1.0 ABSTRACT

The purpose of this experiment is to obtain the flow rate/discharge of 3 particular flow

measuring apparatus which are the rotameter, orifice meter and venturi meter in accordance

to Bernoulli’s Equation. The time taken for the water to discharge as the diameter of

rotameter increased was determined and tabulated. Then, the discharge for each apparatus is

calculated using the data obtained through the experiment and the calculations were

tabulated. The results were analyzed and its accordance to Bernoulli’s Equation was

discussed. Besides, the loss coefficient when fluid flows through 90° elbow also determined

in which the Piezometer Head Differential is taken at the elbow. The data recorded with the

different flowrate and time is taken. The experiment was completed and carried out

successfully.

2.0 INTRODUCTION

The aim of this experiment is to obtain the flowrate measurement by utilizing three basics

types of flow measuring techniques which are rotameter, orifice meter and venturi meter

which then gives the Bernoulli’s Principle equation. The rapid enlargement in cross-sectional

area and a 90° elbow are also calculated in this experiment. This will also to investigate the

loss coefficient of fluid through the 90° elbow.

A fluid is any substance which is capable of flowing over a surface which under

continual deformation under applied shear stress and which under appropriate temperature

conditions or state will take the shape of container. All fluids have a certain degree of

compressibility and pose little resistance to a change in form or shape. Fluids can be roughly

divided into liquids and gases.

3.0 OBJECTIVES

The main objectives before conducting this experiment are to obtain the flow rate

measurement by utilizing three basics types of flow measuring techniques which is rotameter,

venturi meter and orifice meter and also to investigate the loss coefficient of fluid through 90

degree elbow.

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4.0 THEORY

a) Rotameter

The rotameter is a flow meter in which a rotating free float is the indicating element.

Basically, a rotameter consists of a transparent tapered vertical tube through which fluid flow

upward. Within the tube is placed a freely suspended “float” of pump-bob shape. When there

is no flow, the float rests on a stop at the bottom end. As flow commences, the float rises until

upward and buoyancy forces on it are balanced by its weight. The float rises only a short

distance if the rate of flow is small, and vice versa. The points of equilibrium can be noted as

a function of flow rate. With a well-calibrated marked glass tube, the level of the float

becomes a direct measure of flow rate.

b) Venturi Meter

The venturi meter consists of a venturi tube and a suitable differential pressure gauge. The

venturi tube has a converging portion, a throat and a diverging portion as shown in the figure

below. The function of the converging portion is to increase the velocity of the fluid and

lower its static pressure. A pressure difference between inlet and throat is thus developed,

which pressure difference is correlated with the rate of discharge. The diverging cone serves

to change the area of the stream back to the entrance area and convert velocity head into

pressure head.

Figure 1: Specification of venturi meterTapping A = 26 mmTapping B = 21.6 mmTapping C = 16 mmTapping D = 20 mmTapping E = 22 mmTapping F = 26 mm

By applying Bernoulli’s equation at section 1 to point 2, we get

2

As pipe is horizontal

= h =

where, h = , differences at sections 1 and 2

from the continuity of equation at the section 1 and 2, we obtain

=>

Hence, h =

Discharge h

3

(Equation 4.1)

The equation 4.1 known as theoretical discharge.

(Equation 4.2)

C) Orifice Meter

The orifice for use as a metering device in a pipeline consists of a concentric square-edged

circular hole in a thin plate, which is clamped between the flanges of the pipe as shown in the

figure below.

Figure 2: Orifice meter

Let

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By applying Bernoulli’s equation at section 1 to point 2, we get

h =

Where h is different head

Let

Coefficient of contraction,

By continuity equation, we have

Hence,

5

Thus, discharge,

Q =

If Cd is the coeeficient of discharge for orifice meter which is defined as

Cd = Cc

Cc = Cd

6

Hence, (Equation 4.3)

The coefficient of discharge of the orifice meter is much more smaller than venturi meter.

c) 90° elbow

Figure below shows fluid flowing in a pipeline where there is some pipe fitting such as bend

or valve, and change in pipe diameter. Included in the figure is the variation of piezometric

head along the pipe run, as would be shown by numerous pressure tappings at the pipe wall.

Figure 4: Piezometric head along a pipeline

If the upstream and downstream lines of linear friction gradient are extrapolated to the plane

of fitting, a loss of piezometric head, ∆h, due to the fitting is found. By introducing the

velocity heads in the upstream and downstream runs of pipe, total head loss, ∆H can be

determined in which

Energy losses are proportional to the velocity head of the fluid as it flows around an elbow,

through an enlargement or contraction of the flow section, or through a valve. Experimental

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values for energy losses are usually expressed in terms of a dimensionless loss coefficient K,

where

depending on the context.

For results of better accuracy, long sections of straight pipe are required to establish with

certainty the relative positions of the linear sections of the piezometric lines. However, in a

compact apparatus as described in this manual, only two piezometers are used, one placed

upstream and the other downstream of the fitting, at sufficient distances as to avoid severe

disturbances. Thesepiezometers measure the piezometric head loss, ∆ h’ between the tapping.

Thus

∆h = ∆h −∆hf ' ……………………………..………………………………………(10)

Δhf = friction head loss which would be incurred in fully developed flow along the run of pipe between the piezometer tappingsf = friction factorL = distance between the piezometer, measured along the pipe center lineD = pipe diameterV = average velocity of fluid flow in pipe

The friction head loss is estimated by choosing a suitable value of friction factor, f for fully

developed flow along a smooth pipe. The method used in this manual to determine the

friction factor is the prandtl equation

Typical values derived from this equation are tabulated in the table below:

8

In determination of the fraction factor, f, it is sufficient to establish the value of f at just one

typical flow rate, as about the middle of the range of measurement due to the fact that f varies

only slowly with Re, and the friction loss is generally fairly small in relation to the measured

value of ∆h’.

Characteristic of flow through elbow and at changes in diameter.

90° Elbow

Figure below shows flow round a 90° elbow which has a constant circular cross section.

Figure 5: 90° elbow

The value of loss coefficient K is dependent on the ratio of the bend radius, R to the pipe inside diameter D. As this ratio increase, the value of K will fall and vice versa.

5.0 APPARATUS AND MATERIALS

Hydraulic Bench (Model: FM110)

Water

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Flow meter Measurement Apparatus (Model: FM 101)

Manometer tubes

Discharge valve

Staddle valve

Rotameter

90º elbow

Orifice

Venture

6.0 EXPERIMENTAL PROCEDURE

A) General Start-up Procedures

1. The apparatus is placed on top of a suitable hydraulic bench.

2. The apparatus is levelled on the bench top.

3. The hydraulic coupling was connected to the outlet supply of the hydraulic bench.

4. The discharge connect of the flow apparatus hose was connected to the collection

tank of the hydraulic bench.

Starting up the Apparatus:

1. The flow control valve of hydraulic bench was fully closed and the discharge valve

was fully opened.

2. The discharge hose was ensured it is properly directed to volumetric tank of Fibre

glass before starting up system. Also ensure that volumetric tank drain valve was left

opened to allow flow discharge back into sump tank.

3. Once step (b) is confirmed the pump supply was start up from hydraulic bench. The

bench valve was opened slowly. At this point, the water flowing from hydraulic bench

through to the flow apparatus and discharge through into the volumetric tank of

hydraulic bench and then drained back into sump tank of hydraulic bench.

4. The flow control was proceeded to fully open valve. When the flow in the pipe is

steady and there is no trapped bubble, the bench valve was started to close to reduce

the flow to the maximum measurable flow rate.

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5. The water level in the manometer board are begin to display different level of water

heights. (If the water level in the manometer board is too high where it is out of

visible point, the water level was adjusted by using the staddle valve. With the

maximum measurable flow rate, maximum readings are retained on manometer).

6. At this point, the flow was slowly reduced by controlling the flow discharge valve of

apparatus; this discharge valve was totally closed.

7. The water level in the manometer board was began to level into a straight level. This

level maybe at the lower or maybe at the higher end of the manometer board range.

(Take note that the pump from the hydraulic bench is at this time, still supplying

water at a certain pressure in the system).

8. Lookout for “Trapped Bubbles” in the glass tube or plastic transfer tube. Remove

them from the system for better accuracy. To do this, you can either slowly “press the

plastic tube to push the bubbles up or lightly “tab” the glass tube to release the

bubbles upwards.

B) Demonstration of the operation and characteristic of three different basic types

of flowmeter

Procedures:

1. The apparatus was placed on bench, the inlet pipe was connected to bench supply and

outlet pipe into volumetric tank.

2. With the bench valve was fully closed and the discharge valve was fully opened, the

pump supply was start up from hydraulic bench.

3. The bench valve was slowly opened until it is fully opened.

4. When the flow in the pipe is steady and there is no trapped bubble, the bench valve

was started to close to reduce the flow to the maximum measurable flow rate.

5. By using the air bleed screw, the water level in the manometer board was adjusted.

The maximum readings are retained on manometers with the maximum measurable

flowrate.

6. Note readings on manometers (A - J), rotameter and flow rate was measured.

7. Step 6 is repeated for different flow rates. The flow rates can be adjusted by utilizing

both bench valve and discharge valve.

8. To demonstrate similar flow rates at different system static pressures, the bench was

adjusted and flow control valve together. Adjusting manometer levels as required.

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C) Determination of the loss coefficient when fluid flows through a 90 degree elbow

1. The apparatus was placed on bench, inlet pipe was connected to bench supply and

outlet pipe into volumetric tank.

2. With the bench valve fully closed and the discharge valve fully opened, the pump

supply was start up from hydraulic bench.

3. The bench valve was slowly opened until it is fully opened.

4. When the flow in the pipe is steady and there is no trapped bubble, the bench valve

was started to close to reduce the flow to the maximum measurable flow rate.

5. By using the air bleed screw, the water level in the manometer board was adjusted.

The maximum readings was retained on manometers with the maximum measurable

flowrate.

6. Note readings on manometers (I and J) and flow rate was measured.

7. Step 6 is repeated for different flow rates. The flow rates can be adjusted by utilizing

both bench valve and discharge valve.

8. The tables was completed.

9. Plot graph ∆H against for 90 degree elbow to determine the coefficient of losses.

D) General Shut-down Procedures

1. The water supply valve and venturi discharge valve was closed.

2. The water supply pump was turned off.

3. The water from the unit was drained off when not in use.

7.0 RESULTS

7.1 DEMONSTRATION OF THE OPERATION AND CHARACTERISTICS OF DIFFERENT BASIC TYPE OF FLOWMETER.

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Manometer reading (mm) rotameter

(L/min)

volume (L)

time (min)

Flow rate, Q (L/min)

Flowrate calculated using

Bernouli’s equation (L/min)

venturi orifice

A B C D E F G H I J

239 238 231 285 236 237 237 222 229 228 5 3 0.37 8.11 3.234 4.41

256 251 225 241 246 250 250 186 212 210 10 3 0.17 17.65 2.556 9.81

291 281 222 260 270 277 277 130 186 184 15 3 0.10 30.00 9.54 13.95

339 320 216 285 300 315 314 45 154 150 20 3 0.08 37.50 12.72 18.87

7.2 DETERMINATION OF THE LOSS COEFFICIENT WHEN FLUIDS FLOWS

THROUGH A 90º ELBOW.

Volume (L) Time (sec) Flowrate, Q (L/min)

Differential Piezometer Head, ∆h’

(mm) elbow (hi –hj)

V (m/s) V2/2g (mm)

3 0.37 8.11 1 0.672 23

3 0.17 14.65 2 1.214 75

3 0.10 30.00 3 2.486 315

3 0.08 37.50 4 3.108 492

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7.3 The graph for ∆h against v2/2g

Figure 7.1 : ∆h against v2/2g

8.0 CALCULATION

8.1 DEMONSTRATION OF THE OPERATION AND CHARACTERISTICS OF

DIFFERENT BASIC TYPE OF FLOWMETER.

8.1.1 ORIFFICE CALCULATION

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when = 0.015 m

= m3/ s x 60000

= 4.41 L/min

when = 0.064 m

= m3/ s x 60000

= 9.81 L/min

when = 0.147 m

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= m3/ s x 60000

= 13.95 L/min

when = 0.269 m

= m3/ s x 60000

= 18.87 L/min

8.1.2 VENTURI CALCULATION

when = 7.772 X 10-3 m

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=3.234 L/min

when = 4.993 X 10-3 m

=

when = 0.069 m

=

=

when = 0.122 m

=

=

8.2 DETERMINATION OF THE LOSS COEFFICIENT WHEN FLUIDS FLOWS THROUGH A 90º ELBOW.

Calculate velocity

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V =

A =

when Q = 8.11 L/min

V =

=

when Q = 14.65 L/min

V =

=

when Q = 30.0 L/min

V =

=

when Q = 37.5 L/min

V =

18

=

Calculate

when Q = 8.11 L/min

=

= 0.023 m x

=

when Q = 14.65 L/min

=

= 0.075 m x

= 75.0 mm

when Q = 30.0 L/min

=

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= 0.315 m x

= 315 mm

when Q = 37.5 L/min

=

= 0.492 m x

= 492 mm

Coefficient loss,k when fluid flow through a 90 degree elbow. The coefficient loss value is

determined as the gradient,m of graph ∆H against .

At point (1,23) and (4,492)

= 0.0064

Since m = k

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9.0 DISCUSSION

In this experiment, the flow rates of venturi meter and orifice meter are calculated

using the Bernoulli’s equation as shown in calculation before. For example, as a rota meter

flowrate is fixed to 5 L/min the time taken is recorded after it reached at volume of 3 L. Then,

flowrate is calculated again as volume over the time taken. This shows the flowrate of rota

meter is only a small change with the flowrate taken manually. Flowrate of rotameter is

higher than the flowrate of venturi meter when calculated using the equation of Bernoulli’s

Equation. In venturi meter, the flowrate calculated using the Bernoulli’s equation is 3.23

L/min compared to the fixed flowrate at 5 L/min which is slightly different in flowrate. This

may be caused by the converging portion, a throat and diverging portion to increase the

velocity of fluid and lower the statics pressure. By using the Bernoulli’s equation, the venturi

meter flowrates are less than that given because of frictional effects and consequent head loss

between inlet and throat.

In orifice meter, the flowrates also gives a slightly different in flowrate of rotameter.

For example, at rotameter flowrate of 5L/min, the orifice flowrate gives 4.41 L/min by using

the Bernoulli’s equation. This shown the flowrate of rotameter is higher than the orifice meter

when calculated using Bernoulli’s equation. This is because of the concentric square-edged

circular hole in a thin plate which gives a pressure at holes in the pipe walls on both side of

the orifice plate.

For experiment in determination of loss coefficient in 90° elbow, the piezometric head is

calculated by subtracting the head loss in I and J column of manometer. If the upstream and

downstream lines of linear friction gradient are extrapolated to the plane of fitting, a loss of

piezometric head, ∆h, due to the fitting is found. The velocity head is calculated by using the

formula V2 / 2g. The graph of piezometric head against velocity head was plotted. The slope

of the graph are shown that the energy loss proportional to the velocity head of the fluid as it

flows around an elbow, through an enlargement or contraction of the flow section, or through

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a valve. Experimental values for energy losses are usually expressed in terms of a

dimensionless loss coefficient K, where the value from the graph gives 0.0064.

10.0 CONCLUSION

In this experiment, the flow rates in the venturi meter, orifice meter and rotameter can

be determined by using Bernoulli’s Equation. The flowrates beween the venturi meter,

orifice meter and rotameter give a slightly different flowrate when calculated using

Bernoulli’s Principle. The ideal flowrates of venture and orifice meter is calculated using

the Bernoulli’s equation. In venturi meter losses are less so coefficient of discharge is

higher whereas in orifice meter due to no convergent and divergent cones there are more

losses and hence its coefficient of discharge is less. In venturi meter losses are low due to

steam line shape of the diffuser and the pressure gradient is not abrupt as in case of orifice

meter. As the graph is plotted, the slope of the graph gives the loss coefficient, K which is

0.0064. This shows the loss coefficient is 0.0064 when its flow through the 90° elbow.

11.0 RECOMMENDATIONS

There are some recommendation is made up in order to get more accurate results in this

experiment.

Parallax error must be avoid when readings is taken at the manometer tubes. The value that

appears on the equipment we must wait until it becomes stable then the readings can be

taken. This is because of the stable condition that we are taking the readings are in the steady

state condition. Other than that, in the way to get accurate calculations of the result, we must

ensure that we used suitable formulas and calculated without any error occurs. Others than

that, we must ensure that when we reads the readings of the manometer, the eyes must be

perpendicular to the manometer readings. This is to avoid parallax error. This error is caused

when the eyes is not perpendicular to the manometer readings thus obtaining a wrong

measurement.

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Besides that, in order to take an accurate result, the air in the manometer tubes must be

flush out. The water supply must flows through it for bleeding until the air bubbles escaped

then we can start up the experiment with different flowrate with the saddle valve is depressed

until all the water in manometer tubes turns half of it.

The control valve of water must be controlled all the time so that there is no slightly different

in the flowrate meter while taking the readings in manometer. Lastly, repeat the experiment at

least four times. Because of that, we take three readings of the rotameter which is 5 L/min,

10L/min,15L/min and 20 L/min to get the obtain the accurate results.

12.0 REFERENCES

1. Equipment for Engineering Education and Research. (n.d.). Flowmeter Measurement

Apparatus Solution Manual, Model 101. SOLTEQ Company. Retrieved from

http://www.solution.com.my/pdf/FM101(A4).pdf;

2. Department of Civil and Environmental Engineering. Water Resources Engineering

(CE 3620). (Spring 2013). Laboratory 1: Flow Measurement. Michigan Technological

University. Retrieved from http://www.cee.mtu.edu/~vgriffis/CE

%203620%20materials/CE3620-Labs/Lab%201-Flow%20Measurement.pdf

 Coulson J. M.  and Richardson J. F. (2005). Chemical Engineering Design. Volume

6. 4th Edition. Chap 3. pp. 87.-93. Oxford: Elsevier Butterworth-Heinemann.

3. McCabe,L., Smith,J.C., and Harriot,P. (2001). Unit Operations of Chemical

Engineering’, 5th Edition, New York: McGraw Hill pp.214-221.

13.0 APPENDICES

See the next page.

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