Question

A non-viscous liquid of constant density $1000\, kg\, m ^{-3}$ flows in a streamline motion along a tube of variable cross-section. The tube is kept inclined in the vertical plane as shown in figure. The areas of cross-section of the tube at P and Q at heights of 2 m and 5 m are respectively $4 \times 10^{-3} \,m ^{2}$ and $8 \times 10^{-3} \,m ^{2}$. the work done by the force of gravity per unit volume is

• A. $+2.94 \times 10^{4} \,J \,m ^{-3}$
• B. $-2.94 \times 10^{4} \,J \,m ^{-3}$
• C. $1.92 \times 10^{4}\, J \,m ^{-3}$
• D. $-1.92 \times 10^{4} \,J \,m ^{-3}$

Answer 1

Answer: (B)

$W_{g}=\frac{-m g\left(h_{2}-h_{1}\right)}{V}=-\rho \cdot g \cdot\left(h_{2}-h_{1}\right)$
$=-\left(1000\, kg m ^{-3}\right) \cdot\left(9.8 \, m s ^{-2}\right) \cdot(5 m -2 m )$
$=-2.94 \times 10^{4} J m ^{-3}$