Flow Through An VenturiMeter

A Venturi meter constricts the flow in some fashion, and pressure sensors measure the differential pressure before and within the constriction. This method is widely used to measure flow rate in the transmission of gas through pipelines, and has been used since Roman Empire times. The coefficient of discharge of Venturi meter ranges from 0.93 to 0.97. The first large-scale Venturi meters to measure liquid flows were developed by Clemens Herschel, who used them to measure small and large flows of water and wastewater beginning at the very end of the 19th century.

The main parts of a venturimeter are:

1. A short converging part: It is that portion of the venturi where the fluid gets converges.
2. Throat: It is the portion that lies in between the converging and diverging part of the venturi. The cross section of the throat is much less than the cross section of the converging and diverging parts. As the fluid enters in the throat, its velocity increases and pressure decreases.
3. Diverging part: It is the portion of the venturimeter (venturi) where the fluid gets diverges.

Considered a venturimeter is fitted to a horizontal pipe through which fluid ( water) is flowing as shown in the figure given below.

Let d1, p1, v1 & a1, are the diameter at the inlet, pressure at the inlet, velocity at the inlet and area  at the cross section 1.

And d2, p2, v2 and a2 are the corresponding values at section 2.

Applying bernoulli’s equation at sections 1 and 2

As the pipe is horizontal, so z1 = z2

Therefore

(P1 – P2)/ρg is the difference of pressure heads at section 1 and 2 and it is equal to h. so

Substituting this value of h in equation (1), we get

Now applying continuity equation at section 1 and 2

Substituting this value of v1 in equation (2) and solving, we get

Discharge

Substituting value of v2 in above equation

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

Where Cd is the coefficient of venturimeter and its value is less than 1.

Credit:- (i) https://en.m.wikipedia.org/wiki/Flow_measurement

(ii) https://www.google.com/amp/www.mechanicalbooster.com/2016/06/venturimeter-principle-construction-working-diagram.html/amp