Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer The velocity components for a two dimensional incompressible flow of a fluid are \[u=x-4y.\] and \[v=-y-4x.\] It can be concluded that:

    A) The flow does not satisfy the continuity equation

    B) The flow is rotational

    C) The flow is irrotational

    D) None of the above

    Correct Answer: C

    Solution :

    \[u=x-4\,v,\] \[v=-\,y-4x\] \[\frac{\partial u}{\partial x}=1,\] \[\frac{\partial u}{\partial y}=-4,\]   \[\frac{\partial v}{\partial x}=-\,4,\] \[\frac{\partial v}{\partial y}=-\,1\]                        Continuity equation is: \[\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=1-1=0\]Hence continuity equation is satisfied.   For the flow to be irrotational, \[\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}\] i.e., \[-\,4=-\,4.\] hence the flow is irrorational

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