Sunday, July 28, 2013

Known and Unknown Variables in the Node Continuity Equation of SWMM5

Subject: Known and Unknown Variables in the Node Continuity Equation

The new node depth is calculated based on the old inflow to the node, the old outflow from the node, the old node depth, a fixed time step, node evaporation and infiltration losses, new inflow to the node, new outflow from the node and the new total surface area of the node. The inflow, outflow and surface area are updated before the new iteration based on the last iteration link flows and node depths. The node depth equation is iterated until the depth in the node is less than 0.005 feet between the current iteration or the last iteration with a maximum of 8 iterations in SWMM 5.0.020
New Iteration Node Depth = Old Node Depth + [ ½ * (New Inflow – New Outflow) + ½ * (Old Inflow – Old Outflow) - Node Losses ] / New Surface Area * Time Step
1st Iteration: New Node Depth = New Iteration Node Depth
2nd to 8th Iteration: New Node Depth = ½ * New Iteration Node Depth + ½ * Old Iteration Node Depth

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