Velocities and Pressure
u and v velocities can be computed by the following equations:
u = \frac{\delta \Phi}{\delta x} = \frac{\delta \Psi}{\delta y}
v = \frac{\delta \Phi}{\delta y} = -\frac{\delta \Psi}{\delta x}
and pressure:
c_p = \frac{\Delta p}{\frac{\rho}{2} v_{ref}^2} = \frac{p - p_{ref}}{\frac{\rho}{2} v_{ref}^2} = \frac{-\frac{\rho}{2} v^2 - \left(-\frac{\rho}{2} v_{ref}^2\right)}{\frac{\rho}{2} v_{ref}^2} = 1 - \frac{v^2}{v_{ref}^2}
with p = p_{dyn}
and v_{ref} = \sqrt{u_\infty^2 + v_\infty^2}
, p_{ref} = p_\infty