General and approximate solutions of the boundary layer equation for radial flow of incompressible liquid

•Prandtl׳s boundary layer equation for radial flow is derived.•General solution of equation in particular case is found.•The corresponding flows are studied, three types of flow are found.•The quasi-exact solution is found and norm of the residual function is presented.

Non-linear partial differential equation for description of a laminar, incompressible, Newtonian radial flow in half-subspace is derived taking into account free slipping at a border. The boundary layer approximation is used and the equation with one free parameter for a steam function is obtained. The general solution for one value of this parameter is found and analysed. Some approximate solutions of the special form are constructed.