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 t wo points.
+ +
=
Where, V = fluid velocity, g = acceleration acceleration due to gravity, Z = elevation, P = pressure at selected point and
= density of the f luid.
Fig.1. Experimental set up
1
…1
Calculation of discharge coefficient of orifice plate, venture, pitot tube
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, Q A =
..ℎ
(1− ( )4 )
….2
Where, Q A = Actual discharge (m3/s), Cc = Coefficient of contraction, A = Area of orifice (m2), g = Acceleration due to gravity (m/s 2), 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
Fig.2. Orifice plate 2
….3
Calculation of discharge coefficient of orifice plate, venture, pitot tube
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,
Q A =
(ℎ)⁄ ( − )/
…4
Where, Q A = Theoretical discharge (m 3/s), a1 = Area of venturi meter at inlet (m 2), a2 = Area of venturi meter at throat (m2), g = Acceleration due to gravity (m/s 2) 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 3
Calculation of discharge coefficient of orifice plate, venture, pitot tube 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 = Velocity (V) = (2gH) 1/2
Fig.4. Pitot tube
7. Formula 7.1.
Orifice meter D
1. Inlet area of the orifice meter =
2. Orifice area of the meter (a) =
2
(m2)
4
d
2
(m2)
4
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 =
D 4
2. Throat area of the meter (a) =
3. Venturi meter constant (K) =
2
(m2) d 4 a1 a2
2
(m2)
2 g
( a12 a22 )1 / 2 4
V g
….5 ….6
Calculation of discharge coefficient of orifice plate, venture, pitot tube 4. Actual discharge (Qa) = Q/t (m3/s) 5. Theoretical discharge (QT) = k H (m3/s) 6. Coefficient of discharge (Cd) = Qa/QT
7.3.
Pitot tube D
1. Inlet area of the pitot tube meter (A) =
2
(m2)
4
2. Actual discharge (Qa) = Q/t (m3/s) 3. Theoretical fluid velocity (V) =
2
2 gH (m/s
)
4. Theoretical discharge (QT) = AV (m3/s) 5. Coefficient of discharge (Cd) = Qa/QT
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 (V 2) 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.
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Calculation of discharge coefficient of orifice plate, venture, pitot tube
10. Tabulations Table.1. Venturi meter S.No.
Rotameter
Time taken to
Actual
Pressure
Theoretical
Coefficient
Reading
fill 1.5L of
discharge
difference
discharge
of
(LpH)
water in tank
( x10-5
across Orifice
(× 10-5
Discharge
(s)
m3/s)
H (m)
m3/s)
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
Time taken to
Actual
Pressure
Theoretical
Coefficient
Reading
fill 1.5L of
discharge
difference
discharge
of
(LpH)
water in tank
( x10-5
across Orifice
(× 10-5
Discharge
(s)
m3/s)
H (m)
m3/s)
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
Average discharge coefficient = 0.6116
Table.3. Pitot tube S.No.
Rotameter
Time taken to
Actual
Pressure
Theoretical
Coefficient
Reading
fill 1.5L of
discharge
difference
discharge
of
(LpH)
water in tank
( x10-5
across Orifice
(× 10-5
Discharge
(s)
m3/s)
H (m)
m3/s)
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
Average discharge coefficient = 0.81594
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Calculation of discharge coefficient of orifice plate, venture, pitot tube
11. Graph 18
16 15.3
) s 14 / 3
13.68
m
5 -
0 12 1 x ( e 10 g r a h c s i 8 d l a c i t 6 e r o e h 4 T
11.56 10.64 10.6 9.959 9.272
10.34
7.31
7.529
6.52
6
Venturi
8.41 7.715
Orifice Pitot
5.143
2
0 0
1
2
3
4
5
6
7
8
9
Actual discharge (x 10 -5 m3/s)
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 =
a1 a2
(
2 a1
2 g 2 1/ 2 a2
)
= 3.637 x 10-4
Actual discharge Q A = Q / t = 1.75 x 10-3 / 37 Q A = 4.729 x 10-5 m3/s Theoretical discharge Q t = K(H)1/2 = 3.637 x 10-4 (20 x 10-3)1/2
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Calculation of discharge coefficient of orifice plate, venture, pitot tube Qt = 5.143 x 10-5 m3/s Co-efficient of discharge C d = Q A / 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 Actual discharge Q A = Q / t = 1.75 x 10-3 / 37 Q A = 4.729 x 10-5 m3/s Theoretical discharge Q t = 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 Co-efficient of discharge C d = Q A / Qt = 4.729 x 10-5 / 7.31 x 10-5 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 Actual discharge Q A = Q / t = 1.75 x 10-3 / 37 Q A = 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 Q t = A x V = 2.688 x 10-4 x 0.242 Qt = 6.521 x 10-5 m3/s 8
Calculation of discharge coefficient of orifice plate, venture, pitot tube Co-efficient of discharge C d = Q A / Qt = 4.729 x 10-5 / 6.521 x 10-5 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.
+ + = 2
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.
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Calculation of discharge coefficient of orifice plate, venture, pitot tube 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.
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Calculation of discharge coefficient of orifice plate, venture, pitot tube
Reference 1. Bela G. Liptak, “Process Measurement and Analysis”, CRC Press, 2001. 2. Donald P. Eckman, “Industrial Instrumentation”, Wiley publication, 1951.
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