Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer In a two-dimensional fluid flow,\[u=6x+xy.\] which one of the following gives the component of the velocity to satisfy the continuity equation?

    A) \[6x+xy\]                     

    B) \[6+xy\]

    C) \[-\,\left( 6x+xy \right)\]              

    D) \[-\,\left( 6y+\frac{1}{2}\,{{y}^{2}} \right)\]

    Correct Answer: D

    Solution :

    \[u=6x+xy\] Continuity equation in two-dimension is: \[\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0\] \[u=\frac{\partial \phi }{\partial x},\] \[v=\frac{\partial \phi }{\partial y}\] \[\frac{\partial v}{\partial y}=6+y\] A. \[\frac{\partial v}{\partial y}=x\frac{\partial }{+\,1}\] \[6+y+x\ne 0\] B. \[\frac{\partial v}{\partial y}=x,\] \[6+y+x\ne 0\] C. \[\frac{\partial v}{\partial y}=-\,\,(6+x)=-\,\,(6+x)\] \[6+y-6-6x\ne 0\] \[(6+y)-(6+y)=0)\]

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