Find the equation of streamlines.

Consider a velocity field where the \(x\) and \(y\) components of velocity are given by \(u = cx\) and \(v = −cy\), where \(c\) is a constant. Obtain the equations of the streamlines.

Asked on 27th October 2019 in Aerodynamics.
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    Here \(u=cx\) and \(v=-cy\).Since \[vdx – udy=0\]

    Therefore \[\frac{dy}{dx}=\frac{v}{u}=\frac{-y}{x}
    \\\Rightarrow \frac{dy}{y}=\frac{-dx}{x}\]

    On integrating \[ln(y)=xln(x)+C_{1}
    \\\Rightarrow y=\frac{C_{2}}{x}\]

    These streamlines are in hyperbola shape.

    FigureFigure

    Answered on 27th October 2019.
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