To better fight fires in your seaside community, the local fire brigade has aske

Question

To better fight fires in your seaside community, the local fire brigade has asked you to construct a pump system to draw seawater from the ocean to the top of the steep cliff adjacent to the water where most of the homes are. If the cliff is 10.3 m high, and the pump is capable of producing a gauge pressure of 145 kPa, how much water can be pumped using a hose with a radius of 3.8 cm? (Neglect the viscosity of the water.)
  L/s

the answer is not 35.6 I have already tried that. Please help been stucl on this question for forever!!

Explanation / Answer

from Bernoullis principle

P1 + (1/2)*rho*v1^2 + rho*g*h = P2 + (1/2)*rho*v2^2 + rho*g*h2

P1 - P2 = (1/2)*rho*(v2^2 - v1^2) + rho*g*(h2-h1)

given P1 - P2 = 145*10^3 Pa

v1 = 0

h2 - h1 = 10.3 m

145*10^3 = (1/2)*1027*v2^2 + (1027*9.8*10.3)

v2 = 8.97 m/s

volume flow rate A*v2 = pi*0.038^2*8.97 = 0.0407 m^3/s

volume flow rate = 40.7 L/s = 41 L/s (2 significant)

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