A Venturi meter is a device for measuring the speed of a fluid within a pipe. Th

Question

A Venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at speed v2 through a horizontal section of pipe whose cross-sectional area is A2 = 0.0884 m2. The gas has a density of ? = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0318 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 143 Pa. Find (a) the speed v2 of the gas in the larger original pipe and (b) the volume flow rate Q of the gas.

Explanation / Answer

Applying law of continuity

A1v1= A2v2

0.0318 V1= 0.0884 V2

V1= 2.78 V2

Bernoulli 's equation.

P1+ 1/2 v1^2 = P2 + 1/2 v2^2

P1- P2 = 1/2 ( V2^2 - V1^2)

-143 = 0.5( 1.30 ) ( V2^2 - {2.78 V2}^2)

- 220 = -v2^2 ( 45.27)

V2= 2.2 m/s apprx

Volume flow rate= A2 V2 = 0.0884 ( 2.2)= 0.195 m^3 / sec apprx

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