Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/424

App. II. Now it by no means follows that the mean pressure throughout the region is the same as the mean pressure on the walls of the enclosure; in fact, we know from hydrodynamic principles that in many cases of fluid motion it is not so. In the case in point, however, it is manifest that the mean pressure is the same whether the integration is taken over the surface or throughout the volume, for (Fig. 160) the pressure on the walls of the box is point for point the same as for any surface parallel to these walls passing longitudinally through the region, and the pressure on the ends is of the same mean value, for the velocity of sound can be correctly computed on this basis. It is therefore evident that for a fluid obeying Boyle's law the existence of wave motion does not give rise to any change of pressure.

Under these circumstances it follows that change of pressure will take place in a region containing an ordinary gas ($$P / \rho^\gamma =$$ constant), the magnitude of which can be calculated from the energy of wave motion that passes into, and exists in, the thermodynamic system.