Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer From a reservoir, water is drained through two pipes of 10 cm and 20 cm diameter respectively. If the frictional head loss in both the pipes is same, then the ratio of discharge through the larger pipe to that through the smaller pipe will be:

    A) \[\sqrt{2}\]                                

    B) \[2\sqrt{2}\]

    C) 4                                 

    D) \[4\sqrt{2}\]

    Correct Answer: D

    Solution :

    Frictional head loss in a pipe \[{{h}_{f}}=\frac{4fl{{v}^{2}}}{2gd}\] \[Q=\frac{\pi }{4}\,{{d}^{2}}v\] or \[v=\frac{4Q}{\pi {{d}^{2}}}\] \[\therefore \]   \[{{h}_{f}}=\frac{4fl}{2gd}\times \frac{16{{Q}^{2}}}{{{\pi }^{2}}{{d}^{4}}}=\left( \frac{32fl}{{{\pi }^{2}}g} \right)\times \frac{{{Q}^{2}}}{{{d}^{5}}}\propto \frac{{{Q}^{2}}}{{{d}^{5}}}\] For  \[{{h}_{f1}}={{h}_{f2}}\] \[\frac{Q_{1}^{2}}{d_{1}^{5}}=\frac{Q_{2}^{2}}{d_{2}^{5}}\] \[\frac{{{Q}_{2}}}{{{d}_{1}}}={{\left( \frac{{{d}_{2}}}{{{d}_{1}}} \right)}^{5/2}}\] \[={{\left( \frac{20}{10} \right)}^{5/2}}\] \[{{2}^{5/2}}=\sqrt{32}=4\sqrt{2}\]


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