Question

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s.

Answer 1

we know, power = Force × velocity

e.g., P = Fv .........(1)

we also know Force = mass × acceleration

or, Force = mass × change in velocity/time taken

if intial velocity = 0,

then, Force = mass × velocity/time taken

e.g., F = m(v/t) ..........(2)

put equation (2) in equation (1),

P = m(v/t)v = mv²/t

now, mass = density × volume

or , mass = density × base area × length

e.g., m = , put it in above equation.

so, P =

P =

here,  is nothing mass per unit length . e.g.,  = 100kg/m

hence, P = 100 × (2)³ = 100 × 8 = 800W