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Question

A venturimeter is used to


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Solution

Explanation,

  1. The flow of speed of the incompressible fluid is measured by Venturimeter.
  2. The pressure difference between the downstream flow and the narrow pipe area can be calculated by two equations and they are: Bernoulli’s theorem, the Continuity equation, and the Euler equation.

Deriving the measure of the rate of flow,

A venturi meter has two openings, one wide and the other narrow with a cross-sectional area of A1 and A2 respectively.

Assuming the velocity of the fluid at these openings is v1 and v2 at these openings with a pressure of P1 and P2.

Let's take the flow of fluid to be streamlined with a density of ρ and using Bernoulli’s theorem,
P1+12ρv12=P2+12ρv22P1P2=12ρ(v22v12)

The difference in level in the vertical tubes ish, thus
P1P2=ρgh
On equating both the equations:
ρgh=12ρ(v22v12)v22v12=2ghequation1
We see,
A1v1=A2v2A1A2=v2v1equation 2
From equation1, we get:
v12[(v22v12)1]=2gh
From equation2, we get:
v12[(A12A22)1]=2ghv12=A222ghA12A22v1=A22ghA12A22
Hence the rate of flow of a liquid is
v1=A22ghA12A22
Hence, the flow speed of the incompressible fluid is measured by Venturimeter.


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