Water is pumped steadily out of a flooded basement at a speed of 5.4 m/s through a uniform hose of radius 0.83 cm. the hose passes out through a window to a street ditch 3.5 m above the waterline. what is the power of the pump?

To solve this problem it is necessary to apply the concepts related to the flow as a function of the volume in a certain time, as well as the potential and kinetic energy that act on the pump and the fluid.

The work done would be defined as

Where,

PE = Potential Energy

KE = Kinetic Energy

Where,

m = Mass

g = Gravitational energy

h = Height

v = Velocity

Considering power as the change of energy as a function of time we will then have to

The rate of mass flow is,

Where,

= Density of water

A = Area of the hose

The given radius is 0.83cm or m, so the Area would be

We have then that,

Final the power of the pump would be,

Therefore the power of the pump is 57.11W

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