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Water flow in a streamline manner through a capillary tube of radius a, the pressure difference being P  and the rate of flow Q. If the radius is reduced to  a/2  and the pressure increased to 2P, then rate of flow becomes

Option: 1

4Q


Option: 2

Q


Option: 3

\frac{Q}{4}


Option: 4

\frac{Q}{8}


Answers (1)

best_answer

\text { Use, } V=\frac{\pi P r^4}{8 \eta l}

\therefore \quad V \propto P r ^{4}

\begin{aligned} \therefore \quad \frac{V_2}{V_1}=\left(\frac{P_2}{P_1}\right)\left(\frac{r_2}{r_1}\right)^{4} & =2 \times\left(\frac{1}{2}\right)^4 \\ & =\frac{1}{8} \end{aligned}

\therefore \quad V_2=\frac{Q}{8}

Posted by

himanshu.meshram

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