First slide

Viscous flow/Laminar flow

Question

A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference P. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is

Moderate

A

P
B

$\frac{3 P}{4}$
C

$\frac{P}{2}$
D

$\frac{P}{4}$

Solution

$\begin{array}{l} From V = \frac{{Pπr}^{4}}{8 ηl} \Rightarrow P = \frac{V 8 ηl}{{πr}^{4}} \\ \Rightarrow \frac{P_{2}}{P_{1}} = \frac{V_{2}}{V_{1}} \times \frac{l_{2}}{l_{1}} \times {(\frac{r_{1}}{r_{2}})}^{4} = 2 \times 2 \times {(\frac{1}{2})}^{4} = \frac{1}{4} ∣ \\ \Rightarrow P_{2} = \frac{P_{1}}{4} = \frac{P}{4} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App