Question

Water is pumped steadily out of a flooded basement at a speed of 5.3 m/s through a uniform hose of radius 0.89 cm. The hose passes out through a window to a street ditch 3.2 m above the waterline. What is the power of the pump?

Answer 1

59.885966 W

Step-by-step explanation:

Mass flow rate of pump is given by

`(\Delta m)/(\Delta t)=\rho Av\\\Rightarrow \dot m=1000* \pi 0.0089^2* 5.3\\\Rightarrow \dot m=1.318\ kg/s`

Power is given by

`P=\Delta P+\Delta K\\\Rightarrow P=\dot m gh+(1)/(2)\dot mv^2\\\Rightarrow P=1.318* 9.81* 3.2+(1)/(2)* 1.318* 5.3^2\\\Rightarrow P=59.885966\ W`

As we are using mass flow rate the energy can be taken as power.

So, power of the pump is 59.885966 W