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 ? = 1.80 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 = 110 Pa.

(a) Find the speed v2 of the gas in the larger original pipe.
m/s

(b) Find the volume flow rate Q of the gas.
m3/s

Explanation / Answer

(1/2 v*2 + g h + P)_1 = (1/2 v*2 + g h + P)_2
the pipe is horizontal so rho g h cancels
P2 - P1 = 1/2 ( v1^2 - v2^2)
and
v1 / v2 = A2 / A1
v1 = 8/5 v2
so
110 = 1/2(1.80)(2.56-1)v2^2
v2 = sqrt( 220/(1.80*1.56) =8.85 m/s

Q = A2*v2 = 0.0800*8.85 = 0.708 m^3/s

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