A turbulent boundary layer problem has been studied analytically and compared with an available experiment in the literature. Correlations of the experimental data were made to investigate the validity of the commonly used empirical relations on turbulent shear stresses. It was found that the model which related the local turbulent shear stress linearly with the local turbulent kinetic energy, as used by Bradshow et. al., appeared to be most reasonable. combining this model with the expression of turbulent viscosity given by Boussinesq, it was then possible to introduce the turbulence-energy equation in addition to the governing equations of continuity and momentum. consequently, the turbulent viscosity was able to be considered as one of the dependent variables to be solved for simultaneously with all other related flow parameters. Using the main-flow direction and the stream function as the two independent variables, the governing equations were reduced to two simultaneous parabolic-type partial differential equations through the von Mises transformation. The finite difference technique of Partankar was applied. The numerical solutions were obtained for the average velocity and the turbulent kinetic energy distributions. In comparison with the experimental results of Klebanoff in the fully developed region along a flat plate, very good agreement was reached on average velocity distribution. However, the turbulent kinetic energy distribution was not completely satisfactory, since the energy dissipation term of the turbulence-energy equation was not able to be expressed adequately due to the lack of sufficient experimental information. It is then concluded that the use of the turbulence-energy equation in boundary layer study is possible to eliminate the uncertainty resulting with empirical models of the turbulent viscosity. However, further experimental investigations are needed to improve the understanding of the structure of turbulence --Abstract, page i-ii
