Question

A pump, taking water from a large reservoir is used to spray a jet of water with speed 20ms^-1 and radius 0.05meters, from a nozzle level with tue surface of the reservoir. calculate the power of the pump

Answer 1

Answer:

by given data we can find volume flow rate

$v.f.r = area \times velocity \\ = \pi \times {0.05}^{2} \times 20 \\ = 0.05\pi \\ = 0.1572 {m}^{3}$

and then with this volume and density of water which is 1000kg/m^3, we can find the mass

$density = \frac{mass}{volume} \\ volume \times density = mass \\ 1000 \times 0.1572 \\ 157.2kg$

and the energy will be KE

$ke = \frac{1}{2} m {v}^{2} \\ = \frac{1}{2} \times 157.2 \times {20}^{2} \\ = 31440j$

since the energy is generated in one second then let's find the power

$power = \: \frac{workdone}{time} \\ = \frac{31440}{1} \\ = 31.44kw$