# Working of Venturimeter – Construction, Principle with Diagram

Venturimeter is a device that is used to measure the rate of flow of fluid through a pipe. This device is based on the principle of Bernoulli’s Equation. Venturimeter is named after G.B Venturi who developed the principle of venturimeter in 1797 but this principle comes into consideration with the help of C. Herschel who developed the first venturimeterin 1887.

Main parts of venturimeter :-**1. Covering part :** It is the part of the venturimeter where the fluid converges .**2. Throat :** It is the portion that lies in between the converging and diverging part of venturi. In the throat portion the cross section is much less than converging and diverging portion. When the reaches the throat, its velocity increases and pressure decreases.**3. Diverging part :** It is the part of the venturimeter where the fluid gets diverges and the cross-section area increases.

**Construction :**

As stated above it has three parts converging part, throat and diverging part. These three parts are arranged in systematic order.

First one is **inlet section or converging section. **It is the region where the cross section emerges into conical shape for the connectivity with the throat region. . In this part cross section area decreases from beginning to ending. This section is connected to inlet pipe on one end and cylindrical throat on the other end. The angle of convergence is generally 20-22 degrees .

Second one is **cylindrical throat .**It is the middle part of the venturimeter. It is the cylindrical pipe in venturimeter through which the fluid passes after converging in the convergent section. Throat has generally a diameter of throat is half the diameter of pipe. The diameter of the throat remains same through out its length.

Last one is **diverging section . **It is the end of the venturimeter. On one side it is attached to throat of venturimeter and on the other side it is attached to the pipe. The divergent section has an angle 5 to 15 degrees . The diverging angle is less than the converging angle because the length of the diverging cone is larger than converging cone. The main reason of the small diverging angle is to avoid flow seperation from the walls.

### Working :-

Venturimeter works on the principle of Bernoulli’s equation i.e when velocity increases pressure decreases . Cross section of throat is less than cross section of inlet pipe. Since the cross -section decreases from inlet pipe to throat, the velocity of the fluid increases and hence the pressure decreases. Due to decrease in pressure, a pressure difference is created between the inlet pipe and throat of the venturimeter . This pressure difference can be measured by placing a differential manometer between the inlet section and throat section or by using two guages at inlet section and throat. After getting the pressure difference flow rate through pipe is calculated.

## Expression for the rate of flow through Venturimeter

Consider a venturimeter is fitted in a horizontal pipe through which fluid ( water ) is flowing as shown in figure below.

Let a1 = cross-section area of inlet pipe

d1= diameter of inlet pipe

v1 = velocity at inlet pipe

p1 = pressure at inlet pipe

also,

a2 = cross-section area of throat

d2= diameter of throat

v2 = velocity at throat

p2 = pressure at inlet throat

Applying bernoull’s equation at section (1) and (2) , we get_{}

As the pipe is horizontal, so Z_{1 }= Z_{2}

Hence we get,

(P_{1 }– P_{2})/ ρg is the difference of pressure heads at section 1 and 2 and is equal to h. So eq (1) becomes

Now applying continuity at section (1) and (2), we get

Placing the value of v1 in eq (2) and solving, we get

Now , Rate of flow of fluid or Discharge (Q) can be stated as

Substituting value of v2 in this equation, we get

Q is the the theoretical discharge under ideal conditions. Actual discharge will be less than this. The actual discharge is given by,

Where C_{d }is coefficient of venturimeter and its value is always less than 1.