Railways Technical Ability Fluid Mechanics and Machinery Question Bank Fluid Mechanics

  • question_answer If \[u=ax\] and \[v=-\,ay\] give the velocity distribution for a two-dimensional flow, what is the equation of a stream line passing through the point (3, 1)?

    A) \[xy=3\]                       

    B) \[x+y=4\]

    C) \[x+3y=6\]                   

    D) \[{{x}^{2}}y=9\]

    Correct Answer: A

    Solution :

    The equation of stream line is: \[\frac{dx}{u}=\frac{dy}{v}\] \[\frac{dx}{ax}=\frac{dy}{-\,av}\]             \[\frac{1}{a}\,In\,x=-\,\,\frac{1}{a}\,In\,\,\,y+c\]             The stream line passes through point (3, 1) \[\frac{1}{a}\,In\,3=-\,\frac{1}{a}\,In+c=0+c\] \[c=\frac{1}{a}\,In\,3\] \[\frac{1}{a}\,In\,x=-\,\frac{1}{a}\,In\,y+\frac{1}{a}\,In\,3\]             Or \[In\,x=-\,\,In\,y+In\,3\]             \[In\,x+In\,y=In\,3\]             \[In\,xy=In\,3\]             \[xy=3\]

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