Question

An engine pumps water through a hose pipe. water passes through the pipe & 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?

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 = $\rho A.l$, put it in above equation.

so, P = $v^2\rho A\frac{l}{t}$
P = $(\rho A)v^3$

here, $\rho A$ is nothing mass per unit length . e.g., $\mu$ = 100kg/m

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

Answer 2

Answer:

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 = \rho A.lρA.l , put it in above equation.

so, P = v^2\rho A\frac{l}{t}v

2

ρA

t

l

P = (\rho A)v^3(ρA)v

3

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

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