Properties Of Solids And Liquids Question 236
Question: Two capillaries of same length and radii in the ratio 1 : 2 are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is 1 m of water, the pressure difference across first capillary is
Options:
A) $ r _{1}+r _{2} $
B) $ r _{1}^{2}+r _{2}^{2} $
C) $ r _{1}^{4}+r _{2}^{4} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ V=V _{1}+V _{2} $
therefore $ \frac{\pi Pr^{4}}{8\eta l}=\frac{\pi Pr _{1}^{4}}{8\eta l}+\frac{\pi Pr _{2}^{4}}{8\eta l} $
therefore $ r^{4}=r _{1}^{4}+r _{2}^{4} $ \ $ r={{(r _{1}^{4}+r _{2}^{4})}^{1/4}} $
