Dynamic Forces
For any fluid, the force which contributes to its motion will be the sum of its gravity (Fg), viscous (Fv), surface tension (Ft) and elastic (Fe) forces.
The primary force for shallow water which contributes to its motion is due to gravity. As with the force on the face of a dam having area A, width w, water depth h and water density p, it is given by
For shallow water gravity wave action, the effects of surface tension and elastic forces are assumed negligible. The effect of viscosity is found to also be negligible in comparison with that of gravity by calculating values for a typical situation. The viscous force involved with a 1 foot wide sheet of water 1/2 in. deep whose free surface velocity is 1 foot/sec is about 5.8 x 10^{4 }pounds:
The gravity force due to the same sheet of water whose depth is 1/2 in is calculated to be 1.3 pounds, which is about 2,000 times greater than the viscous force.
For sound propagation the viscous, surface tension, and gravity forces of air are assumed negligible in comparison with the effect of its elastic force, which is in terms of its bulk modulus of elasticity β, crosssection area A and volumetric strain dV/V.
The energy per unit volume is constant for air waves even though it varies in form between kinetic and potential (elastic). Equating these two forms results in an expression of volumetric strain in terms already established.
The air elastic force equation can now be rewritten in these more convenient terms including the air flow velocity (v).
The inertial force of either type of fluid is in terms of its specific gravity (p), flow crosssection area (A), and velocity (v).
