Question

Water flows through a horizontal lobe as shown in figure , If the difference of heights of water column in the vertical lobes is $2cm$ and the areas of cross-section at A and B are $4c{m}^2$ and $2c{m}^2$ respectively. Find the rate of flow of water across any section.

Answer 1

$\frac{1}{2}\rho v_B^2-\frac{1}{2}\rho v_A^2=\rho g(h_A-h_B)$
or $v_B^2-v_A^2=2g(h_A-h_B)$
$=2\times 10\times 0.02$
or $v_B^2-v_A^2=0.4$ m${}^2$/s${}^2$ (i)
$v_A{A}_A=v_B{A}_B$
or $4v_A=4v_B$
$\therefore$ $v_B=2v_A$
Solving Eqs. (i) and (ii), we get
$v_A=0.363$ m/s
Volume flow rate$=v_A{A}_A$
$=\left(0.365\right)(4\times {10}^{-4})$
$=1.46\times {10}^{-4}$ m${}^3$/s
$=146$ cm${}^3$/s