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

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    Two capillary tubes of the same length but different radii r1 and r2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

    A)             \[{{r}_{1}}+{{r}_{2}}\]        

    B)             \[r_{1}^{2}+r_{2}^{2}\]

    C)             \[r_{1}^{4}+r_{2}^{4}\]    

    D)             None of these

    Correct Answer: D

    Solution :

                \[V={{V}_{1}}+{{V}_{2}}\]            Þ \[\frac{\pi P{{r}^{4}}}{8\eta l}=\frac{\pi Pr_{1}^{4}}{8\eta l}+\frac{\pi Pr_{2}^{4}}{8\eta l}\]Þ \[{{r}^{4}}=r_{1}^{4}+r_{2}^{4}\]                     \ \[r={{(r_{1}^{4}+r_{2}^{4})}^{1/4}}\]


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