Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/311

Rh any possible disturbances that may be set up in the fluid by the body in motion.

All in Absolute Units.

Then we have (§ 3) $$\mathrm{F} = \mathrm{m}\ \mathrm{v},$$ and the work done usefully per second is Rh

and the energy left in the fluid per second, that is, lost power, is Rh

or total energy per second

or efficiency

Rh

This, according to Rankine, is the theoretical limit to the efficiency of a propeller. It will be shown subsequently that this assertion requires qualification.

If we depart from the simplicity of the assumption and suppose that the different portions of the fluid acted upon receive different velocities, the foregoing demonstration requires appropriate modification; the v of expression (1) and the v of expression (2) are not the same quantity, the v2 in the latter expression becoming the mean square of the velocity v instead of the square of the mean. For a given value of m the efficiency must thus be less than if the velocity v were uniform over the Rh