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 = 0.0600 m2. The gas has a density of ϝ = 1.40 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0400 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 190 Pa. (a) Find the speed v2 of the gas in the larger original pipe. m/s (b) Find the volume flow rate Q of the gas. m3/s

Answer 1

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 = 170 Pa and ? = 1.5 kg/m^3

170 = 0.75 * ( v1^2 - v2^2 )

226.7 = v1^2 - v2^2

v2 = sqrt(v1^2 - 266.7) 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 = 0.07 m^2