Discharge Coefficient

1

CALCULATION OF DISCHARGE COEFFICIENT OF ORIFICE PLATE,

VENTURI AND PITOT TUBE

1. Aim

The aim of the experiment is to calculate the discharge co-efficient of orifice plate,

venturi and pitot tube.

2. Equipments Required

Flow measurement setup

3. Principle

The flow meters are based on the Bernoulli’s principle. According to the principle, in a

flowing stream, the sum of the pressure head, the velocity head, and the elevation head

at one point is equal to their sum at another point in the direction of flow plus the loss

due to friction between the two points.

𝑉2

2+ 𝑔𝑍 +

𝑃

𝜌= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 …1

Where,

V = fluid velocity,

g = acceleration due to gravity,

Z = elevation,

P = pressure at selected point and

𝜌 = density of the fluid.

Fig.1. Experimental set up

Calculation of discharge coefficient of orifice plate, venture, pitot tube

2

4. Orifice Meter

The orifice meter consists of thin circular metal plate with circular sharp edge hole in

it. The concentric orifice is by far the most widely used. As the fluid passes through the

orifice, it contracts the area. The minimum flow area is called vena contracta. Different

types of taps are used for orifice meter. The flow of fluid through the orifice meter

establishes the pressure differential across the orifice plate, which can then be measured

and related to the flow rate.

The actual discharge through orifice meter is given by,

QA = 𝐶𝑐.𝐴.2𝑔ℎ

(1−𝐶𝑐2(

𝐷

𝑑)4)

….2

Where,

QA = Actual discharge (m3/s),

Cc = Coefficient of contraction,

A = Area of orifice (m2),

g = Acceleration due to gravity (m/s2),

h = differential pressure head of the liquid (m),

D = Diameter of orifice (m) and

d = Diameter of pipe (m).

The above expression can be written as,

Q = Cd × A × 2gh ….3

Fig.2. Orifice plate


3

5. Venturi Meter

The venturi is particularly adapted to installation in pipelines not having long,

unobstructed runs. The flow of fluid through the venturi tube establishes the pressure

differential which can then be measured and related to the flow rate. Because of the

gradual reduction in the area of flow, there is no vena contracta and the flow area is

minimum at the throat so that, the coefficient of contraction is unity. The meter is equally

suitable for compressible ad incompressible fluids.

The flow through the venturi meter and hence the flow through the pipe is given by,

QA = 𝑎1𝑎2(2𝑔ℎ)1 2⁄

(𝑎12− 𝑎2

2)1/2 …4

Where,

QA = Theoretical discharge (m3/s),

a1 = Area of venturi meter at inlet (m2),

a2 = Area of venturi meter at throat (m2),

g = Acceleration due to gravity (m/s2) and

H = Differential pressure head of the liquid (m).

Fig.3. Venturi meter

6. Pitot Tube

The pitot tube is primarily a device for measuring fluid velocity. It is a combination of

a total head tube and a static tube. It consists simply of a tube supported in the pipe with


4

the impact opening arranged to point directly towards the incoming fluid. This is called

the impact opening and is used to measure the stagnation pressure. The static pressure

is measured through the ordinary pressure tap. The difference between impact pressure

and static pressure represents velocity head.

Pressure difference (H) = Velocity head = V2

2g ….5

Velocity (V) = (2gH)1/2 ….6

Fig.4. Pitot tube

7. Formula

7.1. Orifice meter

1. Inlet area of the orifice meter = 4

2D (m2)

2. Orifice area of the meter (a) = 4

2d (m2)

3. Actual discharge (Qa) = (Q/t) (m3/s)

4. Theoretical discharge ( QT) = a (2gH)1/2 (m3/s)

5. Coefficient of discharge (Cd) = Qa/QT

7.2. Venturi meter

1. Inlet area of the venturi = 4

2D (m2)

2. Throat area of the meter (a) = 4

2d (m2)

3. Venturi meter constant (K) = 2/12

2

2

1

21

)(

2

aa

gaa


5

4. Actual discharge (Qa) = Q/t (m3/s)

5. Theoretical discharge (QT) = Hk (m3/s)


7.3. Pitot tube

1. Inlet area of the pitot tube meter (A) = 4

2D (m2)

2. Actual discharge (Qa) = Q/t (m3/s)

3. Theoretical fluid velocity (V) = gH2 (m/s2)

4. Theoretical discharge (QT) = AV (m3/s)


8. Commissioning

Remove the tank supply and fill the tank with distilled water. Replace the tank in its

position.

Keep the flow regulating valve (V1) 50% open, the drain valve (V2) 100% open and

switch on the pump. Check the working of the rotameter by manipulating the flow

using the flow regulating valve.

Set the flow rate at 60LpH. Press bulb 2-3 times to lower the water levels in the

manometer tubes. Gently drop the manometer tubes to remove the air entrapped.

Loosen the vent valve slightly. The water will rise in the manometer tubes. Set the

water level at mid scale of the manometer. Ensure that all the air bubbles are

removed by varying the flow rate from minimum to maximum.(i.e) the average level in

the manometer tube can be raised by slightly venting out air or it can be covered by

pumping air into the rubber bulb.

9. Procedure

Adjust the rotameter flow rate in steps of 50LpH from 150 t0 350 LpH and wait till a

steady state is reached.

Note the pressure difference across the orifice meter, venture meter and pitot tube

meter which are all connected in series and will have the same inlet flow rate.

Close the outlet valve at the measuring tank.

Measure the time required for collecting 1.5l of water in the tank.

Drain the measuring tank by opening the drain valve immediately.

Draw the graph between theoretical and actual discharge.


6

10. Tabulations

Table.1. Venturi meter

S.No. Rotameter

Reading

(LpH)

Time taken to

fill 1.5L of

water in tank

(s)

Actual

discharge

( x10-5

m3/s)

Pressure

difference

across Orifice

H (m)

Theoretical

discharge

(× 10-5

m3/s)

Coefficient

of

Discharge

Cd

1 200 37 4.729 20 5.143 0.9194

2 250 28 6.25 30 6.299 0.992

3 300 24 7.29 45 7.715 0.945

4 350 21 8.33 65 9.272 0.90

5 400 20 8.75 85 10.60 0.825

Average discharge coefficient = 0.91628

Table.2. Orifice meter

S.No. Rotameter

Reading

(LpH)

Time taken to

fill 1.5L of

water in tank

(s)

Actual

discharge

( x10-5

m3/s)

Pressure

difference

across Orifice

H (m)

Theoretical

discharge

(× 10-5

m3/s)

Coefficient

of

Discharge

Cd

1 200 37 4.729 20 7.31 0.646

2 250 28 6.25 40 10.34 0.604

3 300 24 7.29 50 11.56 0.630

4 350 21 8.33 70 1.368 0.608

5 400 20 8.75 88 15.3 0.57


Table.3. Pitot tube

S.No. Rotameter

Reading

(LpH)

Time taken to

fill 1.5L of

water in tank

(s)

Actual

discharge

( x10-5

m3/s)

Pressure

difference

across Orifice

H (m)

Theoretical

discharge

(× 10-5

m3/s)

Coefficient

of

Discharge

Cd

1 200 37 4.729 3 6.52 0.7251

2 250 28 6.25 4 7.529 0.830

3 300 24 7.29 5 8.41 0.866

4 350 21 8.33 7 9.959 0.836

5 400 20 8.75 8 10.64 0.822



7

11. Graph

Fig.5. Theoretical Vs actual discharge graph

12. Model calculation

At an inlet flow rate of 200 LpH,

1. Venturi meter

Inlet area of the venturi meter, A = (π/4) D2 = (3.14 / 4) x 0.01852

A = 2.686 X 10-4 m2

Outlet area of the venturi meter, a = (π/4) d2 = (3.14 / 4) x 0.01222

a = 1.1684 x 10-4 m2

Venturi meter constant, K = 2/12

2

2

1

21

)(

2

aa

gaa

= 3.637 x 10-4

Actual discharge QA = Q / t = 1.75 x 10-3 / 37

QA = 4.729 x 10-5 m3/s

Theoretical discharge Qt = K(H)1/2

= 3.637 x 10-4 (20 x 10-3)1/2

5.143

6

7.715

9.272

10.6

7.31

10.34

11.56

13.68

15.3

6.52

7.529

8.41

9.95910.64

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8 9 10

The

ore

tica

l dis

char

ge (

x10

-5m

3 /s)

Actual discharge (x 10-5 m3/s)

Venturi

Orifice

Pitot


8

Qt = 5.143 x 10-5 m3/s

Co-efficient of discharge Cd = QA / Qt = 4.729 x 10-5 / 5.143 x 10-5

Cd = 0.9194

2. Orifice meter

Inlet area of the orifice meter, A = (π/4) D2 = (3.14 / 4) x 0.01852

A = 2.686 X 10-4 m2

Outlet area of the orifice meter, a = (π/4) d2 = (3.14 / 4) x 0.01222

a = 1.1684 x 10-4 m2


QA = 4.729 x 10-5 m3/s

Theoretical discharge Qt = a(2gH)1/2

= 1.168 x 10-4 (2 x 9.81 x 20 x 10-3)1/2

Qt = 7.31 x 10-5 m3/s


Cd = 0.646

3. Pitot tube

Diameter of the pitot tube, D = 0.0185 m

Area of the pitot tube, A = (π/4) D2 = (3.14 / 4) x 0.01852

a = 2.688 x 10-4 m2


QA = 4.729 x 10-5 m3/s

Theoretical fluid velocity, V = (2gH)1/2 = (2 x 9.81 x 3 x 10-3)1/2

V = 0.242 m3/s

Theoretical discharge Qt = A x V = 2.688 x 10-4 x 0.242

Qt = 6.521 x 10-5 m3/s


9


Cd = 0.7257

13. Pre-lab questions

1. State the principle of pitot tube.

Pitot tubes can be used to indicate fluid flow velocity by measuring the difference

between the static and dynamic pressures in fluids. The principle is based on the

Bernoulli’s equation where each term can be interpreted as a form of pressure. It

measures the fluid flow velocity by converting the kinetic energy in the fluid flow into

potential energy.

2. State Bernoulli’s theorem.

Bernoulli’s theorem states that when a liquid is flowing the total of pressure energy,

kinetic energy and potential energy per unit mass should be constant.

𝑉2

2+ 𝑔𝑍 +

𝑃

𝜌= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

3. What are the types of venturi tubes?

Classical venturi

Short form venturi

Rectangular venturi

Eccentric venturi tube

4. Why venturi with piezometer connection is unsuitable for use in purge systems?

Venturi with piezometer connections are unsuitable for use with purge systems but

used for slurries and dirty fluids, because the purging fluid tends to short circuit to the

nearest tap holes.

5. Which type of orifice plate is used in metering fluids? Why?

Eccentric and segmental orifice are used in metering dirty fluids, these orifices are

recommended where horizontal meter runs are required and the fluid contains

extraneous matter to a degree that concentric orifice would plug up.

6. Limitations of Long form venturi?

Long form venturi meters do consume energy whereas the cone design of the

modified short form type meters recovers a significant portion of the consumed energy.


10

Long form venturi have also been characterized by relatively long laying lengths and

relatively expensive to manufacture.

7. Where is the coefficient of discharge significant in industries?

With the help of discharge coefficient, different type of burners used in industrial

combustion applications can be determined, since the burner pressure drop and hence

pressure loss coefficient is necessary to design burner pressure drop at specific Mach

number.

8. What are all the possible sources from which errors may be introduced in measurement

process?

Lack of linearity

Lack of gauge resolution

Drift

Hysteresis

Construction tolerances in meter components

Uncertainty of secondary devices

Data reduction and computation

9. What is the type of rotameter used? What are installation specification of rotameter

which causes error?

Glass tube rotameter has been used.

Density of float should be large than density of liquid

Introduction of air bubbles should be prevented

Rotameter should be vertically installed

Inference

The pressure difference is high for orifice and venturi whereas it is very low for pitot tube.

Since the theoretical discharge of the orifice is very high, it has the least discharge

coefficient whereas the theoretical discharge of venturi is very low, thus it has the highest

discharge coefficient. The discharge coefficient of pitot tube lies in the middle.

Conclusion

Thus the discharge coefficient of orifice plate, venturi and pitot tube were determined by

observing pressure difference.


11

Reference

1. Bela G. Liptak, “Process Measurement and Analysis”, CRC Press, 2001.

2. Donald P. Eckman, “Industrial Instrumentation”, Wiley publication, 1951.

Discharge Coefficient

Documents

Transcript of Discharge Coefficient