Water at a pressure of 4.6 atm at street level flows into an office building at
ID: 2262895 • Letter: W
Question
Water at a pressure of 4.6 atm at street level flows into an office building at a speed of 0.6 m/s through a pipe 7 cm in diameter. The pipes taper down to 2.6 cm in diameter by the top floor, 26 m above. Calculate the water pressure in such a pipe on the top floor. (g = 9.8 m/s2)
Answer in Pascal please
Explanation / Answer
P1 = 4.6 atm = 101325*4.6 Pa = 466095 Pa v1 = 0.6 m/s D1 = 0.07 m z1 = 0 D2 = 0.026 m z2 = 26 m P2 = ? from mass continuity equation; A1*v1 = A2 *v2 => (pi*D1^2/4)*0.7 = (pi*D2^2/4)*v2 => v2 = 0.6*(0.07/0.026)^2 => v2 = 4.35 m/s from Bernoulli's equation; P1 + 0.5*p*v1^2 + p*g*z1 = P2 + 0.5*p*v2^2 + p*g*z2 => 466095 + 0.5*1000*0.6^2 + 0 = P2 + 0.5*1000*4.35^2 + 1000*9.8*26 => P2 = 202013.75 Pa => P2 = 202013.75/101325 atm = 1.994 atm
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