EAMCET Engineering 2006 Solved Paper

If the motor pumps water (density =ρ ) continuously through a pipe of area of crosssection A with velocity v, then mass flowing out per second,
m=Avρ . . . (i)
Rate of increase of kinetic energy
=‌

1

2

mv2=‌

1

2

(Avρ)v2 . . . (ii)
Mass m, flowing out per sec, can be increased to m′ by increasing v to v′, then power increases from P to P′.
‌

P′

P

=‌

‌ 1 2 Aρv′3

1 2 Aρv3

or ‌

P′

P

=(‌

v′

v

)3
Now ‌

m′

m

=‌

Aρv′

Aρv

=‌

v′

v

As ‌‌m′=nm,‌‌v′=nv
∴‌‌

P′

P

=n3
⇒P′‌=n3P