Assigned Flow Waterhammer Theory

With an assigned flow, the flow rate is known at the pipe inlet or outlet (Wylie, et al, 1993Wylie, E.B., V.L. Streeter & L. Suo, Fluid Transients in Systems, Prentice Hall, Englewood Hills, New Jersey, 1993., pp. 43). The unknown is then the pressure, which can be obtained by solving the appropriate compatibility equation. If the flow rate is known at the upstream end of the pipe, the negative compatibility equation is used.

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

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

Assigned Flow Vapor Cavitation Theory

When the calculated pressure at an Assigned Flow junction drops below vapor pressure, a vapor cavity forms at the junction.

Assuming the specified flow is an inflow, the vapor volume calculation is as follows:

The ṁ_up terms are known because they are specified terms for inflow junctions. For outflow junctions the ṁ_down terms are known. Similar to a pipe interior node, when the vapor volume is negative, the cavity collapses and the fluid pressure then rises above the vapor pressure.