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 = 0.0694 m2. The gas has a density of ? = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0323 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 113 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)

Assuming the gas is inviscid, we can apply Bernoulli's Theorem ' p + 1/2 ??u?^2 = constant '

we get

p1 + 1/2 * ? * v1^2 = p2 + 1/2 * ? * v2^2

rearranging to get

p2 - p1 = 1/2 * ? * ( v1^2 - v2^2 )

but p2 - p1 = 113 Pa and ? = 1.3 kg/m^3

113 = 0.0347 * ( v1^2 - v2^2 )

325.6 = v1^2 - v2^2

v2 = sqrt(v1^2 - 325.6) m/s

Are you told anything about v1 in the question? If so plug it in above to find the exact answer for v2

b)

The flow rate Q = ? u . n ds , which in this case is simply the velocity of the gas * area of the pipe

i.e Q = v2 * A2

where

v2 given implicitly above

A2 = 0.0694 m^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.