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%3Cp%3E%3Cspan%20class%3D%22c1%22%3EWater%20flows%20through%20a%20pipe%20as%20sh

ID: 2295219 • Letter: #

Question

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Explanation / Answer

by bernoulli's theorem we have

P1/rho + 0.5v^2 + gh1 = P2/rho + 0.5v2^2 + gh2

P1 /rho = 1.65*10^5 /10^3 = 165

P2/rho = 1.35*10^5 /10^3 = 135

h1 = 0

h2 = 2.75 m

so 165 + 0.5v1^2 + 0 = 135 + 0.5v2^2 + 2.75

=> 0.5v1^2 + 27.25 = 0.5v2^2

=> v1^2 + 54.5 = v2^2


A1 = pi*(0.025)^2

A2 = pi*(0.0145)^2


v1*A1 = v2*A2

so v2 = v1*A1 /A2 = v1*(0.025/0.0145)^2 = 2.973*v1


so v1^2 + 54.5 = 8.839v1^2

=> v1 = 2.637 m/s

v2 = 7.84 m/s

volume flow rate = pi*(0.025)^2 * 2.637 = 5.178*10^-3 m^3/s