MEC2404/CHE2161

LAB REPORT

Lab 1

FLOW MEASUREMENT

MEMBERS : Tan En Yi (25515063)

Kelvin Lim Ming Ken (25841122)

Surin Varma Pillai Hariharan (25053663)

Arrijal Fadhila Suryana (25642081)

DATE : 22 April 2015

Abstract

The purpose of the experiment is to apply the principles of the Bernoulli equation in the analysis

of the flow of water in two separate apparatus set up: the Didacta Italia Rig and the Armfield Rig.

For both rigs, the flow rate of water is measured in two ways: a) Calculate actual flow rate manually

by recording the time taken to collect a specific volume of water, b) Calculate ideal flow rate by

analysing the pressure drop across the obstacle in the piping system (venturi meter and orifice

plate). The ratio between the actual and ideal flow rate is reported as the discharge coefficient of

the obstacles. The results are then plotted against Reynolds number of the fluid flow for data

analysis.

In conclusion, both rigs produced values and results that show similar trends to the theoretical

predictions that would be expected from the respective flow changes. However, the Didacta Italia

Rig is shown to be more accurate due to its higher sensitivity in detecting different flow rates and

flow velocity at different parts of the piping when different restraints are applied on the flow of

water in the pipeline. Due to human inconsistencies, there was a slight shift in the readings

obtained in comparison with the theoretical values, which also proved the existence of errors such

as parallax error and unsynchronised timing in the manipulation of the flow with the time taken.

1. Introduction

In this experiment, we assumed that no energy is loss for the fluid flow (negligible pipe friction

loss). Thus, the Bernoulli equation can be applied in investigating the flow dynamics in the pipes.

The Bernoulli equation expressed in terms of total head is given by:

𝑣2

2𝑔+

𝑝

𝜌𝑔+ 𝑧 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

Based on the equation above, the velocity head, pressure head and elevation head were all

calculated based on the respective effective points along the pipeline. Theoretical predictions were

made based on the understanding in the relation of the equation with each component in it as they

all refer to the pressure difference in the flow rate.

The assumptions made in the analysis of the results are:

- Constant properties of water at 30 C

- No energy and head loss

- Viscous effects and friction in the pipe is negligible

- Pipe is aligned horizontally, therefore position 1 and 2 are at equal height ( h1 = h2)

- Water flow is at steady state and is incompressible

Special steps were taken to ensure that these assumptions are valid. For example, the fluid is let

to flow for a certain period of time before measurements were done so that the fluid flow is steady.

These assumptions would reduce the complexity of the calculation by removing the effects of other

manipulated variables present during the experiment. However, the results obtained from

calculations will deviated slightly from the actual results due to these assumptions since in real

world conditions, energy loss in fluid flow is unavoidable.

Several flow measuring techniques are used in this experiment: a) manually using a stopwatch,

b) pressure drop across venturi meter, c) pressure drop across orifice plate and d) using a

rotameter. The rotameter would show the highest accuracy as it is placed in series with the fluid

flow, but due to the size of its scale (±1/min and ±50L/hr), slight changes in flow rate would not be

obvious. Manual measurement using the stopwatch would be the most cost efficient method and

most accurate after the rotameter. This is because the energy loss in pipes is taken into

consideration. However this is only applicable to measuring flow rate in a small scale, thus making it

impractical for industrial usage. The third most accurate method would be analysing the pressure

drop across the venturi meter. Venturi meter is more accurate than the orifice plate because it

does not cause turbulence, which induces head loss. Moreover, the venturi meter does not clog

with slurries while the orifice plate does. Having that said, the venturi meter has a higher

installation cost than the orifice plate.

2. Experimental Procedures

2.1. Didacta Italia Rig*

Mercury manometers and water manometers are connected to the venturi meter and

orifice plate to measure the change in pressure across the pipes. A water pump is used to draw

the water from the supply tank to flow through the pipes. Once this set up is done, the tap is

turned on and then the flow rate is adjusted using the turbine flow meter. The water was

allowed to flow for a short period of time before any readings were taken to allow for any

trapped bubbles in the system to flow out. During the experiment, the flow rate is obtained by

measuring the time taken to fill up 4.5 litres of water in the collection tank. The height

differences of the liquids in the manometers which are connected to the venturi meter and

orifice plate are recorded together with the reading on the rotameter. These procedures are

repeated another 7 times for different flow rates and their respective readings.

2.2. Armfield Rig*

The tap is turned on before turning on the pump. Then the flow rate is adjusted by varying

the tap opening. The water is let to flow for a few minutes to make sure no bubbles are trapped

inside the pipes. Once the fluid flow has stabilised, the flow rate is obtained by measuring the

time needed to collect 5 litres of water. The reading on the rotameter and the height of the

water manometers, which are connected to separate parts of the Venturi tube and Orifice plate,

are also recorded at the same time. The experiment is then repeated for another 7 times. The

flow rate is varied by increasing the flow rate of the rotameter by 2 litres per minute intervals

until the water in the water manometer is at its maximum capacity.

*(see Appendix A for schematics for Didacta Italia rig and Armfield Rig)

3. Results

3.1. Calculations for results

The Bernoulli equation and equation of continuity was used to express the volumetric flow

rate Q, in terms of upstream area (A1) and throat area (A2), pressure difference (∆P) and

fluid density (ρ).

- Continuity equation: m1 = m2 → ρwaterA1V1 = ρwaterA2V2

- Bernoulli equation: 𝑃1 + 1

2𝜌𝑤𝑎𝑡𝑒𝑟𝑉1

2 + 𝜌𝑤𝑎𝑡𝑒𝑟𝑔ℎ1 = 𝑃2 + 1

2𝜌𝑤𝑎𝑡𝑒𝑟𝑉2

2 + 𝜌𝑤𝑎𝑡𝑒𝑟𝑔ℎ2

The Bernoulli equation is simplified using the assumptions made (see Introduction). Details

on simplification of equations can be found in Appendix B.

3.2. Discharge coefficient against Reynolds number for venturi meter and orifice plate

Figure 1: Graph of discharge coefficients against Reynolds number for both

Armfield rig and Didacta Italia rig

0.50

0.70

0.90

1.10

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000

Dis

char

ge C

oef

fici

ent

Reynolds Number

Discharge Coefficients against Reynolds number

Armfield -Venturi

Armfield -Orifice

Didacta -Venturi

Didacta -Orifice

Log.(Armfield -Venturi)

Log.(Armfield -Orifice)

3.3. Literature values of the venturi tube coefficient and the orifice plate discharge coefficient

Figure 2: Literature values of the venturi Figure 3: Literature values of the orifice

tube coefficient plate discharge coefficient

3.4. Rotameter reading against volumetric flow rate measured manually

Figure 4: Rotameter reading against actual flow rate

3.5. Error analysis

Error analysis is done for Reynolds number, Discharge coefficient and Rotameter reading

(only Didacta rig) and shown as error bars in the graphs.

y = 1.0199xy = 0.9654x

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 0.00045

Ro

tam

eter

rea

din

g (m

3/s

)

Volumetric flowrate measured manually (m3/s)

Rotameter reading against Flow Rate

Armfield Rig

Didacta rig

5. Discussion

Compared to the theoretical prediction, the result shows similar trend but with slightly deviated

values. The venturi meter in the Didacta rig is slightly out of range, but the orifice plate’s trendline

is nearer to the theoretical trend. The value obtained from venturi meter in the Armfield rig is still

in range, but orifice plate’s values are deviated from its theoretical line.

All assumptions made such as constant temperature of water, no change in elevation, no

viscous effect, steady state, and incompressible fluid are accurate. However, the assumption of

energy loss for head loss due to friction in pipe causes deviation in the calculated values from the

analysis of pressure drop. It is because there is h than the ideal case. As a result, the calculations

are slightly deviated.

The main sources of error that occurred during the experimental procedures and analysis of the

results were from human inconsistency with the recording of the readings, the probability that the

water in the pipes still had bubbles, measurements were taken before the flowrate could

completely settle down, the minor fluctuation in the meters due to the constantly flowing water in

the pipes thus not getting a fixed value and the possibility of parallax error when taking down the

readings. Those main sources affect the recorded results to be slightly deviated, thus the calculated

values show differences with theoretical values.

The orifice plate’s function to act as an obstacle to the flow of water in the pipe causes

intermediate convergence where the water has to abruptly pass through a much narrower opening

which in turn causes a significant loss in pressure, increasing the velocity (in conjunction with

Bernoulli’s principle) and a large amount of turbulence at the exit end of the plate. This turbulence

causes the decrease of flow rate and is affected by sudden contractions and expansions of fluid

water. When the contractions and expansions are large, the loss in flow rate would increase, thus

reducing the discharge coefficient significantly. However, the venturi tube’s water flow is

considered to be smooth as the contraction is gradual. As a result, viscous effects can be neglected.

Gradual contractions would lead to a smaller reduction in flow rate thusthe discharge coefficient

would be much lower for the orifice plate (Co = 0.6) compared to the venturi tube (Cv = 1).

6. Conclusion

By varying the volumetric flow rate of fluid flow rate of water in pipe is measured both manually

and by analyzing the pressure drop across the pipe fittings. From the analysis of the results, the

initial prediction of the accuracy of the instruments was proven to be correct. The Didacta Italia rig

is more accurate than the Armfield rig based on the overall results and calculations done. This is

supported by the significant error in the values obtained from the Didacta Italia rig as compared to

the theoretical values recorded that are smaller than the values obtained from the Armfield rig.

However, some discrepancies were faced due to the various potential reasons for errors as stated

in the discussion. Hence, in conclusion, the main objective of the experiment to apply Bernoulli’s

principle in the analysis of fluid flow in a pipe while assuming that the fluid obeys the assumption of

incompressibility was achieved thus proving that this experiment has achieved its objective.

Appendix A : Experiment schematics

- Armfield rig:

- Didacta Italia rig:

Appendix B : Raw Data

A.1) Flow Measurement experiment (Armfield Rig)

Specifications: Venturi Tube, D = 31mm, d = 15mm

Orifice Plate, D = 31.75mm, d = 20mm

No Volume

(L) Time(s)

Rotameter

(L/min)

Water Manometer (mm)

h1 h2 h3 h4 h5 h6 h7 h8

1 5 44.81 6 277.5 235.0 247.5 242.5 192.5 192.5 177.5 182.5

2 5 36.87 8 267.5 232.5 242.5 247.5 195.0 197.5 175.0 182.5

3 5 29.69 10 280.0 232.5 260.0 252.5 197.5 200.0 165.0 177.5

4 5 25.94 12 297.5 250.0 270.0 257.5 200.0 205.0 155.0 170.0

5 5 21.81 14 312.5 225.0 285.0 265.0 205.0 207.5 145.0 165.0

6 5 20.06 16 335.0 217.5 297.5 275.0 210.0 215.0 132.0 160.0

7 5 16.87 18 355.0 210.0 315.0 285.0 215.0 222.5 117.5 150.0

8 5 15.31 20 377.5 200.0 330.0 295.0 222.5 230.0 100.0 142.5

A.2) Flow Measurement experiment (Didacta Italia Rig)

No

Rotary Vane Water

Meter

Orifice Plate, Water

Manometer

𝐷 = 50 𝑚𝑚,

𝑑 = 20 𝑚𝑚

Venturi Meter,

Mercury Manometer

𝐷 = 20 𝑚𝑚,

𝑑 = 10 𝑚𝑚

Rotameter

(m3/h)

Volume

(litres)

Time

(seconds) ℎ1 (cm) ℎ2 (cm) ℎ1 (cm) ℎ2 (cm)

1 4.5 24.87 5.2 1.2 13.7 16.1 0.60

2 4.5 20.31 8.4 2.6 13.5 16.3 0.75

3 4.5 18.87 10.7 3.8 13.1 16.7 0.85

4 4.5 15.75 15.4 5.5 12.3 17.5 1.00

5 4.5 15.25 16.5 5.9 12.2 17.6 1.00

6 4.5 12.81 21.9 7.3 11.8 18.5 1.20

7 4.5 11.44 27.1 8.6 10.2 19.6 1.40

8 4.5 10.87 29.4 7.9 9.7 20.0 1.45

Appendix C : Equations for calculations

i) Simplification of continuity equation:

m1 = m2

ρwaterQ1 = ρwaterQ2

ρwaterA1V1 = ρwaterA2V2

V2 = A1

A2V1 ----------------------------------- [1]

ii) Simplification of Bernoulli Equation:

𝑃1 + 1

2𝜌𝑤𝑎𝑡𝑒𝑟𝑉1

2 + 𝜌𝑤𝑎𝑡𝑒𝑟𝑔ℎ1 = 𝑃2 + 1

2𝜌𝑤𝑎𝑡𝑒𝑟𝑉2

2 + 𝜌𝑤𝑎𝑡𝑒𝑟𝑔ℎ2

1

2𝜌𝑤𝑎𝑡𝑒𝑟(𝑉1

2 − 𝑉22) = 𝑃2 − 𝑃1 = ∆𝑃

𝑉12 − 𝑉2

2 =2∆𝑃

𝜌𝑤𝑎𝑡𝑒𝑟

𝑉12 =

2∆𝑃

𝜌𝑤𝑎𝑡𝑒𝑟+ 𝑉2

2 ------------------------ [2]

Combining equation [1] and [2],

𝑉1 =√

2∆𝑃

𝜌𝑤𝑎𝑡𝑒𝑟 [(𝐴1

𝐴2)

2

− 1]

Therefore,

𝑸𝒊𝒅𝒆𝒂𝒍 = 𝑨𝟏𝑽𝟏 = 𝑨𝟏√

𝟐∆𝑷

𝝆𝒘𝒂𝒕𝒆𝒓 [(𝑨𝟏

𝑨𝟐)

𝟐

− 𝟏]

iii) Calculating pressure drop:

- For mercury manometer: ∆𝑃 = (𝝆𝒎𝒆𝒓𝒄𝒖𝒓𝒚 − 𝝆𝒘𝒂𝒕𝒆𝒓)𝒈(𝒉𝒖𝒑𝒑𝒆𝒓 − 𝒉𝒍𝒐𝒘𝒆𝒓)

- For water manometer: ∆𝑃 = 𝝆𝒘𝒂𝒕𝒆𝒓𝒈(𝒉𝒖𝒑𝒑𝒆𝒓 − 𝒉𝒍𝒐𝒘𝒆𝒓)

iv) Calculating actual volumetric flow rate:

𝑄𝑎𝑐𝑡𝑢𝑎𝑙 =𝑽𝒐𝒍𝒖𝒎𝒆

𝑻𝒊𝒎𝒆

v) Calculating Reynolds number:

𝑅𝑒𝐷 =𝜌

𝑤𝑎𝑡𝑒𝑟𝑉1𝐷

𝜇𝑤𝑎𝑡𝑒𝑟

=𝝆

𝒘𝒂𝒕𝒆𝒓𝑫𝑸𝒂𝒄𝒕𝒖𝒂𝒍

𝝁𝒘𝒂𝒕𝒆𝒓

𝑨𝟏

vi) Calculating discharge coefficient:

𝐶𝑣 =𝑸𝒂𝒄𝒕𝒖𝒂𝒍

𝑸𝒊𝒅𝒆𝒂𝒍

Appendix D : Calculated data for Armfield rig

- Actual flow rate (from manual measurement with stopwatch):

Q actual

m3/s

0.000112

0.000136

0.000168

0.000198

0.000229

0.000249

0.000296

0.000327

- Venturi meter (V) and Orifice plate (O):

- Rotameter:

Q

m3/s

0.00010

0.00013

0.00017

0.00020

0.00023

0.00027

0.00030

0.00033

Q ideal (V)

V1 (V) Re (V) Cv Q ideal

(O) V1 (O) Re (O) Co

m3/s m/s - - m3/s m/s - -

0.000166 0.2093 8292 0.6730 0.000186 0.2344 9288 0.6009

0.000150 0.1900 7526 0.9013 0.000227 0.2871 11376 0.5962

0.000175 0.2213 8767 0.9608 0.000284 0.3581 14188 0.5937

0.000175 0.2213 8767 1.0997 0.000339 0.4280 16958 0.5685

0.000238 0.3004 11899 0.9637 0.000379 0.4785 18959 0.6048

0.000276 0.3481 13789 0.9042 0.000437 0.5515 21848 0.5706

0.000306 0.3866 15317 0.9678 0.000491 0.6203 24574 0.6032

0.000339 0.4278 16947 0.9639 0.000547 0.6902 27343 0.5974

Appendix E : Calculated data for Didacta Italia rig

- Actual flow rate (from manual measurement with stopwatch):

Q actual m3/s

0.00018094

0.00022157

0.00023847

0.00028571

0.00029508

0.00035129

0.00039336

0.00041398

- Venturi meter (V) and Orifice plate (O):

- Rotameter:

Q

m3/s

0.0001667

0.0002083

0.0002361

0.0002778

0.0002778

0.0003333

0.0003889

0.0004028

Q ideal (V)

V1 (V) Re (V) Cv Q ideal

(O) V in (O) Re (O) Co

m3/s m/s - - m3/s m/s - -

0.000198 0.6303 15731 0.9135 0.000282 0.1435 3583 0.6416

0.000213 0.6808 16991 1.035 0.000340 0.1729 4314 0.6525

0.000242 0.7720 19266 0.9830 0.000370 0.1885 4706 0.6439

0.000291 0.9278 23155 0.9800 0.000444 0.2259 5637 0.6440

0.000297 0.9455 23596 0.9932 0.000459 0.2337 5833 0.6428

0.000330 1.0532 26284 1.0615 0.000539 0.2743 6846 0.6520

0.000391 1.2475 31132 1.0035 0.000606 0.3088 7706 0.6486

0.000410 1.3059 32589 1.0089 0.000654 0.3329 830 0.6332

References

[1] Chemical Engineering. (undated). IC125D - Fluid Mixing Studies Apparatus - Code 994006.

[Online]. Viewed 2015 April 11. Available:

http://didacta.it/allegati/main_catalogs/CE_IC125D_E.PDF

[2] Munson, Bruce Roy, T. H Okiishi, and Wade W Huebsch. Fundamentals Of Fluid Mechanics.

6th Edition. Hoboken, NJ: J. Wiley & Sons, 2010.