A Single Formula for the Complete Velocity Profile in a Turbulent Boundary Layer

An expression for the wake deficit g(Π, y/δ) in a turbulent boundary layer is combined with a function f(U+) for the inner layer to yield a single formula for the complete velocity profile in the form y+ exp {Kg(Π, y/δ)} = f(U+). Close agreement is shown with data from boundary layers in a wide range of pressure gradients and beneath a turbulent free stream. The formula will be particularly useful for integral and differential calculation methods.