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 = 0.0622 m2. The gas has a density of = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0237 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 176 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

a)

From Continuity equation

A1V1 = A2V2

0.0237V1=0.0622V2

V1=2.6245V2

From Bernoulli's equation is

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

P2-P1=(1/2)p(2.6245V2)2-(1/2)pV22=2.944pV22

176=2.944*1.3*V22

V2=6.78 m/s

b)

flow rate of gas

Q=A2V2=0.0622*6.78

Q=0.4218 m3/s

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