A) \[\frac{8}{9}X\]
B) \[\frac{9}{8}X\]
C) \[\frac{5}{7}X\]
D) \[\frac{7}{5}X\]
Correct Answer: A
Solution :
[a] Fluid resistance is given by \[R=\frac{8\eta L}{\pi {{r}^{4}}}\] When two capillary tubes of same size are joined in series, then equivalent fluid resistance is \[{{R}_{S}}=\frac{8\eta L}{\pi {{R}^{4}}}+\frac{8\eta \times 2L}{\pi {{(2R)}^{4}}}=\left( \frac{8\eta L}{\pi {{R}^{4}}} \right)\times \frac{9}{8}\] \[Rate\,of\,flow=\frac{P}{{{R}_{S}}}=\frac{\pi P{{R}^{4}}}{8\eta L}\times \frac{8}{9}=\frac{8}{9}X\left[ as\,X=\frac{\pi P{{R}^{4}}}{8\eta L} \right]\]
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