In the figure shown, a liquid is flowing through a tube at the rate of $0.1\, m^3/sec$. The tube is branched into two semicircular tubes of cross-sectional area $A/3$ and $2A/3$. The velocity of liquid at $Q$ is ......... $ m/sec$ (The cross-section of the main tube $= A =10^{-2}\, m^2$ and $v_p = 20\, m/sec$)
Diffcult
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Equation of continuity
Rate $=\mathrm{r}=\frac{\mathrm{A}}{3} \mathrm{V}_{\mathrm{p}}+\left(\mathrm{A}-\frac{\mathrm{A}}{3}\right) \mathrm{V}_{\mathrm{Q}}$
$\therefore \mathrm{V}_{\mathrm{P}}+2 \mathrm{V}_{\mathrm{Q}}=\frac{3 \mathrm{r}}{\mathrm{A}}=\frac{3 \times 0.1}{10^{-2}}=30 \mathrm{m} / \mathrm{sec}$
$\text { As } \quad \mathrm{V}_{\mathrm{P}}=2 \mathrm{m} / \mathrm{sec}$
Hence, $\mathrm{V}_{\mathrm{Q}}=5 \mathrm{m} / \mathrm{sec}$
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