Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer A hydraulic jump is formed in a 5.0 wide rectangular channel with sequent depths of 0.2 m and 0.8 m. The discharge in the channel, in \[{{\text{m}}^{\text{3}}}\text{/s,}\] is:

    A) 2.43                             

    B) 3.45

    C) 4.43                             

    D) 5.00

    Correct Answer: C

    Solution :

    \[{{y}_{1}}=0.2\,m,\] \[{{y}_{2}}=0.8\,m,\] \[\frac{{{y}_{2}}}{{{y}_{1}}}=\frac{1}{2}\,\left[ \sqrt{1+8F_{1}^{2}-1} \right]\] \[\frac{0.8}{{{y}_{1}}}=\frac{1}{2}\,\left[ \sqrt{1+8F_{1}^{2}-1} \right]\] \[8=\sqrt{1+8F_{1}^{2}}-1\] \[1+8F_{1}^{2}={{9}^{2}}=81\] \[8F_{1}^{2}=80\] \[F_{1}^{2}=80\] \[{{F}_{1}}=3.16\] \[F_{1}^{2}=\frac{v_{1}^{2}}{g{{y}_{1}}}\] \[10=\frac{v_{1}^{2}}{9.81\times 0.2},\] \[v_{1}^{2}=19.62\] \[{{v}_{1}}=4.429\,\,\text{m/s}\] \[Q=b{{y}_{1}}{{v}_{1}}=5\times 0.2\times 4.429\times 4.43\,{{\text{m}}^{\text{3}}}\text{/s}\]

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