# Use Bentley Transition Equation

The conventional EPA SWMM solver treats the flow states change between gravity flow and surcharged flow (pressurized flow) by switching equations between node continuity equation and a perturbation equation for pressure flow, this sometimes does not provide smooth transitions between the flow states and results in instabilities and abrupt depth change in one time-step.

To improve the model stability in such conditions, a new method of transitional continuity equation is developed and provided as a new calculation option.

The new method assumes that when a node is surcharged (pressurized), there is still a small node area (Minimum Surface Area as specified in the calculation option) even the connection conduits are all filled full. Then the conventional continuity equation is universally applied to both gravity and surcharged conditions. To ensure a smooth transition between gravity and fully surcharge states, a transition equation is applied when the depth is between 0.99 crown depth and 1.25 crown depth as:

Ta = Sa - (Sa - Na) * (y/D - 0.99) / (1.25 - 0.99)

In which Ta is the transitional area used in the continuity equation, Sa is the area from the connecting conduits, Na is the node area (Minimum Surface Area), y is the flow depth and D is the outlet conduit crown depth. Ta becomes Sa when y/D < 0.99 and Na when y/D > 1.25.