Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer A two-dimensional fluid flow is described by the velocity components \[u=5{{x}^{3}},\] \[v=-\,15{{x}^{2}}\,y.\] The stream function at point will be:

    A) \[2\,{{\text{m}}^{\text{2}}}\text{/s}\]              

    B) \[2\,{{\text{m}}^{3}}\text{/s}\]

    C) \[10\,{{\text{m}}^{3}}\text{/s}\]                      

    D) \[20\,{{\text{m}}^{3}}\text{/s}\]

    Correct Answer: A

    Solution :

    \[u=5{{x}^{3}},\] \[v=-\,15{{x}^{2}}yu=\frac{\partial \psi }{\partial y}=5{{x}^{3}}\]     \[y=5{{x}^{3}}y+{{c}_{1}}\] \[v=\frac{\partial \psi }{\partial y}=-\,15{{x}^{2}}y\] \[\psi =5{{x}^{3}}y+{{c}_{2}}\] Taking \[{{c}_{1}}={{c}_{2}}=0\]  \[\psi =5\times 1\times 2=10\,\,{{\text{m}}^{\text{3}}}\text{/s}\]

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