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  4. The capillaries of radius r and 2 r and lengths l and 2 l, respectively, are joined in series. The streamline flow is maintained in capillaries. The pressure difference across first and second capillary is P1 and P2, respectively. Find P1 / P2.

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Q. The capillaries of radius $r$ and $2 r$ and lengths $l$ and $2 l$, respectively, are joined in series. The streamline flow is maintained in capillaries. The pressure difference across first and second capillary is $P_{1}$ and $P_{2}$, respectively. Find $P_{1} / P_{2}$.

Mechanical Properties of Fluids

Solution:

$Q_{1}=Q_{2}$
$\Rightarrow \frac{\pi r^{4} P_{1}}{8 \eta l}=\frac{\pi(2 r)^{4} P_{2}}{8 \eta(2 l)}$
$\frac{P_{1}}{P_{2}}=8$