Question

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 1m/s. The mass per unit length of water in the pipe is 100kg/m. What is the power of the engine?
A. 100W
B. 400W
C. 200W
D. 800W

Answer 1

Power is defined as the ability to act over others. An example of power is the strength needed to run five miles. We know that the, power = Force × velocity
e.g., P = Fv .........(1) we also know that Force = mass × acceleration
or, the Force = mass × change in velocity/time taken .

Complete answer:
The correct answer is D.
if initial velocity is = 0,
then, the Force = mass × velocity/time taken
e.g., F =$m\left( \dfrac{v}{t} \right)$..........(2)

put the equation (2) in the equation (1),
$P=m\left( \dfrac{v}{t} \right)v=\dfrac{m{{v}^{2}}}{t}$
now, the mass = density × volume
$\Rightarrow$ mass = density × base area × length
m = ${{\rho }.{A.l}}$
Put it in the above equation.
so, P =${{v}^{2}}\rho A.\dfrac{l}{l}$
P = $(\rho A){{v}^{3}}$
Here is nothing but it is the mass per unit length e.g., = 100kg/m
Hence, P = 100 $\times$ (2)$^3$ = 100 × 8 = 800W
For an engine that delivers the force through turning the shaft, it is the most extreme result of force and rotational recurrence the motor is fit for creating. Pull separates that number by a constant to decide the number of ponies that could accomplish work at a similar rate.

Note: For a train, one can likewise characterize drawbar drive, which is the result of power communicated at the drawbar and the speed at which it is moving, again separated by a constant that relies upon the unit framework.
It is a really out of date measure as even hundreds or thousands of the ponies can't go 60 MPH, yet any other of the vehicles can.