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 11.7 m high, and the pump is capable of producing a gauge pressure of 142 kPa, how much water can be pumped using a hose with a radius of 4.8 cm? (Neglect the viscosity of the water.)

----------(L/s)

Answer 1

Using bernoulli's equation

P1 + 0.5*rho*V1^2 + rho*g*h1 = P2 + 0.5*rho*V2^2 + rho*g*h2

h1 = 0 and h2 = 11.7 m

v1 = 0 m/sec & v2 = ?

P1 - P2 = 142 kPa = 1.42*10^5 Pa

rho = seawater density = 1026 kg/m^3

0.5*rho*v2^2 = (P1 - P2) + 0 + 0 - rho*g*h2

v2^2 = 2*(P1 - P2)/rho - 2*g*h2

v2 = sqrt [2*(P1 - P2)/rho - 2*g*h2]

Using given values:

v2 = sqrt [2*1.42*10^5/1026 - 2*9.81*11.7]

v2 = 6.87 m/sec

Now flow rate is given by:

Q = A2*v2

Q = pi*r^2*v2

Q = pi*0.048^2*6.87 = 0.04975 m^3/sec

1 m^3 = 1000 L

Q = 49.75 L/sec

Please Upvote.