What is Venturi-meter? Explain how it is used.

Explanation

Venturi-meter: the venturi-meter is a device to measure the flow speed of incompressible fluid.
It consists of a tube with a broad diameter and a small constriction at the middle as shown in the figure.

The manometer contains a liquid of density `rho_m`. the speed `v_1` of the liquid flowing through the tube at the broad neck area A is to be measured. From equation of continuity,
the speed at the constriction ,`v_2=A/a v_1`
According to Bernoulli's equation,
`P_1+1/2rhov_1^2=P_2+1/2rhov_1^2(A//a)^2`
`impliesP_1-P_2=1/2rhov_1^2[(A/a)^2-1]......(1)`
This pressure difference causes the fluid in the U-tube connected at the narrow neck to rise in comparison to the other arm.
The difference in height h measures the pressure difference.
`P_1-P_2=rho_mgh=1/2rhov_1^2[(A/a)^2-1]......(2)`
So, the speed of fluid at wide neck is
`v_1=sqrt((2rho_mgh)/rho)[(A/a)^2-1]^(-1//_2).......(3)`
Uses: Venturi-meter is used for measuring the speed of imcompressible liquid and rate of flow of liquid through pipes.