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Falkner and Skan generalized the Blasius boundary layer by considering a wedge with an angle of   from some uniform velocity field .  Falkner and Skans first key assumption was that the pressure gradient term in the Prandtl x'-momentum equation could be replaced by the differential form of the Bernoulli equation in the high Reynolds number limit.  Thus: 
Here  is the velocity of at the boundary layer edge and is the solution the Euler equations (fluid dynamics) in the outer region.
Having made the Bernoulli equation substitution, Falkner and Skan pointed out that similarity solutions are obtained when the boundary layer thickness and velocity scaling factors are assumed to be simple power functions of x.  That is, they assumed the velocity similarity scaling factor is given by:
where  is the wedge length and m is a dimensionless constant.  Falkner and Skan also assumed the boundary layer thickness scaling factor is porpotional to:   
Mass conservation is automatically ensured when the Prandtl momentum boundary layer equations are solved using a stream function approach.  The stream function, in terms of the scaling factors, is given by: 
where  and the velocities are given by:
This means
The non-dimensionalized Prandtl x-momentum equation using the similarity length and velocity scaling factors together with the stream function based velocities results in an equation known as the Falkner–Skan equation and is given by:
where each dash represents differentiation with respect to  (Note that another equivalent equation with a different  involving an  is sometimes used. This changes f and its derivatives but ultimately results in the same backed-out  and  solutions).  This equation can be solved for certain  as an ODE with boundary conditions:
The wedge angle, after some manipulation, is given by:
The  case corresponds to the Blasius boundary layer solution. When , the problem reduces to the Hiemenz flow. Here, m . For more negative values of m, that is, for stronger adverse pressure gradients, all solutions satisfying the boundary conditions at &eta; = 0 have the property that f(&eta;) > 1 for a range of values of &eta;. This is physically unacceptable because it implies that the velocity in the boundary layer is greater than in the main flow. Further details may be found in Wilcox (2007).
With the solution for f and its derivatives in hand, the Falkner and Skan velocities become:
and
The Prandtl -momentum equation can be rearranged to obtain the -pressure gradient, /, (this is the formula appropriate for the =1 and =2m/(m+1) case) as
where the displacement thickness, , for the Falkner-Skan profile is given by:
and the shear stress acting at the wedge is given by