lab 1 complete 15-08

1.0 INTRODUCTION

Many types of devices have been developed to measure fluid velocities and

flowrates based on the Bernoulli equation. The orifice, nozzle meter and the venturi

meter are the three common used types of flow meter. The operation of each is based on

the same physical principles: an increase in velocity causes a decrease in pressure.

In venturi meter, the pressure difference between the upstream side of the cone

and the throat is measured and provides the signal for the rate of flow. Fluid is

accelerated through a converging cone of angle 15-20o. The orifice meter consists of a

flat orifice plate with a circular hole drilled in it. There is a pressure tap upstream from

the orifice plate and another just downstream. There are in general three methods of

placing the taps. The coefficient of the meter depends upon the position of taps.

In this experiment, the water level readings were taken for each controlled flow

rate after the water was pumped into venturi and orifice meter. There are total 10

readings of pressure drop. The pressure drop against each device is used for calculation.

Then , the operation and performance of each device was compared.

The remainder of the report provides detailed analysis of the Theory and

Working equations for this experiment. The procedure can be found at material and

method section. Presentation of the findings and detailed discussion of the result can be

found in Result and Discussion section. Finally, the conclusion and recommendation part

will show summary of this experiment.

1

2.0 THEORY AND WORKING EQUATIONS

Bernoulli's principle states that in fluid flow, an increase in velocity occurs

simultaneously with decrease in pressure. This principle is a simplification of Bernoulli's

equation which states that the sum of all forms of energy in a fluid flowing along an

enclosed path (a streamline) is the same at any two points in that path. The Bernoulli

equation is an approximate relation between pressure, velocity, and elevation, and is

valid in regions of steady, incompressible flow where the net frictional forces are

negligible. The Bernoulli equation is a very handy equation useful in almost any

engineering application. Bernoulli’s equation neglects friction, but friction effects in

these devices become significant and are normally accounted for by introducing

empirical coefficients and retaining the frictionless form of Bernoulli’s equation, rather

than by introducing the friction term into Bernoulli’s equation. Bernoulli's equation is

only valid if one assumes the following: incompressible fluid (fluid velocity less than

one third the speed of sound) and inviscid flow (this just means that the point in question

along the flow is going to be away from where the flow and the object come into

contact). The value of discharge coefficient, Cd differs for each device. The devices used

in this experiment to measure flow rate are venturi meter, orifice meter, rotameter and

bench device. Each of these meters operates on the principle that a decrease in flow area

in pipes causes an increase in velocity that is accompanied by the decrease in pressure.

In this experiment, a few assumptions are made for data analysis:

1) density of water is constant and taken to be 1000kg/m3

2) the flow is steady and incompressible

3) the pipe is horizontal which means no change in elevation

2

http://en.wikipedia.org/wiki/Streamline

http://en.wikipedia.org/wiki/Pressure

http://en.wikipedia.org/wiki/Velocity

http://en.wikipedia.org/wiki/Fluid

Bernoulli's equation reduces to an equation relating the conservation of energy at two

points in the fluid flow: Z1 = Z2

Bernoulli’s equation

or:

with: or V = Q / A

Venturi meter

The venturi meter was invented by an American engineer, Clemans Herschel

(1842-1930) and named by him after Italian Giovanni Venturi (1746-1822) for his

pioneering work on conical flow section, is the most accurate flow meter in this group,

but it is also the most expensive.The angle of the convergent cone is usually 200, the

length of throat is equal to the throat diameter and the angle of divergent cone is 5 0 to 70

to ensure a minimum loss of energy. Venturi meter consists of a short converging

conical tube, leading to a cylindrical portion called “throat” which is followed by a

diverging section.

A fluid passing through smoothly varying constrictions is subject to changes in

velocity and pressure in order to satisfy the conservation of mass-flux (flow rate). The

reduction in pressure in the constriction can be understood by conservation of energy.

The fluid gains kinetic energy as it enters the constriction, and that energy is supplied by

a pressure gradient force from behind. The pressure gradient reduces the pressure in the

constriction, in reaction to the acceleration. Likewise, as the fluid leaves the constriction,

3

http://en.wikipedia.org/wiki/Pressure_gradient_force

http://en.wikipedia.org/wiki/Kinetic_energy

http://en.wikipedia.org/wiki/Conservation_of_energy



it is slowed by a pressure gradient force that raises the pressure back to the ambient

level. Therefore, the flow rate through a venturi meter is given by:

Flow rate, Q = Cd x Ao [1 – (Ao /A) 2]-1/2 x [2(P2 – P3 )/ ρ]1/2

Where Cd = discharge coefficient (0.97)

Ao = throat area = 2.011 x 10-4 m2

A = inlet area = 3.8 x 10-4 m2

ρ = density of water = 1000 kg/m3

P2 = inlet pressure (Pa)

P3 = throat pressure (Pa)

g = 9.81 ms-2

D2 = inlet diameter = 0.022 m

D3 = throat diameter = 0.016 m

Orifice meter.

The orifice meter has the simplest design and it occupies minimal space as it

consists of a plate with a hole in the middle. It is usually placed in a pipe in which fluid

flows. There are considerable variations in design such as sharp-edged, beveled and

rounded. An orifice meter is used to measures the rate of fluid flow. As fluid flows

through the pipe, it has a certain velocity and a certain pressure. When the fluid reaches

the orifice plate, with the hole in the middle, the fluid is forced to converge to go through

the small hole; the point of maximum convergence actually occurs shortly downstream

of the physical orifice, at the so-called "vena contracta". As it does so, the velocity and

the pressure changes. Beyond the vena contracta, the fluid expands and the velocity and

4



http://en.wikipedia.org/wiki/Fluid_flow

pressure change once again. By measuring the difference in fluid pressure between the

normal pipe section and at the vena contracta, the volumetric and mass flow rates can be

obtained from Bernoulli's equation.

Flow rate, Q = Cd x Ao x [2g (H7-H8)] 1/2 x [1-(Ao/A) 2]-1/2

Where Cd = discharge coefficient (0.61)

D4 = orifice diameter (0.20 m)

D = orifice upstream diameter (0.025 m)

Ao = orifice area (3.1 x 10-4 m)

A = orifice upstream area (4.9 x 10-4 m)

(H7-H8)= pressure difference across orifice (m)

Rotameter

A simple, reliable, inexpensive, and easy-to-install flow meter with low pressure

drop and no electrical connections that gives a direct reading of flow rate for a wide

range of liquids and gases is the variable-area flow meter, also called a rotameter. A

rotameter consists of a vertical tapered conical transparent tube made of glass or plastic

with a float inside that is free to move. As fluid flows through the tapered tube, the float

rises within the tube to location where the float weight, drag force, and buoyancy force

balance each other and the net force acting on the float is zero. The flow rate is

determined by simply matching the position of the float against the graduated flow scale

outside the tapered transparent tube.

Pressure drop

5

http://en.wikipedia.org/wiki/Bernoulli's_equation

Pressure drop can be expressed as the loss of pressure head hL and acceleration of

gravity g.

∆P/ρ=ghL where hL is the head loss

Pipe losses, H = K x V2/2g where: K = coefficient of losses

V = velocity of flow

g = 9.81m/s2

3.0 MATERIALS AND METHODS

The apparatus is shown in figure diagram. The Bernoulli’s Theorem apparatus is

level on the hydraulics bench by using adjustable feet. A small amount of wetting agent

was injected into the test section and had been ensured that the section has the tapered

14˚ tapered duct converging in the direction of flow. To reverse the test section, the total

head probe was withdrawn before releasing the couplings.

The manometer tubes were filled with water to discharge all pockets of air from

the system. By adjusting the flow control valve, the level in the manometers had been

raised or lowered as required. The flow control valve once again had been adjusted to

provide the combination of flow rate and system pressure, which give the largest

convenient difference between the highest and lowest manometer levels. The scale

reading of each manometer level was noted. Three sets of readings of volume per time

had been taken to find the flow rate using the volumetric tank. The specific procedures

of the experiment are as follows:

6

1. The probe was inserted to the end of the parallel position of the duct, and the

tapered portion was moved in 1cm at a time. For each position (100mm, 150mm

and 200mm), the distance from the end of the parallel portion had been noted,

and the scale readings of the manometer levels were recorded.

2. This was repeated to give high flow rates at both high and low static pressure for

different combinations of valve openings.

3. The inlet feed was stopped, the apparatus were drained, the probe was fully

withdrawn, the couplings were undo, the test sections were reversed and the

couplings were replaced.

4. The above procedures were repeated.

Equivalent static pressure in the convergent and divergent configurations was set up

using the remote tapping at the flow control valve.

7

4.0 RESULTS AND DISCUSSION

According to the theory, we found that the flow rate that recorded by rotameter

should be higher than the flow rate of venturi and orifice meter. This shows that losses

occurred at venturi and orifice meter. Losses of energy in pipeline are due to shock from

the sudden change of flow rate at the interchanges of section area, this losses also known

as head loss. That is kinetics energy converted into pressure. Losses can also occur due

to the frictional resistance to flow.

However, there is an abnormal in the data obtained from the venturi, where the

flow rate that calculated are larger than that of the rotameter. This deviates from the

theoretical expectation. This is due to the discrepancies during the experiment such as:

Some bubbles still remain in the manometer tube and the water level was resisted

from raised to the actual height.

8

Since the water level of the manometer board fluctuate all the time, it is difficult for

us to measure or observed the actual water level. What we do is took the average

value of the water level fluctuation height.

According to the data tabulated in table 1.1, 2.1 and 3.1 where the discharge of

the venturi is larger than the orifice. This implies that the losses at the orifice always

greater than that at venturi. This is due to the stopping effect of the flow at the orifice

while the contraction at the venturi neck (point 2) are slower, guided by a tapering tube.

The sudden enlargement from vena- contracta (minimum area) formed downstream in

the orifice with an area which is smaller than the actual area of the orifice cause the flow

rate calculated is smaller compared to the venturi meter.

Other reason that cause the deviation is the head loss in the pipe flow such as:

Major losses ( losses occur in straight pipe )

Minor losses ( losses occur in pipe system components)

Percentage of error of venturi is higher than orifice, therefore the accuracy of

venturi is higher than the orifice. This is because:

Orifice meter has relatively high-pressure loss for a given flow rate.

The orifice plate and meter run must be kept clean and retain the original conditions

specified by the standard.

To assume this, periodic inspection should be conducted to reaffirm condition.

Inspection frequency depends on problems of foreign material collection and

9

possible damage. Inspections will confirm the orifice diameter and coefficient of

discharge.

The most important variable in the equation – the one that directly determines flow-

measurement accuracy – is the differential pressure. Therefore, a major effort should

be made to have as a high a differential as possible (considering flowing conditions),

and the best available differential transducers should be specified. Anything that can

be done should be done to improve this most critical measurement factor.

More sensitive to flow disturbances than some meter.

Flow pattern in the meter does not make meter self- cleaning.

Venturi has low permanent pressure loss.

Venturi can be used on slurries and dirty fluids.

Figure 4.1.1 Graph of Head loss versus Velocity for venturi meter and orifice meter (1st

Trial)Figure 4.1: Graph of head loss versus velocity for venturi and orifice (1st Trial)

y = 0.03x - 0.0088R2 = 1

y = 0.0085x - 0.0048R2 = 0.9973

00.0020.0040.0060.008

0.010.012

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

velocity, m/s

head

loss

, m

venturiorificeLinear (orifice)Linear (venturi)

Figure 4.1.2 Graph of Head loss versus Velocity for venturi meter and orifice meter (2nd

Trial)

10

Figure 4.1: Graph of head loss versus velocity for venturi and orifice (2nd Trial)

y = 0.0187x - 0.0032R2 = 0.9982

y = 0.008x - 0.0042R2 = 0.9949

0

0.002

0.004

0.006

0.008

0 0.2 0.4 0.6 0.8 1 1.2 1.4

velocity, m/s

head

loss

, m


Figure 4.1.3 Graph of Head loss versus Velocity for venturi meter and orifice meter (3 rd

Trial)

y = 0.0275x - 0.0072R2 = 1

y = 0.0091x - 0.0055R2 = 0.9958

00.0020.0040.0060.008

0.010.012

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

velocity, m/s

head

loss

, m


5.0 CONCLUSION AND RECOMMENDATIONS

11

In this experiment, flow rate was measured by using the flow apparatus which

consisted of venturi and orifice. Rotameter was acted as a control to the apparatus and

bench device was used to present the actual value of the flow discharge. From the result

achieved, the average percentage error for the venturi meter is between 3.7% to 16.53%

while the orifice reading deviates in the range of 11.79% to 31.42%. On the other hand,

the percentage of error for rotameter is between 9.33% to 15.56%. From the theory,

venturi meter was preferred for the flow rate measurement than rotameter because

venturi meter had lower pipe losses and percentage error compared to the rotameter. So

venturi meter was more accurate than rotameter.

To avoid any error in the experiment result, all precaution when doing this

experiment might be taken. Discharge hose was ensured properly directed to sump tank

of fibre glass before starting up system. Collection tank drain valve also was ensured left

opened to allow flow discharge back into sump tank. In addition to that, ‘Trapped

bubbles’ in the glass tube or plastic transfer tube was ensured been removed. Any

parallax deviation when taking the reading also might be avoided by reading the result

perpendicular to the water meniscus. Besides that, all kind of organism or unwanted

particle was also made sure not been in the apparatus. Moreover, in order to have a

better fluid flow, the flow apparatus might not dissipate in eddies downstream.

REFERENCES

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Douglas J.F. and Matthews R.D. (1985). Solving Problems In Fluid Mechanics, Vol. 1.

Longman Publication. New York.

Hauser B.A. (1992). Hydraulics For Operations, 3rd Ed. Lewis Publishers. London

Manohar M. and Krishnamachar P. (1990). Fluid Mechanics, Vol. 2. Hydraulic

Machinery & Advanced Hydraulics. Vikas Publishing House Pvt. Ltd. Melbourne.

Massey B.S. (1997). Mechanics Of Fluids, 6th Ed. Van Nostrand Reinhold

(International). Cambridge.

Munson,Young and Okiishi (1998). Fundamentals of fluid mechanics, 3rd Ed. John

Wileys & Sons: New York.

Streeter Victor L., Benjamin Wylie E., and Bedford Keith W. (1995). Fluid Mechanics,

9th Ed. WCB McGraw-Hill. New York.

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APPENDICES

APPENDIX A

RAW DATA

The following are tables related to readings taken at the first trial.

Table A1.1 : Relationship between pressure head and flow rate for both venturi and orifice

MANOMETER

READING ROTAMETER VOLUME TIME

FLOW

RATE,Q

(L/min) (min) USING BERNOULLI'S EQN

(L/min)

1 2 3 4 5 6 7 8 9 10 VENTURI ORIFICE

17.2 14.3 5.2 11 13.7 14.6 15 9 12.7 11 20 20 1 18.29 15.89

18.4 18.5 11.5 16.8 16.4 16.9 17 13.7 15.8 14.8 15 15 1 16.17 18.2

188 18.6 15.5 16.9 17.8 18.1 17.5 17.0 17.6 17 10 10 1 10.75 7.946

14

Table A1.2 : Comparison of percentage error for Venturi Meter and Orifice with Rotameter readings

BENCH VENTURI ORIFICE ROTAMETER

FLOW

RATE

FLOW

RATE % ERROR FLOW RATE % ERROR FLOW RATE % ERROR

(L/min) (L/min) (L/min) (L/min)

22 18.29 8.55 15.89 20.55 20 10

17.5 16.17 7.8 18.2 9 15 16.7

10 10.75 7.5 7.946 20.45 10 5

Table A1.3 : Comparison between venturi and orifice velocity and head loss

VENTURI ORIFICE

HEAD LOSS,m VELOCITY (m/s) HEAD LOSS ,m VELOCITY (m/s)

0.82*10^-2 1.52 0.74*10^-2 0.54

0.64*10^-2 1.34 0.98*10^-2 0.62

0.28*10^-2 0.89

15

The following are tables related to readings taken at the second trial.

Table A2.1: Relationship between pressure head and flow rate for both venturi and orifice

MANOMETER

READING ROTAMETER VOLUME TIME FLOW RATE,Q

(L/min) (min) USING BERNOULLI'S EQN

(L/min)

1 2 3 4 5 6 7 8 9 10 VENTURI ORIFICE

21.3 20.5 9.2 15.1 17.9 19 19.2 13.2 16.9 15 1 20 1 15.29 13.5

22.1 21.7 15.5 18.6 20 29.7 20.8 17.7 19.5 18.5 15 15 1 15.21 8.91

22.4 22.2 `9.2 20.5 21.3 21.7 21.8 20.3 21.1 20.8 10 10 1 10.58 7.95

16

Table A2.2: Comparison of percentage error for Venturi Meter and Orifice with Rotameter readings

Table A2.3: Comparison between venturi and orifice velocity and head loss


FLOW

RATE

FLOW

RATE % ERROR

FLOW

RATE % ERROR FLOW RATE % ERROR


23 15.29 23.55 13.5 32.5 20 15

17 15.21 1.4 8.91 40.67 15 13

11 10.58 5.8 7.95 20.57 10 10

VENTURI ORIFICE

HEAD

LOSS, m VELOCITY (m/s) HEAD LOSS,m VELOCITY (m/s)

0.6*10^-2 1.267 0.54*10^-2 0.46

0.57*10^-2 1.261 0.23*10^-2 0.3

0.28*10^-2 0.88 0.19*10^-2 0.27

17

The following are tables related to readings taken at the third trial.

Table A3.1: Relationship between pressure head and flow rate for both venturi and orifice

MANOMETER

READING ROTAMETER VOLUME TIME FLOW RATE,Q

(L/min) (min)

USING BERNOULLI'S

EQN

(L/min)

1 2 3 4 5 6 7 8 9 10 VENTURI ORIFICE

26 25.1 13.9 19.7 22.4 23.6 23.9 17.8 21.6 19.6 1 20 1 20.44 13.39

26.4 26.9 19.5 22.8 24.3 24.9 25.1 21.8 23.7 22.7 15 15 1 13.38 18.20

26.5 26.2 23.4 24.7 25.4 25.7 21.8 20.3 25.3 24.7 10 10 1 10.22 10.58

18

Table A3.2: Comparison of percentage error for Venturi Meter and Orifice wit Rotameter readings


FLOW

RATE

FLOW

RATE % ERROR

FLOW

RATE % ERROR FLOW RATE % ERROR


21.5 20.44 2.20 13.39 33.05 20 7.5

17 13.38 10.80 18.20 21.33 15 13

11.5 10.22 17.50 10.58 5.80 10 15

Table A3.3: Comparison between venturi and orifice velocity and head loss

VENTURI ORIFICE

HEAD

LOSS, m VELOCITY HEAD LOSS,m VELOCITY

1*10^-2 1.694 0.54*10^-2 0.46

0.44*10^-2 1.111 0.98*10^-2 0.62

0.36*10^-2 0.974

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APPENDIX B

Calculation

Calculations for Table A1.1 and A1.2,

For the venturi,

For the flow 20 L/min.,

Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (14.3 – 5.2)(9.81) ]0.5

= 3.049 x 10-4 m3/s = 18.29 liter/min.

Percentage error = (18.29-20.00)/20 x 100

= 8.55 %


Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (18.5 – 11.5)(9.81) ]0.5

= 2.694 x 10-4 m3/s = 16.17 liter/min.

Percentage error = (16.17 – 15.00)/15 x 100

= 7.8 %


Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (18.6 – 15.5)(9.81) ]0.5

= 1.793 x 10-4 m3/s = 10.75 liter/min.


= 7.5 %

20

For the orifice,


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(15.1 – 9.0)]1/2 x [1- (0.633)2]-1/2

= 2.649 x 10-4 m3/s = 15.89 liter/min.


= 20.55 %


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(17.0-13.7)]1/2 x [1- (0.633)2]-1/2

= 3.034 x 10-4 m3/s = 18.20 liter/min.


= 9.0%


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(18.5 – 16.5)]1/2 x [1- (0.633)2]-1/2

= 1.324 x 10-4 m3/s = 7.946 liter/min.

Percentage error = (7.946-10)/10 x 100

= 20.54%

21

Calculations for Table A2.1 and A2.2

For the venturi,


Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (20.5 – 9.2)(9.81) ]0.5

= 2.548 x 10-4 m3/s = 15.29 liter/min.


= 23.55 %


Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (21.7 – 15.5)(9.81) ]0.5

= 2.535 x 10-4 m3/s = 15.21 liter/min.


= 1.4 %


Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (22.2 – 19.2)(9.81) ]0.5

= 1.764 x 10-4 m3/s = 10.58 liter/min.


= 5.8 %

22

For the orifice,


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(19.2-13.2)]1/2 x [1- (0.633)2]-1/2

= 2.25 x 10-4 m3/s = 13.50 liter/min.


= 32.5 %


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(20.8-17.7)]1/2 x [1- (0.633)2]-1/2

= 1.485 x 10-4 m3/s = 8.91 liter/min.


= 40.67 %


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(21.8-20.3]1/2 x [1- (0.633)2]-1/2

= 1.324 x 10-4 m3/s = 7.946liter/min.


= 20.54 %

23

Calculations for table A3.1 and A3.2,

For the venturi,


Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (25.1-13.9)(9.81) ]0.5

= 3.407 x 10-4 m3/s = 20.44 liter/min.


= 2.2 %


Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (25.9-19.5)(9.81) ]0.5

= .2.23 x 10-4 m3/s = 13.38 liter/min.


= 10.8 %


Q = 0.97 x 2.011 x 10-4 [ 1-(0.53)2 ]-0.5 x [ 2 (26.2-23.4)(9.81) ]0.5

= 1.704 m3/s = 10.22 liter/min.


= 17.5%

For the orifice,


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(23.9-17.8)]1/2 x [1- (0.633)2]-1/2

= 2.232 x 10-4 m3/s = 13.39 liter/min.

24


= 33.05


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(25.1-21.8)]1/2 x [1- (0.633)2]-1/2

= 3.034 x 10-4 m3/s = 18.20 liter/min.


= 21.33 %


Q = 0.61 x 3.1 x 10-4 x [2(9.81)(22.1-20.6]1/2 x [1- (0.633)2]-1/2

= 1.764 x 10-4 m3/s = 10.58liter/min.


= 5.8 %

25

CALCULATION FOR HEAD LOSSES OF VENTURI METER,

Hventuri = V2 2 / 2g [ A2 / At - 1]2 ------------ (1)

Hpipe losses = K x V2 2 / 2g -------------(2)

Compare equation (1) and (2), we have

K = [ A2 / At - 1]2

= (3.8 x 10-4 - 1 )2 = 0.22

2.011 x 10-4

Calculations for Table A1.3

V@20L/min = Q/At Hventuri = K x V2 2 / 2g

= 3.049 x 10-4 / 2.011 x 10-4 = 0.22 x (1.525)2 / 2 x 9.81

= 1.525m/s = 0.824 x 10-2 m


= 2.694 x 10-4 / 2.011 x 10-4 = 0.22 x (1.34)2 / 2 x 9.81

= 1.34 m/s = 0.64 x 10-2 m


= 1.793 x 10-4 / 2.011 x 10-4 = 0.22 x (0.89)2 / 2 x 9.81

= 0.89 m/s = 0.28 x 10-2 m

26



= 2.548 x 10-4 / 2.011 x 10-4 = 0.22 x (1.267)2 / 2 x 9.81

= 1.267m/s = 0.6 x 10-2 m


= 2.535 x 10-4 / 2.011 x 10-4 = 0.22 x (1.261)2 / 2 x 9.81

= 1.261 m/s = 0.57 x 10-2 m


= 1.764 x 10-4 / 2.011 x 10-4 = 0.22 x (0.88)2 / 2 x 9.81

= 0.88m/s = 0.28 x 10-2 m



= 3.407 x 10-4 / 2.011 x 10-4 = 0.22 x (1.694)2 / 2 x 9.81

= 1.694m/s = 1 x 10-2 m


= 2.23 x 10-4 / 2.011 x 10-4 = 0.22 x (2.23)2 / 2 x 9.81

= 1.109 m/s = 0.44 x 10-2 m


= 1.704 x 10-4 / 2.011 x 10-4 = 0.22 x (0.974)2 / 2 x 9.81

= 0.974m/s = 0.38 x 10-2 m

27

CALCULATION OF HEAD LOSSES FOR ORIFICE,

For orifice, there are 2 losses, exit loss and entry loss.

For entry loss, assume that the entry is sharp- edged.

Thus, H1 = 0.5 V2 2 / 2g

For exit loss, H2 = V2 2 / 2g [ A2 / At - 1]2

K = [ A2 / At - 1]2

= ( 3.1 x 10-4 / 4.9 x 10-4 – 1 )

= 0.13

Calculations for Table A1.2,

V@20L/min = Q/A2 H = 0.5 V2 2 / 2g

= 2.649 x 10-4 / 3.1 x 10-4 = 0.5 x (0.54)2 / 2 x 9.81

= 0.54 m/s = 0.0074 m

V@15L/min = Q/A2 H1 = 0.5 V2 2 / 2g

= 3.034 x 10-4 / 3.1 x 10-4 = 0.5 x (0.62)2 / 2 x 9.81

= 0.62 m/s = 0.98 x 10-2 m

V@10L/min = Q/A2 H1 = 0.5 V2 2 / 2g

= 1.324 x 10-4 / 3.1 x 10-4 = 0.5 x (0.27)2 / 2 x 9.81

= 0.27 m/s = 0.19 x 10-2 m


V@20L/min = Q/A2 H1 = 0.5 V2 2 / 2g

= 2.25 x 10-4 / 3.1 x 10-4 = 0.5 x (0.46)2 / 2 x 9.81

= 0.46 m/s = 0.0054 m

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V@15L/min = Q/A2 H1 = 0.5 V2 2 / 2g

= 1.485 x 10-4 / 3.1 x 10-4 = 0.5 x (0.30)2 / 2 x 9.81

= 0.30 m/s = 0.23 x 10-2 m

V@10L/min = Q/A2 H1 = 0.5 V2 2 / 2g

= 1.324 x 10-4 / 3.1 x 10-4 = 0.5 x (0.27)2 / 2 x 9.81

= 0.27 m/s = 0.19 x 10-2 m


V@20L/min = Q/A2 H1 = 0.5 V2 2 / 2g

= 2.23 x 10-4 / 3.1 x 10-4 = 0.5 x (0.46)2 / 2 x 9.81

= 0.46 m/s = 0.0054 m

V@15L/min = Q/A2 H1 = 0.5 V2 2 / 2g

= 3.034 x 10-4 / 3.1 x 10-4 = 0.5 x (0.62)2 / 2 x 9.81

= 0.62 m/s = 0.98 x 10-2 m

V@10L/min = Q/A2 H1 = 0.5 V2 2 / 2g

= 1.324 x 10-4 / 3.1 x 10-4 = 0.5 x (0.27)2 / 2 x 9.81

= 0.27 m/s = 0.19 x 10-2 m

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APPENDIX C

Figure C1 : Installation drawing for Flowmeter Demonstration Apparatus

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Figure C2 : Graph of Orifice meter discharge coefficient

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Figure C3 : Venturi meter discharge coefficient

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lab 1 complete 15-08

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