With an assigned pressure, the pressure is known at the pipe endpoint. The unknowns are therefore the velocity, which can be obtained by solving the appropriate compatibility equation, and the density.

If the static pressure is known at the upstream end of the pipe, the negative compatibility equation is used.

The density can then be determined directly from the equation of state as a function of pressure and temperature.

Conversely, if the static pressure is known at the downstream end, the positive compatibility equation is used.

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

If the known pressure changes with time, then a current pressure is obtained for the current time step and used in the equations.

If the known pressure is a stagnation pressure instead of the static pressure, additional complexities are introduced as the velocity must be known to convert the given stagnation pressure to a static pressure. Therefore, iterations must be performed using the corresponding compatibility equations as shown above combined with the stagnation property relationships.

Sonic Choking Transient Theory

An outlet assigned pressure 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 pressure 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 pressure junction a different solution method must be enacted. See Transient Sonic Choking for more information.