Question

an engine pumps water from a river 10m an below its own level and discharge it through a nozzle of diameter 10cm with a speed of 50m/s .find the power required assuming a.no losses
b.70% efficiency(density of water =1000kg/m^2)≡

Answer 1

Answer:

56.14kW

Explanation:

Power = work / time = F x v

power = force x velocity.

volume of water coming out

= volume of pipe = pi r^2 h

r = 10 / 2 = 5 cm = 0.05m

V = pi r^2 h = 3.142 x 0.05 x 0.05 x 10

= 0.0786m^3

p = m/v; m = pv = 1000 x 0.0786

m = 78.6kg of water.

(a) P = force x velocity = mgv

= 78.6 x 10 x 50 = 39

300W = 39.3kW

(b) efficiency = power(output)/power(input) x 100%

70 / 100 = 39.3 / pi; pi = 100 x 39.3 / 70 = 56.14kW