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 10.4 m high, and the pump is capable of producing a gauge pressure of 160 kPa, how much water can be pumped using a hose with a radius of 3.1 cm? (Neglect the viscosity of the water.) The water being drawn from the ocean is at rest initially. Use the volume flow rate equation and Bernoulli's equation.

Explanation / Answer

We can equate the pressure energy per unit volume (= P, static pressure at the top) to kinetic energy (= rho*v^2/2).

rho = 1000 kg/m^3
P = (1.6*E5)-(rho*gh)

    = (1.6*E5)-(1000*9.8*10.4)

    = 58080 Pa

v = sqrt(2P/rho)

    = sqrt(2*58080/100)

   = 10.77 m/s

Volume flow rate Q = vA

Q = 10.777*pi*0.031^2
Q = 0.03254 m^3/s = 32.54 L/s ---- > Answer

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