With an assigned flow, the flow rate is known at the pipe inlet or outlet. The unknowns are then the velocity, the pressure, and the density.

If the flow rate is known at the upstream end of the pipe, the negative wave compatibility equation is used to determine the pressure based on an initial guess for velocity.

The density can then be determined directly from the equation of state as a function of pressure and temperature. Once the pressure and density are calculated, the mass flowrate can be recalculated using the continuity equation. If the difference between the defined and calculated mass flow rate is too large the velocity is adjusted and the process is repeated until the specified flow is met within a reasonable tolerance.

Conversely, if the flow is known at the downstream end, the positive wave compatibility equation is used to calculate the velocity based on an initial guess for pressure.

The density can then be found using the particle path compatibility equation.

Similar to the process above with a known inflow the mass flow can be recalculated using the continuity equation, and the pressure will be iterated on until the calculated mass flow is within a reasonable tolerance of the specified mass flow.

Sonic Choking Transient Theory

An outlet assigned flow junction can experience endpoint choking during the steady state, or can become choked during the transient due to transient events in the system. An inlet assigned flow junction cannot be choked in the steady state, but may experience choking during the transient as a result of rapid transients in the system. If sonic choking occurs at the assigned flow junction a different solution method must be enacted. See Transient Sonic Choking for more information.