Discharge coefficient

Objective To determine the discharge coefficient of the venturi meter and us it to measure flow rate.

Introduction In industrial practice one of the problems most frequently encountered by engineers is the

measurement of fluid properties, such as density, viscosity, pressure, velocity, flow rate. This apparatus

is designed to obtain the flow rate by using a venturi meter. It consists of a venturi tube and differential

pressure gauge. The venturi tube has a converging portion, a throat and a diverging portion as shown.

The converging portion increases the velocity of the fluid and

lowers its static pressure. A pressure difference between inlet and

throat develops, which is related to the rate of discharge. The

diverging cone changes the area of the stream back to the entrance

area and converts velocity head into pressure head.

Assuming incompressible flow and no frictional losses, and using the continuity Equation (Q = A1V1 = A2V2)

with Bernoulli’s Equation, we get:

2

2

221

2

11

22Z

g

VpZ

g

Vp

2

1

2

2

221 1

2

21

A

A

g

VZZ

pp

2

1

2

2121

1

22

2

A

A

ZZpp

g

V

Ideally, 2/1

21

2/12

22221

1

2 21 ZZgAVAQpp

A

A

i

(1)

However, in the case of real fluid flow, the flow rate will be expected to be less than that given by equation (1) because of

frictional effects and consequent head loss between inlet and throat. Therefore,

21

21

212

221

1

2 21 ZZgACQpp

A

A

da

(2)

In practice, this non-ideality is accounted by insertion of an experimentally determined discharge coefficient, Cd

that is termed as the coefficient of discharge. With Z1 = Z2 in this apparatus, the discharge coefficient is:

iad QQC (3)

Apparatus The apaprtus consists of a classical Venturi made of transparent acrylic. A series of wall tappings allow

measurement of the static pressure distribution along the converging duct. These tappings are

connected to a manometer bank incorporating with air bleed screw.

1. Staddle Valve

2. Manometer Tubes

3. Manometer Board

4. Control Valve

5. Venturi Outlet Connection

6. Baseboard

7. Unions

8. Venturi Inlet Connection

9. Venturi Meter

10. Adjustable Feet

Procedure

Discharge coefficient determination

1. Connect the venture meter apparatus to the hydraulic bench and turn on the water supply

pump with the inlet valve fully closed and the outlet valve fully open.

2. Slowly open the inlet valve and allow the water to fill the venture meter, make sure that the

manometer tubes are properly connected and free of air-bubbles.

3. Adjust the discharge valve to a high measurable flow rate and after the level stabilizes, measure

the water flow rate using volumetric method and record the manometers reading.

4. Repeat step 1 to 3 with at least three decreasing flow rates by regulating the venturi control

valve.

5. Obtain the actual flow rate, Qa from the volumetric flow measurement method.

6. Calculate the ideal flow rate, Qi from the head difference between hA and hC using Equation 1.

7. Plot Qa Vs Qi and finally obtain the discharge coefficient, Cd which is the slope.

Flow rate measurement

1. Connect the venture meter apparatus to the hydraulic bench and turn on the water supply

pump with the inlet valve fully closed and the outlet valve fully open.

2. Slowly open the inlet valve and allow the water to fill the venture meter, make sure that the

manometer tubes are properly connected and free of air-bubbles.

3. After the level stabilizes, measure the water flow rate using volumetric method and record the

manometers reading.

4. Repeat step 1 to 3 with three other decreasing flow rates by regulating the venturi control valve.

5. Calculate the venturi meter flow rate (Equation 2) of each data by applying the discharge

coefficient obtained.

6. Compare the volumetric flow rate with venturi meter flow rate.