Equations in Cartesian Coordinates

The velocity components are given by

$\displaystyle u $ $\displaystyle = {{\partial \phi} \over {\partial x}} = {{\partial \psi} \over
 {\partial y}}$    
$\displaystyle v $ $\displaystyle = {{\partial \phi} \over {\partial y}} = -{{\partial \psi}
 \over {\partial x}}$ (4.67)

The Laplacian is given by,

$\displaystyle {{\partial^2 \phi} \over {\partial x^2}} + {{\partial^2 \phi}
 \o...
...rtial^2 \psi} \over {\partial
 x^2}} + {{\partial^2 \psi} \over {\partial y^2}}$ (4.68)

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney