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 = 0.0700 m2. The gas has a density of ? = 1.70 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0300 m2 and has been substituted for a section of the larger pipe. The pressure difference between the sections is P2 - P1 = 130 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

v2 = 10.70 m/s (Here A1v1= A2 v2, because total volume of water flowing is constant. So v1 is expressed as v1 = (A2 v2/ A1)= 7/3 v2.

So putting this in Bernoulli's equation in case of Venturi effect...

P2 - P1 = D/2 (v2^2 - v1^2),

D= 1.70 kg/m3. P2 - P1 = 130 Pa, solve for v2, we get...

a. v2 = 10.70 m/s

Volume rate: A2 = 0.0700 m2. v2 = 10.70 m/s

b. A2  v2 = 0.749 m3/s

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