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} $ .



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