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 a speed v2 through a horizontal section of pipe whose cross-sectional area A2 = 0.0800 m2. The gas has a density of ? = 1.40 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0500 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 180 Pa.

A venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at a speed v2 through a horizontal section of pipe whose cross-sectional area A2 = 0.0800 m2. The gas has a density of ? = 1.40 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0500 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 180 Pa. Find the speed v2 of the gas in the larger original pipe. Find the volume flow rate Q of the gas.

Explanation / Answer

(a) By Q = A1 x v1 = A2 x v2
=>0.050 x v1 = 0.080 x v2
=>v1 = 1.6 x v2 -------------(i)
By Bernoulli's theorem:-
=>P1 + 1/2?v1^2 = P2 + 1/2?v2^2
=>P2 - P1 = 1/2?[v1^2 - v2^2]
=>150 = 1/2 x 1.40 x v2^2[(1.6)^2 -1]
=>v2 = sqrt[137.36]
=>v2 = 11.72 m/s
(b) Q = A2 x v2 = 0.080 x 11.72 = 0.94 m^3/s
or Q = 0.94 x 1.40 = 1.31 kg/sec

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