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.
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.
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.
