Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer A pipe of diameter D conveying a discharge Q is to be replaced by parallel pipes of smaller diameter d to discharge the same quantity. What will be the ratio of \[\frac{D}{d}\,?\](\[f\]Is same for all pipes)

    A) \[\frac{D}{d}=2\]                     

    B) \[\frac{D}{d}=\sqrt{2}\]

    C) \[\frac{D}{d}={{4}^{1/5}}\]               

    D) \[\frac{D}{d}={{4}^{1/3}}\]

    Correct Answer: C

    Solution :

    \[Q={{Q}_{1}}+{{Q}_{2}}\] Since \[{{d}_{1}}={{d}_{2}}=d\] \[\therefore \]  \[{{Q}_{1}}={{Q}_{2}}\] \[\therefore \]  \[Q=2{{Q}_{1}}\] \[{{D}^{2}}v=2{{d}^{2}}{{v}_{1}}\]                                               ?1 Also \[\frac{fL{{v}^{2}}}{2gD}=\frac{fl{{v}^{2}}}{2g{{d}_{1}}}\] \[\frac{{{v}^{2}}}{D}=\frac{v_{1}^{2}}{{{d}^{11}}}\] \[{{\left( \frac{v}{{{v}^{1}}} \right)}^{2}}=\frac{D}{{{d}_{1}}}=\frac{D}{d}\] From eq. \[1.,\frac{v}{{{v}_{1}}}=2\,{{\left( \frac{d}{D} \right)}^{2}}\] \[{{\left( \frac{v}{{{v}_{1}}} \right)}^{2}}=4\,{{\left( \frac{d}{D} \right)}^{4}}\] \[\therefore \]  \[\frac{D}{d}=4\,{{\left( \frac{d}{D} \right)}^{4}}\] \[\frac{D}{d}\times 4\,{{\left( \frac{d}{D} \right)}^{4}}=4\] \[{{\left( \frac{D}{d} \right)}^{5}}=4\] \[\frac{D}{d}={{4}^{1/5}}\]


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