The stream function for the flow field is $$\psi =2x^{2}-y^{2}$$ Velocity component $u$ and $v$ of the two-dimensional flow field is $$u=\frac{\partial \psi }{\partial y},v=-\frac{\partial \psi }{\partial x}$$ Therefore, $$u=\frac{\partial \psi }{\partial y}=\frac{\partial }{\partial y}\left ( 2x^{2}-y^{2} \right ) =\frac{\partial }{\partial y}\left ( 2x^{2} \right )-\frac{\partial }{\partial y}\left ( y^{2} \right )=0-2y=-2y$$ $$v=-\frac{\partial \psi }{\partial x} =-\frac{\partial }{\partial x}\left ( 2x^{2}-y^{2} \right ) =-\frac{\partial }{\partial x}\left ( 2x^{2} \right )+\frac{\partial }{\partial x}\left ( y^{2} \right )=-4x+0=-4x$$ Therefore, at point $(2,3)$, $$u=-2y=-2\left ( 3 \right )=-6\\v=-4x=-4\left ( 2 \right )=-8$$ Velocity, $V=-6i-8j$
Magnitude of velocity = $$\sqrt{u^{2}+v^{2}}=\sqrt{\left ( -6 \right )^{2}+\left ( -8\right)^{2}}=\sqrt{36+64}=10$$