Fluid Mechanics Viscosity Question 109
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} $ Þ $ P=\frac{V8\eta l}{\pi r^{4}} $ Þ$ \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} $ Þ $ P_{2}=\frac{P_{1}}{4}=\frac{P}{4} $ .
BETA
