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Venturimeter
- Venturimeter is a device to measure the flow of incompressible liquid.
- It consists of a tube with a broad diameter having a larger cross-sectional area but there is a small constriction in the middle.
- It is attached to U-tube manometer. One end of the manometer is connected to the constriction and the other end is connected to the broader end of the Venturimeter.
- The U-tube is filled with fluid whose density is ρ.
- A1= cross-sectional area at the broader end, v1 = velocity of the fluid.
- A2=cross-sectional area at constriction, v2= velocity of the fluid.
- By the equation of continuity, wherever the area is more velocity is less and vice-versa.As A1 is more this implies v1 is less and vice-versa.
- Pressure is inversely ∝ to Therefore at A1 pressureP1 is less as compared to pressure P2 at A2.
- This implies P1<P2 as v1>v2.
- As there is difference in the pressure the fluid moves,this movement of the fluid is marked by the level of the fluid increase at one end of the U-tube.
A schematic diagram of Venturimeter
Venturimeter: determining the fluid speed
- By Equation of Continuity: -A1v1=A2v2.
- This implies v2=(A1/A2)v1(Equation(1))
- By Bernoulli’s equation:- P1 + (1/2) ρ v12 + ρg h = (1/2) ρ v22 + ρg h
- As height is same we can ignore the term ρg
- This implies P1-P2=(1/2) ρ(v22- v12)
- =1/2ρ(A12/A22v12- v12)(Using equation(1)
- =1/2ρv12(A12/A22 -1)
- =1/2ρv12(A12/A22-1)
- As there is pressure difference the level of the fluid in the U-tube changes.
- (P1-P2) = hρmgwhere ρm(density of the fluid inside the manometer).
- 1/2ρv12(A12/A22-1)=hρmg
- v1 = 2hρmg/ρ[A12/A22-1]-1/2
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Yash Jain 7 years, 1 month ago
3Thank You