What is a venturi - meter ? Explain its constuction and working..

Explanation

The ven meter is a device to measure the flow speed of incompressible fluid.
It consists of a tube with a broad diameter and a small contraction at the middle as shown in figure

A manometer in the form of a U- tube is also attached to it, with one arm at the broad neck point of the tube and the other at construction which is known as throat.
The manometer contains a liquid of density `rho_(m)`.
At point 1, cross section area is A and velocity of liquid is `v_(1)`.
At point 2, cross section area is a and velocity of liquid is `v_(2)`.
According to equation of continuity ,
`Av_(1)=av_(2)`
`thereforev_(2)=(Av_(1))/(a)` .... (1)
Writing Bernoull.s equation at point 1,2.
`P_(1)+(1)/(2)rhov_(1)^(2)+rhogh,=P_(2)+(1)/(2)rhov_(2)^(2)+rhogh_(2)`
but `h_(1)=h_(2)`
`thereforeP_(1)-P_(2)=(1)/(2)rhov_(2)^(2)-(1)/(2)rho_(1)^(2)`
`thereforeP_(1)-P_(2)=(1)/(2)rho(A^(2)v_(1)^(2))/(a^(2))-(1)/(2)rhov_(1)^(2)`
`thereforeP_(1)-P_(2)=(1)/(2)rhov_(1)^(2)[((A)/(a))^(2)-1]` ... (2)
Here `Agta` ,
`thereforev_(1)ltv_(2)` so `P_(1)gtP_(2)`
The pressure difference cause liquid in arm 1 coming down and in arm 2 liquid rise .
Due to height difference , the equation of pressure difference
`P_(1)-P_(2)=rho_(m)gh` .....(3)
Comparing equation (2) and (3),
`(1)/(2)rhov_(1)^(2)[(A^(2))/(a^(2))-1]=rho_(m)gh`
`therefore(1)/(2)rho_(1)^(2)[(A^(2)-a^(2))/(a^(2))]=rho_(m)gh`
`thereforev_(1)^(2)=(a^(2)(2rho_(m)gh))/(rho(A^(2)-a^(2)))`
`thereforev_(1)=sqrt((2rho_(m)gh)/(rho(A^(2)-a^(2))))` ...(4)
where `v_(1)` is the speed of fluid at wide neck