Venturimeter is based on Bernoulli's theorem. It consists of a two truncated tubes connected by a pipe at narrow ends. The pipe connecting the two tubes is called throat as shown in figure.
The venturimeter tube is positioned horizontally and the liquid is made to enter in it at end A and after passing through throat BC, it leaves tube at end D. Let at A, the area of cross-section of tube be a1, pressure of liquid be P1 and velocity be v1 And at the throat, the area of cross-section of tube be a2 pressure of liquid be P2 and velocity be v2
Why does deep water run slow?
Let the liquid enter at A with velocity v1 where area of cross-section is a1 and exit at end B with velocity v2 where area of cross-section is a2.Let ρ1 and ρ2 be the densities of liquid at ends A and B respectively.
Now the volume of liquid that enters in one second at end A is,
V1 = a1 v1
Mass of liquid entering per second at end A is,
Similarly the mass of liquid leaving per second at end B is,
m2 = a2v2ρ2
If there is no source or sink of liquid, then mass of liquid that enters at end A in one second is equal to the mass of liquid that leave in one second, i.e.
a1 v1 p1 = a2 v2 p2
If the liquid is incompressible, then ρ1 = ρ2. Therefore equation (1) reduces to
a1v1= a2v2 ......(2)
This equation is called equation of continuity.
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