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Fluid Mechanics

JEE Main level, single correct, medium

70 of 192

Question 70 of 192

Two tubes of radii ${r}_{1}$ and ${r}_{2}$ and lengths ${l}_{1}$ and ${l}_{2,}$ respectively, are connected in series and a liquid flows through each of them in stream line conditions. ${P}_{1}$ and ${P}_{2}$ are pressure differences across the two tubes. If ${P}_{2}$ is $4{P}_{1}$ and ${l}_{2}$ is $\dfrac{{l}_{1}}{4}$ then the radius ${r}_{2}$ will be equal to :

Show answer and solution

Answer: (D) $\dfrac{{r}_{1}}{2}$

\dfrac{dV}{dt}=\dfrac{\pi }{8}\dfrac{p{r}^{4}}{\eta L}

\dfrac{{p}_{1}{r}_{1}^{4}}{{L}_{1}}=\dfrac{{p}_{2}{r}_{2}^{4}}{{L}_{2}}

\dfrac{{p}_{1}{r}_{1}^{4}}{{l}_{1}}=\dfrac{4{p}_{1}{r}_{2}^{4}}{\left(\dfrac{{l}_{1}}{4}\right)}

\Rightarrow

{r}_{2}^{4}=\dfrac{{r}_{1}^{4}}{16}

\Rightarrow

{r}_{2}=\dfrac{{r}_{1}}{2}

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JEE Main 2025 Apr 2 Shift 1 question paper

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