Practical applications of Bernoulli’s equation ( Venturimeter )

To study the applications of the Bernoulli’s equation

Venturimeter :

Venturimeter : is a device used for measuring the rate of flow of a fluid flowing through a pipe. It consists of three parts:

Let d1 = diameter at the inlet (section 1)

p1 = pressure at section 1

v1 = velocity at section 1

A1= area at section 1

d2, p2, v2, A2 are the corresponding values at the throat (section 2)

Applying Bernoulli’s equations at sections 1 and 2, we get

Where

difference of pressure heads at sections 1 and 2.

Note that the above expression is for ideal condition and is known as theoretical discharge.

Actual discharge will be less than theoretical discharge.

Cd is the coefficient of venturimeter and its value is always less then 1.

Expression of ‘h’ given by differential U-tube manometer:

Case 1 : The liquid in the manometer is heavier than the liquid flowing through the pipe

Sh: Specific gravity of the heavier liquid.

S0: Specific gravity of the flowing liquid.

Case 2 : The liquid in the manometer is lighter than the liquid flowing through the pipe

SL: Specific gravity of the lighter liquid.

X: difference of the liquid columns in U-tube