A non-viscous liquid of constant density `10^(3) kg // m^(3)` flows in streamline motion along a vertical tube PQ of variable cross-section. Height of P and Q are 2m and 2.5 m respectively. Area of tube at Q is three time area of tube at P. Find the work done per unit volume by pressure as liquid flows from P to Q. Speed of liquid at P is `3m//s ( g = 10 m//s^(2))`.

Options

A. `2000 J//m^(3)`
B. `1000 J//m^(3)`
C. `1500J//m^(3)`
D. `9000J//m^(3)`

Answer

B

Explanation

Mass of `1m^(2)` volume `=1000kg`
from equation of continuity
`A_(Q)=3A_(P)`
`V_(Q)A_(Q)=A_(P)V_(P)`
`V_(Q)3.A_(P)(3)=Ap(3)`
`V_(Q)=1m//s`
A change is in P.E `=1000xx10xx(1)/(2)=5000J`
change in `K.E =(1)/(2)xx1000(3^(2)-1^(2))=4000J`
Net workdone by pressure `=1000J//m^(3)`