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 = 0.0685 m2. The gas has a density of ? = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0182 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 121 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

from bernouli's theorem

P2 - P1 = 0.5v1^2 - 0.5v2^2


There are 2 unknowns in this equation: v1 and v2. To solve for v2, we need the flow rate equation:

A1v1 = A2v2.

(2) From the flow rate equation, v1 = v2 (A2/A1)

Substituting (2) into (1), we get:

P2 - P1 = 0.5(v2A2/A1)^2 - 0.5v2^2

P2 - P1 = 1201Pa and A2/A1 = 0.0685/0.0182=3.76

121 Pa = 0.5(3.76v2)^2 - 0.5v2^2

=1.3 kg/m^3

121 Pa = 2.44v2^1 - 0.65v2^2

121 Pa = 1.79v2^2

Finally,

v2 = sqrt(121/1.79) = 8.22 m/s

For question (b), Q=A2v2=(0.0685)(8.22) = 0.56 m^3/s

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