Question

A non-viscous liquid of constant density $500kg/m^3$ flows in a variable cross-sectional tube. The area of cross-section of the tube at two points P and Q at heights of $3m$ and $6m$ are $2\times {10}^{-3}{m}^3$ and $4\times {10}^{-3}{m}^3$ respectively. The work done per unit volume by the forces of gravity as the fluid flows from point P to Q, is:

• A. $29.4J/m^3$
• B. $-1.47\times {10}^{4}J/m^3$
• C. $-2.94\times {10}^{4}J/m^3$
• D. None of these

Answer 1

The correct option is B $-1.47\times {10}^{4}J/m^3$

Difference in heigh of P and Q,$=(6-3)=3m$
work done by gravity per unit volume of the fluid
$workdone=\rho gh$

$=-3\times g\times 500$
$=-14700J/m^3$ = $-1.47\times {10}^{4}J{/}^3$