The present work studies the effects of the physical parameter characterizing the laminar flow regime, namely the Strouhal number, on the evolution of the unsteady dynamic boundary-layer developed along a wedge surface. Similarity method is used to transform unsteady momentum equation to dimensionless form. Using superposition method between diffusion and convective flows solutions, an ad hoc velocity profile formula is proposed. The obtained results confirm perfectly the numerical data given by Blasius, Falkner-Skan and Williams-Rhyne for all Strouhal numbers. A new accurate analytical function of the local skin friction is established for all time values and for different wedge surface directions. In order to give further clarification on the flows evolutions from diffusion flow to convective flow, in the whole space domain, new skin friction coefficient curves are plotted for all Strouhal numbers and for different wedge surface directions.