A) \[8p\]
B) \[p\]
C) \[\frac{p}{8}\]
D) \[\frac{p}{32}\]
Correct Answer: D
Solution :
Poiseuilles studied the streamline flow of liquid in capillary tubes. He found that if a pressure difference p is maintained across the two ends of a capillary tube of length ; and radius r, then the volume of liquid coming out of the tube per second is \[Q=\frac{\pi p{{r}^{4}}}{8\eta l}\] or \[p=\frac{8}{\pi }\frac{Q\eta l}{{{r}^{4}}}\] For first tube \[{{P}_{1}}=\frac{8{{Q}_{1}}\eta {{l}_{1}}}{\pi r_{1}^{4}}\] ... (i) If \[{{r}_{2}}=2{{r}_{1}}\] and \[{{Q}_{2}}=\frac{{{Q}_{1}}}{2}\], and \[{{l}_{1}}={{l}_{2}}\] \[{{p}_{2}}=\frac{8{{Q}_{2}}\eta {{l}_{2}}}{\pi r_{2}^{4}}\] \[{{p}_{2}}=\frac{8{{Q}_{1}}\eta {{l}_{1}}}{2\pi .\,{{(2{{r}_{1}})}^{4}}}\] \[{{p}_{2}}=\frac{8{{Q}_{1}}\eta {{l}_{1}}}{32\pi r_{1}^{4}}\] ?. (ii) From Eqs. (i) and (ii), we get \[{{p}_{2}}=\frac{{{p}_{1}}}{32}\]
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