Fluid Mechanics Viscosity Question 123
Question: Water flows in a streamlined manner through a capillary tube of radius a, the pressure difference being P and the rate of flow Q. If the radius is reduced to a/2 and the pressure increased to 2P, the rate of flow becomes
Options:
A) 9.4 m
B) 4.9 m
C) 0.49 m
D) 0.94 m
Show Answer
Answer:
Correct Answer: D
Solution:
Given, $ l_{1}=l_{2}=1, $ and $ \frac{r_{1}}{r_{2}}=\frac{1}{2} $ $ V=\frac{\pi P_{1}r_{1}^{4}}{8\eta l}=\frac{\pi P_{2}r_{2}^{4}}{8\eta l} $ Þ $ \frac{P_{1}}{P_{2}}={{\left( \frac{r_{2}}{r_{1}} \right)}^{4}}=16 $ Þ $ P_{1}=16P_{2} $ Since both tubes are connectedin series, hence pressure difference across combination, $ P=P_{1}+P_{2} $ Þ 1 = $ P_{1}+\frac{P_{1}}{16} $ Þ $ P_{1}=\frac{16}{17}=0.94m $
BETA
