MOMENTUM, PRESSURE, AND ENERGY IN THE TREFFTZ-PLANE

The distributions of momentum and energy generated by a force working in a fluid together with the associated pressure distributions are dis cussed in detail. The momentum generated by an impulsive point force i n a compressible atmosphere is identified for two-thirds in a moving v irtual sphere of fluid and for one-third in a front expanding with the velocity of sound. in a transverse section of an incompressible atmos phere the net momentum is identically zero when boundary conditions ar e left out of the considerations. It is discussed where and how net mo mentum is imparted to the atmosphere by impulsive and steady, moving f orce distributions. The analogy between an actuator surface and a visc ous boundary layer on a flat plate, both involving the generation of m omentum in a definite jet or wake region, is discussed in the same fra me of reference as the induced drag of a lifting wing. The boundary co nditions on and the dimensions of the control box both play a role in the answer to the question if and where net momentum is to be found. T he statement that the net momentum in a transverse section remains zer o proves to be only approximately valid in a free atmosphere. An impor tant conclusion is that at an overall scale the unsteady pressures in any model, viscous or nonviscous, dominate the momentum balance.