A venturi meter is used to measure the flow speed of a fluid in a pipe. The mete

Question

A venturi meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe (the figure); the cross-sectional area A of the entrance and exit of the meter matches the pipe's cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed V and then through a narrow ''throat'' of cross-sectional area a with speed v. A manometer connects the wider portion of the meter to the narrower portion. The change in the fluid's speed is accompanied by a change p in the fluid's pressure, which causes a height difference h of the liquid in the two arms of the manometer. (Here p means pressure in the throat minus pressure in the pipe.) Suppose that the fluid is fresh water, that the cross-sectional areas are 72 cm2 in the pipe and 36 cm2 in the throat, and that the pressure is 58 kPa in the pipe and 37 kPa in the throat. What is the rate of water flow in cubic meters per second?

Please help I keep getting wrong answers.

Explanation / Answer

the volume flow rate remains same

A1*v1 = A2*v2

v2/v1 = A1/A2

v2/v1 = (72/36) = 2

v2 = 2v1

from Bernoullis theorem

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

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

58*10^3 - 37*10^3 = 0.5*1000*(4v1^2-v1^2)

v1 = 3.74 m/s

rate of water flow = A1*v1 = 72*10^-4*3.74

V = 0.02693 m^3/s

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