high. The minimum measurable quantity in the pressure gage was about few inches. This error of

about few inches could easily modify the results. Also the zero of the pressure gage was not always

obtained in the experiment.

Orifice Meter:

From the theory, the equation governing the flow rate through a orifice meter is shown as

follows:

𝑄2 = 𝐴2𝑣2 = 𝑐𝐴2√2(𝑃1 − 𝑃2)

𝜌(1 − (𝐴2

𝐴1)2)

The data obtained for orifice meter from the experiment is summarized as follows:

Sr. No.

Flow rate

(gpm)

∆P:E-D

∆P:C-F

∆P = P1-P2

∆P = P1-P2

∆P = P1-P2

velocity flow rate Reynolds number

flow rate c

units Gallons

Per Minute

in in in m Pa m/s Qori

m3/s Re

Q m3/s

𝑄

𝑄𝑎𝑐𝑡

1 5 200 160 40 1.016 9963.912 5.25312 0.000257451 41326.3 0.000333 0.772354

2 4.5 150 125 25 0.635 6227.445 4.152956 0.000203533 32671.31 0.0003 0.678444

3 4 127 100 27 0.6858 6725.641 4.315879 0.000211518 33953.02 0.00025 0.846072

4 3 70 60 10 0.254 2490.978 2.62656 0.000128726 20663.15 0.000183 0.70214

5 2 32 23 9 0.2286 2241.88 2.491774 0.00012212 19602.78 0.000117 1.046743

6 1.5 16 7 9 0.2286 2241.88 2.491774 0.00012212 19602.78 8.33E-05 1.46544

Sample Calculations:

15

Inner diameter of the tube = 0.590 in = 0.014986 m.

Orifice Bore = 0.311 in = 0.0078994m. 𝐴2 = 𝜋𝐷2

2

4=

𝜋(0.0078994𝑚)2

4= 49.00925 × 10−6𝑚2

(𝐴2

𝐴1) = (

𝐷2

𝐷1)2 = (

0.0078994𝑚

0.014986𝑚)2 = 0.0.277854

Then,

𝑣2 = √2(𝑃1 − 𝑃2)

𝜌(1 − (𝐴2

𝐴1)2)

= √2(9963.912)𝑘𝑔𝑚/𝑠2

1000𝑘𝑔/𝑚3(1 − (0.277854)2)= 5.25312 𝑚/𝑠

𝑄2 = 𝐴2𝑣2 = 𝐴2√2(𝑃1 − 𝑃2)

𝜌(1 − (𝐴2

𝐴1)2)

= (5.25312𝑚

𝑠) (49.00925 × 10−6𝑚2) = 0.000257451 𝑚3/𝑠

The flow rate in this case is lower than the actual flow rate. This is due to the loss in the flow rate

caused by the turbulence in the orifice. Thus, the measurements need to be calibrated to obtain

the actual flow rate.

The Reynolds number is found as follows:

𝑅𝑒 = 𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝐹𝑜𝑟𝑐𝑒

𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑐𝑒=

𝜌𝑣𝐷

𝜇=

𝑣𝐷

𝜗=

(5.25312𝑚

𝑠)(0.0078994𝑚)

(1.004×10−6)= 41326.3 ≫ 1

The Reynolds number is found to be much greater than 1. Thus I n this case the inertial force will

dominate the viscous force.

The calibration constant is found as follows:

𝑄

𝑄𝑎𝑐𝑡=

0.000257451

0.000333= 0.7732

The calibration for orifice is found to be about 0.7732. This is typical characteristics of an

orifice. The turbulent flow at the orifice plate causes the velocity across the plate to drop. This

reduces the flow rate at the orifice plate of the orifice meter. In some cases, the calibration constant

was found to be more than 1. This may be due to experimental errors. There may be error in taking the

reading. This was because the precision of the pressure gage was not too high. The minimum measurable

quantity in the pressure gage was about few inches. This error of about few inches could easily modify

the results. Also the zero of the pressure gage was not always obtained in the experiment.

Plot of pressure head (in meters) v/s the Reynolds number is shown as follows:

16

The Reynolds number is proportional to the pressure head.

Plot of pressure head (in meters) v/s the flow rate is shown as follows:

Again it can be shown that the pressure head is directly proportional to the flow rate.

Turbine Meter:

y = 3E-05x - 0.4669R² = 0.9916

0

0.2

0.4

0.6

0.8

1

1.2

0 10000 20000 30000 40000 50000

Pre

ssu

re h

ead

(m

ete

rs)

Reynolds number

Pressure head - Reynolds number plot

y = 2E+07x2 - 2E-12x - 7E-16R² = 1

0

0.2

0.4

0.6

0.8

1

1.2

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003

pre

ssu

re h

ead

(m

)

Flow rate (m3 /s)

Flow rate - Pressure head plot

17

The data obtained from the experiment for the turbine meter is as follows:

Sr. No. Flow rate

(gpm)

Actual Flow rate

Frequency

units Gallons

per Minute

m3/s Hz (1/s)

1 5 0.000333 20.1

2 4.5 0.0003 17.6

3 4 0.00025 15.7

4 3 0.000183 12.2

5 2 0.000117 7.8

6 1.5 8.33E-05 6.1

The graph for flow rate and the turbine frequency is obtained as follows:

It is apparent from the plot that the frequency of the turbine is directly proportional to the flow

rate of water through the turbine. The relation between the flow rate and the frequency is shown

as follows:

ω = 55125Q + 1.6125

Where ω = angular frequency and Q is the flow rate. Note that the slope of the graph is very

close to the Reynolds number obtained using a venturi meter.

A plot of pressure head in turbine, orifice, venture meter and Roto meter v/s flow rate is shown

as follows:

y = 55125x + 1.6125R² = 0.9954

0

5

10

15

20

25

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035

Fre

qu

en

cy (

Hz)

Flow Rate (m3/s)

Flow Rate- Frequency plot

18

The Calibration factor - Reynolds Number plot is shown as follows:

The plot is not exactly as predicted in the theory. But it provides an idea that the curve

for venturi is above that of curve of orifice. That is venturi meter gives better prediction of the

flow rate than that of the orifice.

Measurement of Velocity of an Air Jet:

Pitot tube:

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.0001 0.0002 0.0003 0.0004

Pre

ssu

re h

ead

(m

)

Flow rate (m3/s)

Flow rate- pressure head plot for all the flow meters

Venturi

Orifice

Rotometer

Turbine

Poly. (Venturi)

Poly. (Orifice)

Poly. (Rotometer)

Poly. (Turbine)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10000 20000 30000 40000 50000 60000

Cal

ibra

tio

n f

acto

r

Reynolds Number

Calibration constant- Reynolds number plot

Ventuari

orifice

Poly. (Ventuari)

Poly. (orifice)

19

The data obtained from the experiment for the pitot tube velocity measurement is as follows:

Sr No y x=4.5 x=6.5 x=8.5

H1 H2 H3

1 -2 0 0 0

2 -1.5 0 0 0

3 -1 0.6 0.18 0.3

4 -0.5 1.5 1.28 1.18

5 -0.25 2.55 2.24 1.86

6 0 2.93 2.8 2.24

7 0.25 2.65 2.2 1.65

8 0.5 1.34 1.05 0.82

9 1 0.4 0.1 0.12

10 1.5 0 0 0

11 2 0 0 0

For case 1 when x = 4.5:

sr no y x=4.5

U Square U

in m

1 -2 0 0 0 0

2 -1.5 0 0 0 0

3 -1 0.6 0.01524 362.7728 19.04659

4 -0.5 1.5 0.0381 906.9319 30.11531

5 -0.25 2.55 0.06477 1541.784 39.26556

6 0 2.93 0.074422 1771.54 42.08967

7 0.25 2.65 0.06731 1602.246 40.02807

8 0.5 1.34 0.034036 810.1925 28.46388

9 1 0.4 0.01016 241.8485 15.55148

10 1.5 0 0 0 0

11 2 0 0 0 0

The velocity of air jet can be found as follows:

𝑈 = √4𝜌𝑙𝑔ℎ

𝜌

Where,

U = Velocity of Air Jet

h = difference in height in manometer

𝜌𝑙 = density of paraffin = 784 kg/m3

𝜌 = density of air = 1.2922kg/m3

20

The velocity at the center of the profile is calculated as follows:

𝑈 = √4𝜌𝑙𝑔ℎ

𝜌= √

4 (784𝑘𝑔

𝑚3 ) (9.81𝑚

𝑠2 ) (0.07442𝑚)

1.2922𝑘𝑔𝑚3

= 42.089 𝑚

𝑠.

The velocity profile for this case is plotted as follows:

Similarly for case 2: x= 6.5:

Sr. No. y x=6.5 x=6.5 U Square U

in m

m/s

1 -2 0 0 0 0

2 -1.5 0 0 0 0

3 -1 0.18 0.004572 108.815 10.43144

4 -0.5 1.28 0.032512 773.7955 27.81718

5 -0.25 2.24 0.056896 1354.142 36.79867

6 0 2.8 0.07112 1692.678 41.14216

7 0.25 2.2 0.05588 1329.961 36.46863

8 0.5 1.05 0.02667 634.7541 25.19433

9 1 0.1 0.00254 60.45277 7.775138

10 1.5 0 0 0 0

11 2 0 0 0 0

The plot of velocity profile for this case is:

-5

0

5

10

15

20

25

30

35

40

45

-3 -2 -1 0 1 2 3

velo

city

(m

/s)

y

For nearest position from Jet x=4.5

x=4.5

21

Similarly for case 3: x= 8.5:

Sr. No. y x=8.5 x=8.5 U square U

in m

m/s

1 -2 0 0 0 0

2 -1.5 0 0 0 0

3 -1 0.3 0.00762 181.3583 13.46693

4 -0.5 1.18 0.029972 713.3427 26.70848

5 -0.25 1.86 0.047244 1124.422 33.5324

6 0 2.24 0.056896 1354.142 36.79867

7 0.25 1.65 0.04191 997.4707 31.58276

8 0.5 0.82 0.020828 495.7127 22.26461

9 1 0.12 0.003048 72.54332 8.517237

10 1.5 0 0 0 0

11 2 0 0 0 0

The velocity profile for this case is:

-5

0

5

10

15

20

25

30

35

40

45

-3 -2 -1 0 1 2 3

Ve

loci

ty (

m/s

)

y

The velocity profile at x=6.5

x=6.5

22

The overall velocity profile at each location on single plot is summarized as follows:

It can be observed that the velocity of the air jet decreases as the location of

measurement moves away from the initial source of velocity. The velocity also decreases as the

point moves further away from the center of air jet. Thus, an inverted parabolic plot is generated

as the velocity profile in this case. It can also be observes that the velocity profile widens up an

tends to become uniform to an average value as the location moves away from the source of air

jet. At an infinite distance from the source, the velocity profile will be uniform or equivalently

the velocity of air jet will approach zero.

Flow visualization observing vortices:

-5

0

5

10

15

20

25

30

35

40

-3 -2 -1 0 1 2 3

velo

city

(m

/s)

y

Velocity profile at x=8.5

x=8.5

-5

0

5

10

15

20

25

30

35

40

45

-3 -2 -1 0 1 2 3

Ve

loci

ty (

m/s

)

y

Velocity profile for each case

x=4.5

x=6.5

x=8.5

23

From this part of the experiment, the vortices count for 30 seconds for different flow rate was

recorded as follows:

Velocity Number of vortices count

3.5 52

2.5 35

1.5 20

It can be observed that the number of vortices count increases as the velocity of water through

the water tunnel was increases. This shows that as the velocity of water in the water tunnel

increases, the flow becomes more turbulent. This is consistent with the theory. As the velocity of

water increases, the Reynolds number for the process increases, this gives rise to a turbulent flow

once Reynolds number exceeds a fixed value (4000).

Laser Doppler Velocimetry (LDV):

In case 1,

The velocity profile on left side of the cylinder was studied. The average frequency recorded at

each location is summarized as follows: Note that wavelength of red light is taken as 650 nm.

Location Frequency Velocity = wavelength

*frequency

Top- Left 0.02 MHz 13mm/s = 0.512 in/s

Middle- Left 0.02 MHz 13mm/s = 0.512 in/s

Bottom-Left 0.02 MHz 13mm/s = 0.512 in/s

In case 2,

The velocity profile on right side of the cylinder was studied. The average frequency recorded at

each location is summarized as follows:

Location Frequency Velocity = wavelength

*frequency

Top- Right 0.03 MHz 19.5mm/s = 0.767 in/s

Middle- Right -0.00908 MHz -5.889mm/s = -0.231 in/s

Bottom- Right 0.03 MHz 19.5mm/s = 0.767 in/s

The Plots obtained from the software are as follows:

24

For the velocity profile on the left side of the cylinder:

The velocity on the left side of the cylinder was almost the same on top, middle and bottom

location. The velocity in each case was found to be 13mm/s or equivalently 0.512 in/s. The plot

for middle location is shown as below:

For the velocity profile on the right side of the cylinder:

The velocity on the right side of the cylinder was almost the same on top, middle and bottom

location. The velocity at top and bottom of the cylinder was 0.767 in/s. However, the velocity

plot at the middle was not consistent with the top and bottom location. This was because of the

turbulence caused at the center of the location. This turbulence drifted the water in negative

direction due to circular reverse flow (vortices). Thus velocity obtained in that case was negative

v = -0.231 in/s.

The plots for top and bottom as well as middle right location are shown as follows:

Count prevent-frequency plot for the middle-left location of the cylinder

25

Count prevent-frequency plot for the top and bottom right side of the cylinder

Count prevent-frequency plot for middle right location of the cylinder. Note that the velocity

will be negative in this case.

26

The Strouhal number is found as follows:

𝑠𝑡 = 𝑓𝑑

𝑈=

(0.03𝑀𝐻𝑧)(0.018𝑚)

0.0889𝑚/𝑠~0.2

Thus, Strouhal number is about 0.2 which is consistent with the theory.

Velocity profile of the cylinder on right and left location is shown as follows:

27

Conclusions:

The flow measurements with the help of Venturi meter, Orifice meter, Turbine meter and that of

Rota meter were performed effectively. The most accurate results for flow rate were obtained

with the help of venture meter followed by orifice, Rota meter and that of turbine. The flow rate

was found to be directly proportional to the frequency of the turbine. The velocity profile of air

jet obtained with the help of Pitot tube was consistent with the theoretical predictions. The flow

visualization by counting vortex essentially helped to differentiate between turbulent and laminar

flow. The velocity profile across a cylinder was effectively found using a Laser Doppler

Velocimetry. The profile was consistent with the theoretical predictions.

28

References:

J.p. Holman, ‘Experimental Methods for Engineers’, seventh Edition, Mc-graw Hill production,

2001, pg 48-220.

C. Zhu, ‘Measurement of Temperature & Sensor Characteristics’, ME 343 Laboratory

Instructions, NJIT, September 2009, pg 1-5.

Software usage:

Laser Doppler Velocimetry

29

Nomenclature:

Symbol Meaning

P Pressure

𝜌 Density

𝜌𝑙 Density of liquid (paraffin)

v velocity

g Gravitational constant = 9.807m/s2

D Diameter

µ Absolute viscosity

𝜗 Kinematic viscosity

ω Angular velocity

A Area of flow

Q Flow rate

U Air jet Velocity

h Height difference in manometer

f Frequency

Re Reynolds Number

St Strouhal number

30

Appendix:

Lab Data Set:

Flow rate measurement:

Measuremnt device

Test point 1 2 3 4 5 6

Rotameter 5 4.5 4 3 2 1.5

Rotameter ∆P:Q-R 20 16 17.5 10.5 9 12.5

Turbine ∆P:A-B 5 2.5 6 6 5 5

Venturi ∆P:E-D 85 70 55 32 14 5

∆P:C-F 20 15 10 7 4 0

Orifice ∆P:M-L 200 150 127 70 32 16

∆P:K-N 160 125 100 60 23 7

Weight

initial (kg) 30 30 29 28 26.5 26

final (kg) 35 34.5 36.5 33.5 30 28.5

Time (s) 15 15 30 30 15 30

Turbine Counter (Hz) 20.1 17.6 15.7 12.2 7.8 6.1

Pitot tube air jet velocity measurement:

sr no y x=4.5 x=6.5 x=8.5

1 -2 0 0 0

2 -1.5 0 0 0

3 -1 0.6 0.18 0.3

4 -0.5 1.5 1.28 1.18

5 -0.25 2.55 2.24 1.86

6 0 2.93 2.8 2.24

7 0.25 2.65 2.2 1.65

8 0.5 1.34 1.05 0.82

9 1 0.4 0.1 0.12

10 1.5 0 0 0

11 2 0 0 0