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PhysicsFluidBernoulli's theorem and applicationsMedium2 minPYQ_2017

PhysicsMediumsingle choice

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 $\frac{l_{1}}{4}$ then the radius $r_{2}$ will be equal to :

Options:

Answer:

Solution:

$\frac{d V}{d t} = \frac{π}{8} \frac{p r^{4}}{η L}$

$\frac{p_{1} r_{1}^{4}}{L_{1}} = \frac{p_{2} r_{2}^{4}}{L_{2}}$

$\frac{p_{1} r_{1}^{4}}{l_{1}} = \frac{4 p_{1} r_{2}^{4}}{(\frac{l_{1}}{4})}$

$\Rightarrow$ $r_{2}^{4} = \frac{r_{1}^{4}}{16}$

$\Rightarrow$ $r_{2} = \frac{r_{1}}{2}$

Stream:JEESubject:PhysicsTopic:FluidSubtopic:Bernoulli's theorem and applications

⏱ 2mℹ️ Source: PYQ_2017

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