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 = 0.0751 m2. The gas has a density of ? = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0222 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 69.1 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

From Continuity equation

A1V1 = A2V2

=>V1 =(0.0751/0.0222)V2

V1=3.383V2

From Bernoulli's equation

P1+(1/2)pV12+pgh1 =P2+(1/2)pV22+pgh2

Since h1=h2

P2-P1 =(1/2)p(V12-V22)

69.1 =(1/2)*1.3*[(3.383V2)2-V22]

V2 =3.19 m/s

b)

Volume flow rate of gas is

Q=A2V2 =0.0751*3.19

Q=0.24 m3/s

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