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

  • question_answer
    Water flows in a streamlined manner through a capillary tube of radius a, the pressure difference being P and the rate of flow Q. If the radius is reduced to a/2 and the pressure increased to 2P, the rate of flow becomes

    A)             \[4Q\]                                      

    B)             Q

    C)             \[\frac{Q}{4}\]                      

    D)             \[\frac{Q}{8}\]

    Correct Answer: D

    Solution :

                       \[V=\frac{\pi p{{r}^{4}}}{8\eta l}\] \\[V\propto P\,{{r}^{4}}\] (\[\eta \ \text{and }l\] are constants)                     \ \[\frac{{{V}_{2}}}{{{V}_{1}}}=\left( \frac{{{P}_{2}}}{{{P}_{1}}} \right)\ {{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{4}}\]= \[2\times {{\left( \frac{1}{2} \right)}^{4}}\]= \[\frac{1}{8}\]\ \[{{V}_{2}}=\frac{Q}{8}\]


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