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.

Question

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. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Q1=Q2 ⇒ (π r4 P1/8 η l)=(π(2 r)4 P2/8 η(2 l)) (P1/P2)=8

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 $P_{1} / P_{2}$ .

$Q_{1} = Q_{2}$
$\Rightarrow \frac{π r ^{4} P _{1}}{8 η l} = \frac{π ( 2 r ) ^{4} P _{2}}{8 η ( 2 l )}$
$\frac{P _{1}}{P _{2}} = 8$

Q. The capillaries of radius r and 2r and lengths l and 2l, 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​.

Q1​=Q2​ ⇒8ηlπr4P1​​=8η(2l)π(2r)4P2​​ P2​P1​​=8

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 $P_{1} / P_{2}$ .

$Q_{1} = Q_{2}$
$\Rightarrow \frac{π r ^{4} P _{1}}{8 η l} = \frac{π ( 2 r ) ^{4} P _{2}}{8 η ( 2 l )}$
$\frac{P _{1}}{P _{2}} = 8$