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 = 0.0992 m2. The gas has a density of ? = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0377 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 96.2 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

There is no drawing given. However, I will try to solve the problem without the drawing.

(a) By continuity equation -

aV = Av,

=> v = (a/A)V,

Bernoulli's principle:

P + ½ ?V² = p + ½ ?v²,

=> p - P = ½ ?(V² - v²) = ?gh

put the values -

96.2 = 0.5*1.3 [V² - (a/A)²V²]

=> V = ?[(96.2/0.65)/(1 - 0.0377²/0.0992²)] = 11.25 m/s

(b) Volume flow rate of the gas, Q = Va

= 11.25*0.0377 = 0.424 m³/s

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