A 6.0-cm-diameter horizontal pipe gradually narrows to 4.5 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 33.5 kPa and 22.6 kPa, respectively.What is the volume rate of flow?
Question
A 6.0-cm-diameter horizontal pipe gradually narrows to 4.5 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 33.5 kPa and 22.6 kPa, respectively.What is the volume rate of flow?
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General Physics
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Answer ( 1 )
Bernoullli’s theorem
P + 0.5(rho)v^2 = constant
33.5*10^3 + 0.5*1000*u^2 = 22.6*10^3 + 0.5*1000*v^2
also, 6^2*u = 4.5^2*v [ constinuity equation]
10.9*10^3 + 500(0.5625v)^2 – 500v^2 = 0
v = 5.6471 m/s
Flow rate = AV = pi*(0.045)^2*v/4 = 8.9784*10^-3