Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/72

§ 36 Kinematic viscosity, which we will denote by the symbol $$\nu = \frac{\mu}{\rho} ,$$ and and is consequently of the dimensions $$\frac{L^2}{T} .$$

Writing the law of viscous resistance in its kinematic form we have $$R = A\ \nu\ \frac{V}{l}$$ where $$A$$ is the area of the surface; it will be noted that this expression is dimensional.

If we similarly write the law of skin-friction $$R = A\ \nu\ \frac{V^{1.5}}{l} ,$$ we find that the dimensions do not harmonise.

Let us examine this expression in a general form, where

dimensionally:—

The general expression therefore becomes:—

in which

This is the general equation to the kinematic resistance of bodies in viscous fluids, and correlates the variations in respect of viscosity, area, and velocity; the application extends to both normal and inclined planes and bodies of the most diverse form.

It may be illustrated here in its relation to the law of skin-friction; we have, $$R$$ varies as $$V^{1.5}$$ and the full kinematic expression therefore becomes—