Approximate Method for Calculating the Laminar Boundary-Layer using the Energy Thickness

• Published in: Nippon Kikai Gakkai Rombunshū Vol. 24; no. 145; pp. 636 - 641
• Main Author: HATTA, Keiji
• Format: Journal Article
• Language: English; Japanese
• Published: The Japan Society of Mechanical Engineers 1958
• ISSN: 0029-0270; 2185-9485
• DOI: 10.1299/kikai1938.24.636

A simple method for calculating the laminar boundary-layer has been obtained. The method consists in using the approximate formula for the energy thickness and the diagram which gives the relation between σ*, ω* and T*, where σ*=θ*2U'/ν, ω*=σ*2(UU"/U'2), T*(τ0/ρ)×(θ*/νU). The notations are as follows : θ*=energy thickness, χ=arc length of the surface of the body, U(χ)=velocitv just outside the boundary-layer, τ0=shearing stress on the surface of the body, ρ=density of the fluid, ν=kinematic coefficient of viscosity. When U(χ) is given, θ* is calculated by an approximate formula and the relation between σ* and ω* is determined. Then by using the diagram, the values of T* are found, which giveτ0 for each point on the surface of the body. Some results obtained by this method coincide satisfactorily with the exact solutions and the results of experiments. As the necessary calculations are simple, this method is useful for the engineering purpose.