Question

Water flows through the tube as shown in figure. The areas of cross-section of the wide and the narrow portions of the tube are $5c{m}^2$ and $2c{m}^2$ respectively. The rate of flow of water through the tube is $500c{m}^3/s$. Find the difference of mercury levels in the U-tube.

Answer 1

$A_1{v}_1=A_2{v}_2=$rate of flow of water
$5v_1=2v_2=500$ cm${}^3$/s
$\therefore$ $v_1=100$ cm/s$=1.0$ m/s
$v_2=250$ cm/s$=2.5$ m/s
$\frac{1}{2}{\rho }_w(v_2^2-v_1^2)={\rho }_{Hg}g{h}_{Hg}$
$\therefore$ $h_{Hg}=\frac{{\rho }_w(v_2^2-v_1^2)}{2{\rho }_{Hg}g}$
$=\frac{{10}^3(6.25-1)}{2\times 13.6\times {10}^3\times 9.8}$
$=0.0196$ m
$=1.96$ cm