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Compute the gradients of velocity and pressure. Solve the discretized momentum equation to compute the intermediate velocity field. Compute the uncorrected mass fluxes at faces. Solve the pressure correction equation to produce cell values of the pressure correction.
The way of obtaining a velocity field satisfying the above, is to compute a pressure which when substituted into the momentum equation leads to the desired correction of a preliminary computed intermediate velocity. Applying the divergence operator to the compressible momentum equation yields
Therefore, = = = =, where Δp is the change in linear momentum from time t 1 to t 2. This is often called the impulse-momentum theorem (analogous to the work-energy theorem ). As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied.
Momentum depends on the frame of reference, but in any inertial frame of reference, it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum ...
Here the pressure P D is referred to as dynamic pressure due to the kinetic energy of the fluid experiencing relative flow velocity u. This is defined in similar form as the kinetic energy equation: P D = 1 2 ρ u 2 {\displaystyle P_{\rm {D}}={\frac {1}{2}}\rho u^{2}}
The equation above presupposes that the gas density is low (i.e. the pressure is low). This implies that the transport of momentum through the gas due to the translational motion of molecules is much larger than the transport due to momentum being transferred between molecules during collisions.
The radiation pressure again can be seen as the transfer of each photon's momentum to the opaque surface, plus the momentum due to a (possible) recoil photon for a (partially) reflecting surface. Since an incident wave of irradiance I f over an area A has a power of I f A , this implies a flux of I f / E p photons per second per unit area ...
Then the angular equation in the momentum equations and the continuity equation are identically satisfied. The radial momentum equation reduces to ∂p / ∂r = 0, i.e., the pressure p is a function of the axial coordinate x only. For brevity, use u instead of . The axial momentum equation reduces to