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 a speed v2through a horizontal section of pipe whose cross-sectional area A2 = 0.0800 m2. The gas has a density of = 1.20 kg/m3. The Venturi meter has a cross-sectional area of A1 = 0.0300 m2 and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P2 - P1 = 150 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

Explanation / Answer

part A :

from the equation of continuity

A1V1 = A2V2

V2 = 0.08* V1 /0.03

V2 = 2.67 V1

apply Preesure difference P2-P1 = 0.5 rho V2^2 - 0.5 rho v1^2

0.5 * 1.2 * ( v2^2-v1^2) = 150

v2^2 - v1^2 = 150* 2/1.2

(V2^2 - V1^2) = 250

(2.67V1)^2 - v1^2 = 250

V1^2 *(6.129) = 250

V1 = 6.38 m/s

V2 = 17.05m/s

--------------------------

Volume flow Rate = dVdt = AV

dV/dt = area * velocity

dV/dt = 0.08 * 17.05

dV/dt = 1.364 m^3/s

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