# Use Of Venturimeter for Flow Measurement

A venturi meter is a device used to measure the fluid flow through pipes. This flow measurement device is based on the principle of Bernoulli’s equation.

## Bernoulli’s Theorem :

It states that, in a steady flow of real fluid, the total head (total energy per N of flowing fluid) at any section is equal to that at any subsequent section, plus the loss of head occurring between the two sections.
OR
It states that whenever there is a continuous flow of liquid, the total energy at every section remains the same provided that there is no loss or addition of the energy.
Mathematically,
P/W + V^2 / 2g + Z = Constant

Where,

P/W = Pressure energy,
V^2 / 2g  = Kinetic energy,

Z = Potential energy
Applications of Bernoulli’s Theorem :
• Venturimeter,
• Orifice meter,
• Nozzle meter or Flow nozzle,
• Rotameter, Elbow meter (or Pipe-bend Meter),
• Pitot Tube

## Parts Of Venturi Meter

It consists of three parts.

1. A short converging section:

In the converging section, the area of flow is decreases and hence the velocity of fluid increases and the static pressure decreases. Normally the convergent angle is of 21° ± 2°.

2. A throat:

This is the cylindrical section of the minimum area where the velocity is maximum and pressure is minimum. The throat diameter is usually between 0.25 to 0.5 times the inlet diameter of the pipe. The length of the throat equals its diameter.

3. A diverging section:

The diverging section is a diffuser where the area is increased back to the pipe entrance area and hence the pressure is increased. To recover all the pressure energy, the divergent angle is kept of 5° 7°. This angle has to be kept less so that the flowing fluid has the least tendency to separate from the wall of the pipe. However, with small angles, the length and hence the cost of the venturi meter would increase. So where pressure recovery is not important, the divergent angle may be kept as high as 14°.

The small-sized venturi meter, suitable for pipelines less than 5cm diameter, are usually made of brass or bronze. The inside surface is smoothly finished to reduce friction.
Large-sized venturi meters are usually made of cast iron with throat made of brass or bronze. Very large-sized venturi meter, up to 6m pipe diameter has been made of smooth surface concrete. Only the throat is made of machined bronze.

## Venturimeter Principle :

It is based on the principle of Bernoulli’s equation. Inside of the venturi meter pressure difference is created by reducing the cross-sectional area of the flow passage. The pressure difference is measured by using a differential U-tube manometer. This pressure difference helps in the determination of the rate of flow of fluid or discharge through the pipeline. As the inlet area of the venturi is large than at the throat, the velocity at the throat increases resulting in a decrease of pressure. By this, a pressure difference is created between the inlet and the throat of the venturi.

## Construction of Venturi meter

The following are the main parts and areas of venture meter:
1. The entry of the venture is cylindrical in shape to match the size of the pipe through which fluid flows. This enables the venture to be fitted to the pipe.
2. After the entry, there is a converging conical section with an included angle of 19’ to 23’.
3. Following the converging section, there is a cylindrical section with a minimum area called as the throat.
4. After the throat, there is a diverging conical section with an included angle of 5’ to 15’.
5. Openings are provided at the entry and throat (at sections 1 and 2 in the diagram) of the venture meter for attaching a differential pressure sensor (u-tube manometer, differential pressure gauge, etc) as shown in the diagram.

## Working Operation of venturi meter:

• The fluid whose flow rate is to be measured enters the entry section of the venturi meter with a pressure P1.
• As the fluid from the entry section of the venturi meter flows into the converging section, its pressure keeps on reducing and attains a minimum value P2 when it enters the throat. That is, in the throat, the fluid pressure P2 will be minimum.
• The differential pressure sensor attached between the entry and throat section of the venturi meter records the pressure difference(P1-P2) which becomes an indication of the flow rate of the fluid through the pipe when calibrated.
• The diverging section has been provided to enable the fluid to regain its pressure and hence its kinetic energy. Lesser the angle of the diverging section, the greater is the recovery.

## Equation of actual discharge through venturimeter :

The coefficient of discharge ( ) for venturi meter is usually in the range of 0.95 to 0.98.

## Value of ′′ Given by U-tube Manometer

Case-I Heavier fluid in the manometer
If the U-tube manometer contains a liquid that is heavier than the liquid flowing through the pipe. Then,
ℎ = x [ Sℎ / So − 1] = ( P1 /ρg  − P2/ρg ) + (Z1 − Z2)
Where,
Sℎ = Specific gravity of heavier fluid used in the manometer
So = Specific gravity of fluid flowing through the pipe
x = Difference in the level of heavier fluid in the manometer
Case-II Lighter fluid in the manometer
If the U-tube manometer contains a liquid which is lighter than the liquid flowing through the pipe. Then,
ℎ = x [1 − Sl/ So ] = ( P1/ρg − P2 / ρg ) + (Z1 − Z2 )
Where,
Sl = Specific gravity of lighter fluid used in the manometer
So = Specific gravity of fluid flowing through the pipe
x = Difference in the level of lighter fluid in the manometer

## Hydraulic Coefficients,

### Coefficient of Velocity ( Cv)

It is defined as the ratio between the actual velocity of a jet at vena-contracta and the theoretical velocity of jet at orifice plate.
∴ Cv = ν act / v th
The theoretical velocity is given by,
v th = √2ℎ
The value of Cv varies from 0.95 to 0.99 for different orifices. For sharp-edged orifice generally, it is taken as 0.98.

### Coefficient of Contraction (Cc)

It is defined as the ratio of the area of the jet at vena-contracta to the area of the orifice.
Cc= ac / ao
The value of Cc varies from 0.61 to 0.69 for different orifices. In general, it is taken as 0.64.

### Coefficient of Discharge (Cd)

It is defined as the ratio of the actual discharge to the theoretical discharge from an orifice.
Cd = Qact / Q th
Cd  = Cc × Cv
The value of Cd varies from 0.61 to 0.65 for different orifices. In general, it is taken as 0.62.

## Application of Venturimeter:

Venturimeter Applications are as follows,

• It is used where high-pressure recovery is required.
• It can be used for measuring flow rates of water, gases, suspended solids, slurries, and dirty liquids.
• It can be used to measure high flow rates in pipes having diameters in a few meters.

1. Fewer chances of getting clogged with sediments
2. The coefficient of discharge is high.
3. Its behavior can be predicted perfectly.
4. It can be installed vertically, horizontally, or inclined.