In this condition, by taking the divergence of all terms in the momentum equation, one obtains the pressure poisson equation.
32.
As an example for the spatial derivatives, derivative in the west-face diffusion term in the x-momentum equation becomes
33.
One arrives to the "'Crocco Vazsonyi form "'( Crocco, 1937 ) of the Euler momentum equation:
34.
The perturbed pressures are evaluated in terms of streamfunctions, using the horizontal momentum equation of the linearised Euler equations for the perturbations,
35.
The momentum equations for the far field flow dictate that the thrust and torque will induce a secondary flow in the approaching wind.
36.
The first equation is the Euler momentum equation with uniform density ( for this equation it could also not be constant in time ).
37.
Letting g = m w _ i, the momentum of the particle, the integrated Boltzmann equation becomes the conservation of momentum equation:
38.
The Kutta condition allows an aerodynamicist to incorporate a significant effect of viscosity while neglecting viscous effects in the underlying conservation of momentum equation.
39.
These equations are however hard to solve due to quasilinearity in the momentum equations and interdependence of the pressure term in all three equations.
40.
By choosing \ eta as the y-scale, the leading order momentum equation for this " inner boundary layer " is given by:
