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 ? = 1.60 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 = 160 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

we have from continuity A1*v1 = A2*v2 so v1 = (A2/A1)*v2 = (0.07/0.05)*v2 we have from bernoullis equation in venturi meter p + (1/2*d*v^2) = constant where d= density we have p1 + (1/2*d*v1^2) = p2 + (1/2*d*v2^2) 1/2*d*(v1^2-v2^2) = p2-p1 1/2*1.60*[ ((0.07/0.05)*v2)^2 - v2^2] = 160 v2^2 = 208.33 v2 = 14.43 m/s so the speed v2 = 14.43 m/s (b) volume flow rate Q = A2*v2 = 0.07 * 14.43 = 1.01 m^3/s

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