Non Linear Term in the Saint Venant Equation of SWMM 5

Non Linear Term in the Saint Venant Equation of SWMM 5The flow equation has six components that have to be in balance at each time step:

1. The unsteady flow term or dQ/dt

2. The friction loss term (normally based on Manning's equation except for full force mains),

3. The bed slope term or dz/dx

4. The water surface slope term or dy/dx,

5. The non linear term or d(Q^2/A)/dx and

6. The entrance, exit and other loss terms.

All of these terms have to add up to zero at each time step. If the water surface slope becomes zero or negative then the only way the equation can be balanced is for the flow to decrease. If the spike is due to a change in the downstream head versus the upstream head then typically you will a dip in the flow graph as the water surface slope term becomes flat or negative, followed by a rise in the flow as the upstream head increases versus the downstream head.

You get more than the normal flow based on the head difference because in addition to the head difference you also get a push from the non linear terms or dq3 and dq4 in this graph.

If you use the Keep Inertial term option then you use all 5 terms at all times, if you use the Dampen option you use all five terms until the Froude number of the link greater than 1 and then you do not use terms dq3 and dq4, if you use the Ignore option then the dq3 and dq4 terms are not used at all for the calculation of the flow in the link.