Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer The velocity potential function in a two dimensional flow fluid is given by \[\phi ={{x}^{2}}-{{y}^{2}}.\] The magnitude of velocity at the point (1, 1) as:

    A) 2                                 

    B) 4

    C) \[2\,\sqrt{2}\]                

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

    Correct Answer: C

    Solution :

    \[\phi ={{x}^{2}}-{{y}^{2}}\] \[u=\frac{\partial \phi }{\partial x}=-\,2x\] \[v=-\frac{\partial \phi }{\partial y}=+\,2y\] \[v=\sqrt{{{u}^{2}}+{{v}^{2}}}=\sqrt{4{{x}^{2}}+4{{y}^{2}}}\] \[{{v}_{\left( 1,1 \right)}}=\sqrt{8}=2\sqrt{2}\]

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