Venturimeter is a device used to measure the rate of flow of a fluid flowing through a pipe. It works based on Bernoulli’s principle. The main parts of the venturi meter include a short converging part, throat, and diverging part.
Expression for rate of flow through venturimeter:
Consider a venturimeter fitted in a horizontal pipe through which a liquid is flowing.
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 respectively.
And d2, p2, v2 and a2 are the corresponding values at section 2.
And ρ is the density and g is the acceleration due to gravity.
Applying Bernoulli’s equation at sections 1 and 2
As the pipe is horizontal, so z1 = z2
(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
Substituting value of v2 in above equation
Q is the theoretical discharge under ideal conditions. The 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.
Citations: Fluid Mechanics and Hydraulic machines by Dr.R.K. Bansal.