Consider a velocity field where x and y components of velocity are given by u=4x and v=-4y. Obtain the equation of streamlines.
Consider a velocity field where x and y components of velocity are given by u=4x and v=-4y. Obtain the equation of streamlines.
\[\begin{array}{l}\left( {\frac{{dy}}{{dx}}} \right) = \frac{v}{u} = \left( {\frac{{ – 4y}}{4x}} \right) = \left( {\frac{{ – y}}{x}} \right)\\ \Rightarrow \left( {\frac{{dy}}{y}} \right) = \left( {\frac{{ – dx}}{x}} \right)\\ \Rightarrow \ln y = x\ln x + c\\ \Rightarrow y = \frac{{{c_1}}}{x}\end{array}\]So,the streamlines are hyperbolas.
