Two tubes of length l 1 - l 2 and radius r 1- r 2 are connected in series- and allowed to carry a liquid - through it- If p 1 and p 2 are the pressure at the two extreme ends- calculate the pressure at the junction-

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Byju's Answer

Standard XII

Physics

Bernoulli's Principle

Two tubes of ...

Question

Two tubes of length $l_{1}$ , $l_{2}$ and radius $r_{1}$ , $r_{2}$ are connected in series, and allowed to carry a liquid $η$ through it. If $p_{1}$ and $p_{2}$ are the pressure at the two extreme ends, calculate the pressure at the junction.

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Solution

$\frac{d v}{d t} = \frac{π r^{4} (Δ P)}{8 η l}$
$η$ - coeffiecient of viscosity
Let the pressure of the junction is $P$
Since the pipe is connected to each other then rate of flow must be same.
${(\frac{d v}{d t})}_{1} = {(\frac{d v}{d t})}_{2} \Rightarrow \frac{π r_{1}^{4} (P_{1} - P)}{8 η l_{1}} - \frac{π r_{2}^{4} ({P - P}_{2})}{8 η l_{2}} \Rightarrow l_{1} r_{1}^{4} (P_{1} - P) = l_{2} r_{2}^{4} ({P - P}_{2}) \Rightarrow l_{2} {r_{1}^{4} P}_{1} - l_{2} r_{1}^{4} P = l_{1} r_{2}^{4} P - l_{2} r_{2}^{4} P \Rightarrow (r_{1}^{4} l_{2} + r_{2}^{4} l_{1}) P = r_{1}^{4} l_{2} P_{1} + r_{2}^{4} l_{1} P_{2} \Rightarrow P = \frac{r_{1}^{4} l_{2} P_{1} + r_{2}^{4} l_{1} P_{2}}{r_{1}^{4} l_{2} + r_{2}^{4} l_{1}}$

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Two tubes of length l1 ,l2 and radius r1,r2 are connected in series, and allowed to carry a liquid η through it. If p1 and p2 are the pressure at the two extreme ends, calculate the pressure at the junction.

Two tubes of length $l_{1}$ , $l_{2}$ and radius $r_{1}$ , $r_{2}$ are connected in series, and allowed to carry a liquid $η$ through it. If $p_{1}$ and $p_{2}$ are the pressure at the two extreme ends, calculate the pressure at the junction.