# Boundary layer thickness, accelerating flow.

by apc3161
Tags: accelerating, boundary, flow, layer, thickness
 Sci Advisor P: 1,498 It sounds to me like you have a Falkner-Skan Wedge flow. Basically this is a similarity solution (as the flat plate boundary layer). Similarity is achieved by the variable $$\eta = Cyx^a$$, which is consistent with a power-law freestream velocity distrubtion: $$U(x) = Kx^m\,\,\,; m=2a+1$$ The exponent m may be termed the power-law parameter. do some blah blah blah, and the common form of the Falkner-Skan equation for similar flows is: $$f''' + ff'' + \beta(1-f'^2) = 0$$ Where $$\beta = \frac{2m}{1+m}$$ The boundary conditions are the same for the flat plate: $$f(0) = f'(0) = 0; f'(\infty) = 1$$ Where the parameter $$\beta$$ is a measure of the pressure gradient, and is positive for positive for a negative or favorable pressure gradient, and negative for an unfavorable pressure gradient; 0 denotes the flat plate. I won't type the table out, but you should be able to find a table of solutions online somewhere. Basically they are all non-dimensional, so you'll have to find a reference to dimensionalize them to a real-life problem.