## anonymous 5 years ago If we define a stream function $\Psi(x,y) = \ln\sqrt{x^{2} + y^2}$ What are the corresponding velocity components of V {vector} = u * i + v * j

If our stream function is defined in terms of psi, then the u will equal the partial derivative of psi with respect to y and v will equal the partial derivative of psi with respect to x and it's negative. $\Psi _{y}=(1/\sqrt{x^2+y^2})(1/(2\sqrt{x^2+y^2}))(2y)$ $\Psi _{y}=y/\sqrt{x^2+y^2}$ The partial of x is identical except the numerator is an x. $-\Psi _{x}=-x/\sqrt{x^2+y^2}$ v (vector) = $iy/\sqrt{x^2+y^2}-jx \sqrt{x^2+y^2}$