Properties Of Solids And Liquids Question 225
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[EAMCET 2001]
Options:
A)P
B)$ \frac{3P}{4} $
C)$ \frac{P}{2} $
D)$ \frac{P}{4} $
Show Answer
Answer:
Correct Answer: D
Solution:
From $ V=\frac{P\pi r^{4}}{8\eta l} $ therefore $ P=\frac{V8\eta l}{\pi r^{4}} $
therefore $ \frac{P _{2}}{P _{1}}=\frac{V _{2}}{V _{1}}\times \frac{l _{2}}{l _{1}}\times {{\left( \frac{r _{1}}{r _{2}} \right)}^{4}} $
$ =2\times 2\times {{\left( \frac{1}{2} \right)}^{4}}=\frac{1}{4} $
therefore $ P _{2}=\frac{P _{1}}{4}=\frac{P}{4} $ .
