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 = 0.070 m²). The gas has a density = 1.80 kg/m³. The Venturi meter has a cross-sectional area of (A1 = 0.030 m²) and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 190 Pa. Find the speed (v2) of the gas in the larger original pipe. WILL RATE FOR DETAILED ANSWER

Explanation / Answer

Using Continuity equation:

A1v1 = A2v2

v1 = (A2/A1)*v2

v1 = (0.07/0.03)*v2 = (7/3)*v2

Now using bernoulli's equation:

P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2 + rho*g*h2

0.5*rho*(v1^2 - v2^2) = P2 - P1 + rho*g*(h2 - h1)

49v2^2/9 - v2^2 = 2*(P2 - P1)/rho + 2*g*(h2 - h1)

P2 - P1 = 190 Pa

h2 - h1 = 0, Since horizontal pipe

40*v2^2/9 = 2*190/1.80

v2 = sqrt (9*2*190/(1.80*40))

v2 = 6.89 m/sec

Let me know if you have any doubt.

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