where H(\psi) is the total head, c.f. Bernoulli's Principle. and 2\pi\Gamma is the circulation, both of them being conserved along streamlines. Here, p is the pressure and \rho is the fluid density. The functions H(\psi) and \Gamma(\psi) are known functions, usually prescribed at one of the boundary; see the example below. If there are closed streamlines in the interior of the fluid domain, say, a recirculation region, then the functions H(\psi) and \Gamma(\psi) are typically unknown and therefore in those regions, Hicks equation is not useful; Prandtl–Batchelor theorem provides details about the closed streamline regions.
