Numerical Solution of the Blasius Boundary Layer and Accuracy of Polynomial Momentum-Integral Approximations.

The laminar boundary layer on a flat plate at zero incidence is a classical test problem for approximate methods. This technical note solves the Blasius equation numerically with a collocation boundary-value solver (Python, SciPy) and uses the result as a reference to assess von Kármán's momentum-integral method for four assumed velocity profiles: linear, cubic, quartic (Pohlhausen, zero pressure gradient) and sine. The numerical solution reproduces the accepted similarity constants: the wall-shear parameter f''(0) is 0.3320, and the skin-friction coefficient times the square root of the local Reynolds number is 0.6639. Among the profiles tested, the sine profile gives the smallest skin-friction error (-1.3%) and the linear profile the largest (-13.0%). The Python script used to generate all results and figures is included so that the work can be reproduced. This note is a computational study based on the author's master's project on laminar boundary layer flow (Department of Mathematics, Raichur University, 2024). It has not been peer reviewed.