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An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?
A
800 W
B
400 W
C
200 W
D
100 W
Detailed Solution
Mass of water flowing out per second: $\frac{dm}{dt} = (\text{mass per unit length})\times v = 100\times2 = 200$ kg/s
Force exerted by the engine on the water = rate of change of momentum = $v\frac{dm}{dt} = 2\times200 = 400$ N
Power = force × velocity = $Fv = 400\times2$
In symbols, with $\lambda$ = mass per unit length: $P = \lambda v^3 = 100\times2^3$
P = 800 W
Force exerted by the engine on the water = rate of change of momentum = $v\frac{dm}{dt} = 2\times200 = 400$ N
Power = force × velocity = $Fv = 400\times2$
In symbols, with $\lambda$ = mass per unit length: $P = \lambda v^3 = 100\times2^3$
P = 800 W