JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Question Bank Fluid Flow

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    We have two (narrow) capillary tubes T1 and T2. Their lengths are l1 and l2 and radii of cross-section are r1 and r2 respectively. The rate of flow of water under a pressure difference P through tube T1 is 8cm3/sec. If l1 = 2l2 and r1 =r2, what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same as before (= P)

    A)            4 cm3/sec                               

    B)            (16/3) cm3/sec

    C)            (8/17) cm3/sec                     

    D)            None of these

    Correct Answer: B

    Solution :

                       \[V=\frac{\pi {{\Pr }^{4}}}{8\eta l}=\frac{8c{{m}^{3}}}{\sec }\] For composite tube \[{{V}_{1}}=\frac{P\pi {{r}^{4}}}{8\eta \left( l+\frac{l}{2} \right)}=\frac{2}{3}\frac{\pi P{{r}^{4}}}{8\eta l}\]\[=\frac{2}{3}\times 8=\frac{16}{3}\frac{c{{m}^{3}}}{\sec }\]         \[\left[ \because \ \ {{l}_{1}}=l=2{{l}_{2}}\ \text{or}\ {{l}_{2}}=\frac{l}{2} \right]\]


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