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A Falkner-Skan boundary layer is a similarity boundary-layer flow driven by an outer velocity proportional to a power of distance along the wall. Its streamfunction reduction gives the Falkner-Skan equation, with no-slip wall and outer-velocity matching conditions. It generalizes the Blasius flat-plate boundary layer.

The Falkner-Skan equation is a similarity reduction of the steady two-dimensional boundary-layer equations when the imposed outer speed isChoose the streamfunction and similarity coordinatewith kinematic viscosity $\nu$. Then $u={\partial }_y\psi =U{f}^{\prime }(\eta )$ and $v=-{\partial }_x\psi$ automatically satisfy incompressibility.

The streamwise equation $u{u}_x+v{u}_y=U{U}^{\prime }+\nu u_{yy}$ reduces towhere primes differentiate with respect to $\eta$. An impermeable stationary no-slip wall and matching to the outer flow giveThus $f^{\prime }$ is the streamwise speed divided by the local outer speed.

At $m=0$, the outer speed is constant and the equation becomes the Blasius equation. Positive $m$ gives an accelerating outer flow and decreasing outer pressure, since $p_x=-\rho U{U}^{\prime }$; negative $m$ gives an adverse pressure gradient. The equation and boundary conditions determine a Falkner-Skan boundary layer, rather than a generic profile independent of the imposed pressure field.