Sultan Qaboos University

College of Engineering

Petroleum and Chemical Engineering Department

Chemical Engineering Lab.1 ( CHPE4312 ) - Section # ( 20 )

Exp. 2 (Fluid flow measurement)

By :

Hilal Mohammed Ali Al Ghefeili 88549

Maher Mohammed Hamed Al Busaidi 88654

Ahmed Hamed Mohamed Al Qasmi 88805

Mahamood Nasser Hamed Al Rawahi 88812

To :

Dr. Mohammed Al abri

Due Date :

21th November 2012

I

Abstract:

An experimental work was carried out to compare between the theoretical and experimental differential head for venturi meter, orifice plate meter and pitot-static tube at different volumetric flow rate. our experimental work show that the differential head and the volumetric flow rate has directly proportional relationship. Also, it was shown that the absolute relative error between the theoretical and experimental differential head was within 10% for all the flow meters that have been used.

II

Nomenclature:

Symbols description unit

P Pressure mmHg

u Velocity m/s

푉 ̇ Flow rate 푑푚 /푠

ρ Density 푘푔/푚

z Height m

∆ℎ Differential head mmHg

III

Table of Contents:

Abstract: I

Nomenclature: II

Table of Contents: III

List of Figures: IV

List of Tables: V

Introduction: 1

2. Experimental Set Up and Procedure 2

2.1 Apparatus 2

2.2 Procedure 3

Results and Discussion 3

Experiment 2.1 : Venturi Meter 3

Experiment 2.2: Orifice Plate 4

Experiment 2.3: Pitot-static tube 5

Conclusion: 6

References: 8

Appendices: 9

Experiment 2.1: 9

Experiment 2.2: 9

Experiment 2.2: 9

IV

List of Figures:

Figure 1:Experimental apparatus 2 Figure 2: venturi meter 3 Figure 3:pitot meter 3 Figure 4:orifice plate meter 3 Figure 5:differential heed verses flow rate for venturi meter 4 Figure 6: differential heed verses flow rate for orific plate 5 Figure 7:differential heed verses flow rate for pitot - static tube 6

V

List of Tables:

Table 1: calculation of flow rate and the differential head for venturi meter 4 Table 2: calculation of flow rate and the differential head for orifice plate 5 Table 3: calculation of flow rate and the differential head for pitot -static tube 6

1

Introduction: Flow measurement is the quantification of bulk fluid movement. Flow can be

measured in a variety of ways. Positive-displacement flow meters accumulate a fixed volume of fluid and then count the number of times the volume is filled to measure flow. Other flow measurement methods rely on forces produced by the flowing stream as it overcomes a known constriction, to indirectly calculate flow. Flow may be measured by measuring the velocity of fluid over a known area.

Both gas and liquid flow can be measured in volumetric or mass flow rates, such as liters per second or kilograms per second. These measurements can be converted between one another if the material's density is known. The density for a liquid is almost independent of the liquid conditions; however, this is not the case for gas, the density of which depends greatly upon pressure, temperature and to a lesser extent, the gas composition.

There are several types of flow meter that rely on Bernoulli's principle, either by measuring the differential pressure within a constriction, or by measuring static and stagnation pressures to derive the dynamic pressure. The most common three flow meter that used to measure the velocity and the volumetric flow rate in a pipe are Venturi meter , orifice plate meter and pitot-static tube. . This experiment will depend on the Bernoulli's equation to measure the differential head between two points.

푃 + 휌푢 + 푤푧 = 푃 + 휌푢 + 푤푧 (1)

Where

푃 :the pressure at point 1, 푃 :pressure at point 2, 휌:density of the fluid , 푢 : velocity at point 1, 푢 : velocity at point 2, w:weight, 푧 : height at point 1 , 푧 : height at point 2,

This experiment will study the relationship between the differential head and the volumetric flow rate for water at 24℃. Also, it will compare the theoretical and experimental differential head for the most common three flow meters.

2

2. Experimental Set Up and Procedure

2.1 Apparatus

Figure 1:Experimental apparatus

1- control valve

2- Flow meter place

3- hydraulic bench measuring tank

4- pump

3

Figure 2: venturi meter

Figure 3:pitot meter

Figure 4:orifice plate meter

2.2 Procedure

First of all , the Venturi test section was Inserted and the pipe network was primed with water. After that the pump was switched on and the flow control valve was opened to allow a nominal flow through the pipe. Then the water temperature was measured and recorded. Next ,the total volumetric flow rate was measured and recorded using the hydraulic bench measuring tank and a stopwatch. The differential head between the tapings on the flow meter measured and recorded using the mercury manometer. The flow rate was increased by a reasonable amount and the volumetric flow rate and the differential head were measured and recorded. Finally, the pump was Switched off when all measurements have been taken.

Next, Pitot tube test section was Inserted instead of venture test section and we follow the same Procedure of the Venturi test section. After the volumetric flow rate and the differential head were measured , the orifice plate meter was Inserted . We follow the same Procedure of the previous two.

Results and Discussion

Experiment 2.1 : Venturi Meter

The values of flow rate and differential head for the venturi meter were shown in table (1).The upstream pipe diameter 39 mm and throat diameter is 18 mm. The discharge coefficient is 0.98 as given by the manufacturer. A proportional relation was obtained between the differential head and the flow rate as shown in figure (5). At flow rates of 1.027 dm /s and 1.613 dm /s, the differential head was 60.635 푚푚퐻푔 and 149.491 푚푚퐻푔 respectively. A small difference between the theoretical head 235.952푚푚퐻푔

4

and the measured differential head 250푚푚퐻푔 with an error of 5.619%. An inaccurate values reading of the manometer and the stopwatch was the main cause of the errors.

Table 1: calculation of flow rate and the differential head for venturi meter

Test No. Flow rate [dm /s]

theoretical differential

head ∆ℎ[푚푚퐻푔]

Measured differential

head ∆ℎ[푚푚퐻푔]

Error %

1 1.027 60.635 53 14.406 2 1.613 149.491 133 12.399 3 2.026 235.952 250 5.619

Figure 5:differential heed verses flow rate for venturi meter

Experiment 2.2: Orifice Plate

The measurement of differential head and flow rate for the orifice plate was tabulated in table (2). The upstream pipe diameter and throat diameter are 39 mm and 22 mm respectively. The discharge coefficient is 0.6 as given by the manufacturer. From figure (6), it is clear that the differential head is directly proportional to the flow rate. The theoretical differential head at 1.043dm /s was 70.399 푚푚퐻푔 with some differences with measured value 65 푚푚퐻푔. A maximum error of 11.195% appears at a flow rate of 2.134 dm /swhich the theoretical differential head 294.666 푚푚퐻푔 was slightly higher than the measured differential head 265 푚푚퐻푔. The difference between the theoretical

0

50

100

150

200

250

300

0 0.5 1 1.5 2 2.5

diffe

rent

ial h

ead

∆h [m

mH

g]

Flow rate [ L/s]

differential head∆h Vs Flow rate

Measured

theoretical

5

and measured values may be caused by the human error at taken the readings and controlling the stopwatch.

Table 2: calculation of flow rate and the differential head for orifice plate

Test No. Flow rate [dm /s]

theoretical differential

head ∆ℎ[푚푚퐻푔]

Measured differential

head ∆ℎ[푚푚퐻푔]

Error %

1 1.043 70.399 65 8.306 2 1.527

150.753 145 3.968 3 2.134 294.666 265 11.195

Figure 6: differential heed verses flow rate for orific plate

Experiment 2.3: Pitot-static tube

Table (3) shows the calculation of the differential head, velocity and the flow rate of the pitot-static tube. At a flow rate of 1.541dm /s, the theoretical differential head was 6.228 푚푚퐻푔and the measured value was 8 푚푚퐻푔which indicates an error of 22.147%. the smallest error which was 8.039% was found at the highest flow rate of 2.176 dm /s. From the figure (7), it can be seen that the differential head was proportional to the flow

0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5

diffe

rent

ial h

ead

∆h [m

mH

g]

Flow rate [ L/s]

differential head∆h Vs Flow rate

Measured

theoretical

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rate. Taking the manometer readings before the stability moment may probably caused inaccurate results. Water leakage at the joined parts also caused a big errors.

Table 3: calculation of flow rate and the differential head for pitot -static tube

Test No. Flow rate [dm /s]

Average velocity

[m/s]

theoretical differential head ∆ℎ[푚푚퐻푔]

Measured differential head ∆ℎ[푚푚퐻푔]

Error %

1 1.043 0.873 2.855 4 28.615 2 1.541 1.289 6.228 8 22.147 3 2.176 1.822 12.424 11.5 8.039

Figure 7:differential heed verses flow rate for pitot - static tube

Conclusion:

The flow rates and the differential heads for orifice plate, venturi meter and pitot - static tube were measured. A proportional relation was found between the differential head and the flow rate in the three devices. For the orifice plate, the theoretical differential head was 150.753 푚푚퐻푔and 294.666 푚푚퐻푔at flow rates of 1.527 dm /s and 2.134dm /s. For the venturi meter, a small error was observed at a flow rate of 2.026 dm /s. The theoretical differential head was 235.952 푚푚퐻푔and the measured

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2 2.5

diff

eren

tial h

ead

∆h [m

mH

g]

Flow rate [ L/s]

differential head∆h Vs Flow rate

Measured

theoretical

7

differential head was 250 푚푚퐻푔. At a flow rate of 1.043dm /s for pitot - static tube, the theoretical differential head was 2.855푚푚퐻푔and the measured value was 4 푚푚퐻푔.

Comparing the theoretical differential head with the measured differential head, high errors can be observed. The highest error for the orifice plate was 11.195% at a flow rate of 2.134 dm /s. For the venturi meter, at a flow rate of 1.027 dm /s a largest error was obtained which was 14.406%. The high errors appear may be due to the inaccurate reading of the manometer and the controlling of the stopwatch. Water leakage may caused the largest problem with the experiments outcomes.

8

References:

* Fluid Mechanics for Chemical Engineers 3rd edition, Noel de Nevers, McGraw-Hill

* Fluid Mechanics Fundamentals and Applications, Yunus A. Cengel and John M. Cimbala, Second Edition

* Fundamentals of Thermal-Fluid Sciences, Yunus A. Cengel, McGraw-Hill

* Steady Flow Analysis of Pipe Networks, Roland W. Jeppson, Published in 1/1/1974

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Appendices:

Experiment 2.1: Starting with Bernoulli’s equation:

Solving for the differential head :

Where the velocity u :

Experiment 2.2: The calculation of this experiment is mostly same as the calculation of the venturi meter with different input data.

Experiment 2.2: Starting from the Bernoulli’s equation:

Solving for the differential head:

10

∆푃 =

Where the velocity can be calculated from:

푢 =

푉 , is the flow rate.