AP and TS EAMCET Engineering 2020 Model Paper 3

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

1

1

mv2=

1

2

(Avρ)v2
Mass m, flowing out per second can be increased rto 'm' by increasing v to v' , then power increases from P0 to P1

P1

P0

=

1 2 Aρv′3

1 2 Aρv3

or

P1

P0

=(

v′

v

)3
Now

m′

m

=

Aρv′

Aρv

=(

v′

v

)
As‌m′‌n‌m,v′=nv
∴

P1

P0

=n3