Two water pipes P and Q having diameters 2 ti | vedclass

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(A) According to the equation of continuity for an incompressible fluid in steady flow,the volume flow rate (discharge) remains constant throughout th

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Four times that of $Q$

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(A) According to the equation of continuity for an incompressible fluid in steady flow,the volume flow rate (discharge) remains constant throughout the pipe.$A_P V_P = A_Q V_Q$Where $A$ is the cross-sectional area and $V$ is the velocity of water.Since $A = \frac{\pi d^2}{4}$,we have:$\frac{\pi d_P^2}{4} V_P = \frac{\pi d_Q^2}{4} V_Q$$d_P^2 V_P = d_Q^2 V_Q$$V_P = \left( \frac{d_Q}{d_P} ight)^2 V_Q$Given $d_P = 2 	imes 10^{-2} \, m$ and $d_Q = 4 	imes 10^{-2} \, m$:$V_P = \left( \frac{4 	imes 10^{-2}}{2 	imes 10^{-2}} ight)^2 V_Q$$V_P = (2)^2 V_Q$$V_P = 4 V_Q$Thus,the velocity of water in pipe $P$ is four times that of pipe $Q$.

Two water pipes $P$ and $Q$ having diameters $2 \times 10^{-2} \, m$ and $4 \times 10^{-2} \, m$ respectively are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is ........

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