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 = 0.0811 m2. The gas has a density of ? = 1.30 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0171 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 89.8 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

By Bernoulli's equation

P1 + 0.5*rho*v1^2 = P2 + 0.5*rho*v2^2

Or

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

Now 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*rho*(v2A2/A1)^2 - 0.5*rho*v2^2

P2 - P1 = 89.8 Pa and A2/A1 = 4.743

89.8 Pa = 0.5*rho*(4.743v2)^2 - 0.5*rho*v2^2

89.8 Pa = 14.62*v2^2 - 0.65*v2^2

89.8 Pa = 13.97v2^2

Finally,

v2 = sqrt(89.8/13.97) = 2.535 m/s

For question (b), Q=A2v2=(0.0811)(2.535) = 0.206 m^3/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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