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 = 0.0526 m2. The gas has a density of ? = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0399 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 189 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) According to Bernoulli's principle -

(1/2 rho v*2 + rho g h + P)_1 = (1/2 rho v*2 + rho g h + P)_2

Here, we have horizontal pipe so cancel 'rho g h' both sides -

P2 - P1 = 1/2 rho ( v_1^2 - v_2^2)
and
v_1 / v_2 = A2 / A1 = 0.0526 / 0.0399 = 1.32

=> v_1 = 1.31 * v_2

So-

189 = 1/2*(1.30) * (1.32^2 - 1) * v_2^2

=> 189 = 0.65 * 0.74 * v_2^2

=> v_2^2 = 189 / (0.65*0.74) = 393

=> v_2 = sqrt(393) = 19.8 m/s

So, speed of the gas in the larger original pipe = 19.8 m/s

(b) Volume flow rate of the gas, Q = A*v = 0.0526 * 19.8 = 1.04 m^3/s

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