School of Chemical and

Energy Engineering

LAB REPORT SKTG 2741

FLUID MECHANICS LABORATORY
2018/2019 – 02

EXPERIMENT EXPERIMENT 2
LECTURER DR AIZUDDIN BIN SUPEE
SECTION SECTION 03
GROUP NO GROUP 2
1.MUHAMMAD ALI BIN ABD RAZAK
2.MEGHAAN A/L KANIGASALAN
GROUP MEMBERS 3.MOHAMAD AFIQ AIMAN BIN MOKHTAR
4.MUHAMMAD AIMAN AIZAT BIN IBRAHIM

DATE OF EXPERIMENT 12 FEBRUARY 2019

DATE OF REPORT SUBMISSION 18 FEBRUARY 2019

CRITERIA SCORE TOTAL MARKS REMARKS

FORMATTING /10
ABSTRACT /10
INTRODUCTION /10
LITERATURE /10
REVIEW/THEORY
METHODOLOGY /10
RESULTS /10
DISCUSSION /30
CONCLUSION /10
Title

Flow Measurement

1.0 Objective

1. Using the Bernoulli principle, measure water flow using various flow meters (orifice plate
flow meter and measuring nozzle, venturi nozzle and rotameter).

2. Investigate the relationship between flow and pressure in flow using Pitot tube.

3. Determine the corresponding flow coefficients for each flow meters.

4. Calibrate the flow meters.

2.0 Introduction

In this experiment, the ability to operate flow measuring equipment (Orifice, Pitot
tube and Venturi nozzle) for discharge coefficient comparison from each equipment will be
performed. Measuring the flow rate is an important aspect in all industries and there are
several ways to measure the flow of fluids in pipes.

3.0 Theory

3.1 Venturi meter

The Venturi meter is a pipe discharge measuring instrument. It consists of a rapidly

converging section (referred to in Figure 1 as point 3) that increases the flow rate and thus
reduces the pressure. It then returns by a gently diverging diffuser to the original
dimensions of the pipe (point 2). The discharge coefficient can be calculated by measuring
the pressure differences. That's it.

Figure 1: Schematic representation of a Venturi meter

 The Bernoulli equation can be applied to points 1 and 3 in reference to the above
Venturi tube diagram. The flow rate equations can be derived after the analysis.

Volumetric flow rate:

(Eq. 1)

where: Qth theoretical volumetric flow rate (m3/s)

A1 cross sectional area at 1 (m2 )

A3 cross sectional area at 3 (m2)

h1 height of manometer column 1 in meters (m)

h3 height of manometer column 3 in meters (m)

The discharge coefficient is defined as the ratio of the actual flow rate of the volume
to the theoretical flow rate.

Coefficient of discharge, Cd = Qactual/Qtheoretical

Due to the losses caused by wall shear stress, losses in contraction and losses during
expansion, the discharge coefficient is less than unity.

This equation can be written as:

Log Qact = log n + aLog Δh

A graph of Log Qact versus Log Δh can be used to find n and therefore Cd experimentally.

3.2 Orifice Plate Meter

The orifice plate is a restriction with a smaller opening than the diameter of the pipe
inserted into the pipe; the typical orifice plate has a concentrated, sharp opening, as shown
in Figure 2. Due to the smaller area, the fluid speed increases and the pressure decreases
correspondingly. The flow rate can be calculated from the drop in the measured pressure in
the P1-P3 orifice plate. The orifice plate is the most commonly used flow sensor, but due to
the turbulence around the plate it creates a rather large non - recoverable pressure, which
leads to a high energy consumption.

Figure 2: Schematic representation of Orifice meter

The Bernoulli equation can be applied to points 1 and 3 with reference to the orifice
plate diagram. The equations for the volumetric flow rate can be expressed following the
analysis as follows:

(Eq. 3)

where: Qth theoretical volumetric flow rate (m3/s)

a cross-sectional area of plate (m2 )

m ratio of cross-sectional area of plate to pipe, (a/A)

Δh difference in height of manometer column (m)

The discharge coefficient is defined as the ratio of the actual flow rate of the volume to the
theoretical flow rate:

Coefficient of discharge, Cd = Qactual/Qtheoretical

(Eq.4)

3.3 Nozzle

A flow nozzle meter consists of a short nozzle, usually held in place between two
pipe flanges as shown in the diagram at the below. It is simpler and less expensive than a
venturi meter, but not as simple as an orifice meter. The frictional loss in a flow nozzle
meter is much less than in an orifice meter, but higher than in a venturi meter.

Figure 3: Flow Nozzle Parameters

Figure 3: Following the analysis, the equations of the volumetric flow rates can be expressed
as the following
 Qth = a
(√ 2g1-mΔh )
2

where: Qth theoretical volumetric flow rate (m3/s)

a cross-sectional area of plate (m2)

m ratio of cross-sectional area of plate to pipe, (a/A)

Δh difference in height of manometer column (m)

The discharge coefficient is defined as the ratio of actual volume flow rate to theoretical
volume flow rate:

Coefficient of discharge, Cd = Qactual/Qtheoretical

Qact =C d Q
th

(√ 2g1-mΔh )=C a 2g1- a

=Cd a

and Qact =C d
(
2

aA
√) ( )
d

√2g √Δh
A
2 √Δh

. .. .. . .. .. . where
aA
( ) =meter coefficient
A 2 -a 2 A 2 -a2
4.0 Apparatus

The flow measurement experiment apparatus (Figure 3) comprises a Venturi nozzle

(point 9), an orifice plate, a measuring nozzle and a Pitot tube (point 8) for flow
measurement and a rotameter (point 3). The flow rate can be regulated using the gate valve
(point 2). The pressure losses at the measuring elements can be recorded using pressure
connections with rapid action couplings. The connections are connected to a six-tube
manometer (point 6), which is fitted with a ventilation valve. The six-tube manometer is
used in order to determine the pressure distribution in the Venturi nozzle or the orifice
plate flow meter and measuring nozzle. The total pressure is measured by a Pitot tube.
 Figure 4: Flow measurement apparatus set-up (HM 150.13, G.U.N.T Gerätebau GmbH)

The tube manometer panel (Figure 4) has 6 glass cylinders (point 11) with milimeter (mm)
scale for measuring the water column (WC). The unit mmWC is used here (10mmWC ≙ 1mbar). The
measuring range is 390 mmWC. All the tubes are connected to one another at the upper end and
ventilated by a shared ventilation valve (point 12). The measuring connections (point 10) are at the
lower end. Differential pressure measurements are carried out with the ventilation valve closed
(point 12, 13), while relative gauge pressure measurements with the ventilation valve open (point
12). Standard pressure unit is Pascal (Pa), where 1Pa = 1N/m 2= 10-5bar = 0.01mbar

Figure 5: Illustration of multi-tube manometer

Equating the pressure at the level (pressure at the same level in a continuous body of static
fluid is equal),
For the left hand side:

p1 = p A +ρ gh1

For the right hand side:

p2 = p A + ρ gh 2

Pressure difference, p

Δp= p1 − p2 = p A +ρ gh1 − p A + ρ gh 2
Δp= p1 − p2 =ρg(h1 − h2 )

Figure 6: Technique to read the measurement of a rotameter

Rotameter (Figure 6) in this apparatus consists of a vertical conical measuring section,

through which the liquid flows from bottom to top. A specially shaped float moves freely in the liquid
flow and is carried along by the flow due to its flow resistance. This results in equilibrium between
the weight of the float on the one hand and its drag and lifting force on the other. The float adjusts
to a particular height in the measuring tube depending on the flow volume. Because of the operating
principle, a reliable measuring range on a rotameter never begins at zero, but at 5-10% of the final
measuring value. The measured flow rate value is always read at the upper edge of the float. The
maximum flow measured by the rotameter is 1,600 L/h
 Figure 7: Basic bench

Figure 8: Methods of Flow Measurement

5.0 Experimental Procedure

1. Orifice or Nozzle was made sure that it was fixed (Permanently fixed the Venturi
Meter).
2. Manometer tubes were made sure that it were connected (H1 & H2) to the Orifice /
Nozzle.
3. Made a tube connection H1 to H3 for the Venturi Meter.
4. Inlet valve and control valve were closed.
5. Main switch was switched on.
6. Pump was switched on.
TO GET RID OF THE AIR BUBBLE
7. The inlet valve and control valve were opened slowly until maximum level (until
water in the manometer overflowed).
i. Black valve (anticlockwise) on top of the manometer was opened to release
all bubble in the system;
ii. Black valve was closed.
8. Control valve was closed.
9. Pump was switched off and the water level was controlled.
10. White valve was slowly opened until maximum level of 30-40 mm.
11. Pump was switched on again.
12. Control valve was slowly opened until level of water in H1 reach maximum (390 mm)
and manometer H at minimum level. All the readings were taken (Multi-tube
Manometer).
ACTUAL Q FLOWRATE CALCULATION
13. Water was collected in a jar and at the same time, the time taken for the maximum
volume filled/collected or closed the basin tank valve and the time measured for
example, 5 Liter were taken.
14. 4 different flow rate, Q (Range above 200 L/min is the reference flow to all
component).
15. Control valve was closed and pump was switched off again.
BEFORE YOU CHANGE TO ORIFICE or NOZZLE FOR THE NEXT EXPERIMENT PLEASE
DISCONNECT ALL TUBES FROM ORIFICE/VENTURI EXCEPT FROM GLASS
MANOMETER.
16. Pump was switched on and the control valve was slowly opened to get rid of the
bubble.
17. Repeated as previous steps
 6.0 Experimental Data
Nozzle

Flow Volume Time Qact Qtheo H1 H2 Δh Cd,theo

Water water (second) (x10-4) (x10-4) (mm) (mm) (mm)
(L/h) collected (m3/s) (m3/s)
(Liter)
1200 1.74 4.53 3.81 4.22 330 20 310 0.9028
1000 1.59 5.44 2.92 3.56 305 85 220 0.8202
800 1.64 6.75 2.43 2.99 285 130 155 0.8127
600 1.75 9.03 1.94 2.29 265 175 90 0.8471
400 1.84 13.60 1.35 1.61 255 210 45 0.8385
200 1.78 22.88 0.78 0.93 245 235 10 0.8387
 Orifice Plate

Flow Volume Time Qact Qtheo H1 H2 Δh Cd,theo

Water water (second) (x10̄ ⁻⁴) (x10̄ ⁻⁴) (mm (mm) (mm)
(L/h) collecte (m3/s) (m3/s) )
d (Liter)
800 1.88 7.08 2.2222 7.7213 360 80 280 0.2878
700 1.84 7.58 1.9444 6.8442 340 120 220 0.2840
600 1.92 9.39 1.6667 5.9273 315 150 165 0.2812
500 1.52 10.27 1.3888 5.0548 300 180 120 0.2747
400 1.74 12.58 1.1111 4.1272 285 205 80 0.2692
300 1.60 14.75 0.8333 3.4221 275 220 55 0.2435
200 1.80 21.07 0.5555 2.3072 265 240 25 0.2407

Venturi Meter

Flow Volume Time Qact Qtheo H1 H2 Δh Cd,theo

meter water (second) (x10̄ ⁻⁴) (x10̄ ⁻⁴) (mm) (mm) (mm)
(L/h) collected (m3/s) (m3/s)
(Liter)
600 1.69 8.82 0.19 0.21 370 60 310 0.912
500 1.68 10.07 0.17 0.18 335 113 222 0.926
400 1.80 13.25 0.14 0.15 307 157 150 0.906
300 1.76 16.19 0.10 0.12 285 191 94 0.905
200 1.64 21.19 0.07 0.09 270 220 50 0.859

6.1 Calculation

Nozzle
∆H (m) = H1 – H2

= 0.330m – 0.020m
= 0.310m

Qact (m3/s) x 10-3 = Volume of water collected in tank (m3)/time (s)

= 0.00184m3/4.53.91s
 m3
= 0.3841X10−3 ( )
s

2g∆h a
Qtheo (m3/s) x 10-3 =a
√
1−m
7
2 , where m=

49
A
, a=π(14 X 10−3)/4, A= π (22 X 10−3 )/4

m=  m2=
11 121
2 ( 9.81 ) (0.310)
=a
√ 1−m2
m3
= 0.422X10−3 ( )
s

Cd = Qactual / Qtheoretical
= 0.9208

The method above is repeated for the rest of the values.

Orifice Plate
Step 1

# Qactual we get from the rotameter

Step 2

2 x g x Δh
Qtheoretical = a √ (
1−m ²
¿ )¿

Calculation Qtheoretical for 800L/h

2 x 9.81 x (280 x 10 ⁻ ³)
= ( Π )x(
18.5 x 10̄ ³
2
√
)² x 1−( 18.5 x 10 ⁻ ³ )²
32 x 10 ⁻ ³
=7.7213 x 10 ⁻⁴

Then other Qtheoretical for 700,600,500,400,300,200L/h is calculated by change the value of

( value of Δh at table orifice plate)

Step 3

Qactual
From the Qactual and Qtheoretical, the Cd value is calculated Cd = Qtheoretical
For flow meter 800 L/h,

2.2222 x 10⁻ ⁴
Cd = 7.7213 x 10⁻ ⁴ =0.2878
Then for the flow meter of 700,600,500,400,300,200L/h is calculated by change the value of Qactual
and Qtheoretical

( Qactual and Qtheoretical at table orifice plate)

Venturi Meter

∆H (m) = H1 – H2
= 0.370m – 0.060m
= 0.310m

Qact (m3/s) x 10-3 = Volume of water collected in tank (m3)/time (s)

= 0.00169m3/8.82s
m3
= 0.19X10−3 ( )
s

Qtheo (m3/s) x 10-3 = A3 V 3

2 g∆h
= A3
√1−¿ ¿
¿
2(9.81)( 0.310)
= (84.6 ×10−6 )
= 0.21
√ 1−¿ ¿
¿

Cd = Qactual / Qtheoretical
= 0.912

The method above is repeated for the rest of the values.

7.0 Discussion

Nozzle

The trend of the manometer water level in nozzle meter.

The data collection from nozzles shows a trend in such that the water level pressure at H1
increases while at H2 decreases as the flow rate, Qact increases.

Relationship between pressure and flow rate for nozzle meter:

Mean of Cd for Nozzle , Cd= 0.8127

Orifice Plate

The trend of the manometer water level in orifice meter.

The data collection from nozzles shows a trend in such that the water level pressure
at H1 increases while at H2 decreases as the flow rate, Qact increases.

Relationship between pressure and flow rate for orifice meter :

 Mean Cd for orifice plate, Cd=0.244

Venturi Meter

The trend of the manometer water level in orifice meter:

The manometer water level in h1 is higher than h3 in every different flow rate. This is due to
area 1 is larger than area 3 in the venturi meter, thus the pressure in 3 is higher than 1. As
the flow rate decrease, the manometer water level with bigger diameter decrease, while the
manometer water level which connected to the smaller diameter increase.

Relationship between pressure and flow rate for orifice meter :

 Mean Cd for venturi meter, Cd= 0.859

 The figure shows the graph of log Qactual versus log ∆ h. By comparing this equation of

2g
C A
Log Qact = ½ Log H + Log n, where n = d 3
√ A3 2 with the graph plotted,
1−( )
A1
log Qactual is linearly increasing tolog ∆ h and the graph obtained is a linear graph. This
proved that the graph plotted is correct.

 Next, the gradient from the equation is 0.5 while the gradient obtained from the graph
is 0.5652. The theoretical gradient value and the gradient value obtained from the
graph are almost the same.

 While the y-intercept obtained from the graph is -4.4119. From y-intercept, we are able
to calculate the value for C das below:

2g
Log n =
log C d A 3

= -4.4119
√ A3 2
1−( )
A1

2 ( 9.81 )
-4.4119= Log
C d (8.46 x 10−5 )

√(1−
8.464 x 10−5
3.386 x 10−4
2

)
 Cd, Calculated=1.293 while Cd, Obtained=0.859

By comparing the value of Cd calculated and Cd average, there are slightly different.
Therefore, the overall result obtained for the venture meter is incorrect. This is due
to the error that we made during the experiment and also error that might come
from the apparatus that we are using.

The differences in the discharge coefficient, Cd.

From the result we have calculated, the discharge coefficient of venturi meter, nozzle meter
and orifice plate are 0.859, 0.817and 0.244 respectively. The ratio of the actual flow rate to
the theoretical flow rate for average does not exceed 1. This show that the data we
obtained during experiment is almost consistent and thus the accurate data. For each type,
the constriction in the flow path causes a pressure drop across the meter.

The most accurate flow meter based on the experiment.

Based on the experiment, the most accurate flow meter is venturi meter. The value of
discharge coefficient of orifice plate does not exceed 1 and it is the nearest to 1 which is
0.859. This shows that it is very near to the ideal value.

Investigation of relationships between flow and pressure in flow measurement

Firstly, the velocity of water is directly proportional to the pressure in a particular section
based on the Bernoulli’s principle. The velocity of the water increases as the diameter of the
pipe decreases from one point to another. This increases the flow rate of the water. High
flow rate can be only obtained if there is a pressure difference between the points in a
particular section. If we compare the pressure differences among nozzle, orifice plate and
venturi meter, the highest pressure difference is produced by the venturi meter due to its
area difference. Thus, venturi meter gives the most accurate flow rate measurement.

Factors Contributing to Errors or Inaccuracy in Experiment Data

Starting with the human error. No matter how quick we are, there is a limitation for our
response as we all are humans. For example, the observer may not start or stop the
stopwatch simultaneously when the required water level has reached. Next, the error in the
apparatus which is called as the systematic error. The reading of the height of manometer is
affected by the air bubbles present in the flexible tubes. Other than that, it was really hard
to take the manometer scale readings as the surface of manometer ruler was not clear.
Thus, the readings were not that precise.

Recommendations to Improve the Results

Before starting the experiment, we must make sure that the bubbles in the flexible tubes
have been completely nulled, so that it does not affect the readings. We must maintain a
steady flow rate of water at the nozzle to produce a constant velocity. In order to see the
water meniscus much clearer, we can place a white paper behind the ruler to minimize the
parallax error. Make sure all the apparatuses are in good condition before starting the
experiment so that more accurate results can be obtained. Lastly, average readings can be
taken by repeating the experiment for a couple of times.

e) The most accurate flow meter is venturi meter.

8.0 Conclusion

After completing this experiment, the coefficient of discharge, C d, for a series of flow
measurement device, nozzle, venturi meter and orifice plate meter are as shown below:

a) Venturi meter, Cd = 0.859

b) Nozzle meter, Cd =0.817
c) Orifice plate, Cd =0.244
The velocity of the flowrate of the water increases as the pressure in the fluid decreases.
Based on this, we can say that the flow measurements devices do obey the Bernoulli’s
principle. In conclusion, the orifice plate is the most accurate as it has a higher value of
coefficient of discharge and produce less error. The flow measurement device is chosen
based on accuracy, cost and how far it obeys the ideal flowrate that are steady,
incompressible and in viscid.

9.0 References

Sabersky R.H, A. J. (1999). Fluid Flow: A First Course In Fluid Mechanics (Fourth
Edition). London: Prentice Hall.

Yunus A. Cengel and John M.Cimbala (2010). Fluid Mechanics: Fundamentals and
Application. New York: The McGraw-Hill Companies,Inc. 382-384.