The Impact of the yCrown Taper equation in #SWMM5 on Surcharged Nodes

The Impact of the yCrown Taper equation in #SWMM5

We are looking at three ranges of depth in the node:
1.  Node depths below yCrown using the node continuity equation to compute the new node depth,
2. Node Depths above 1.25 * yCrown use the point iteration solution for the node in which there is no node area and the program iterates until the sum of flows is zero for the timestep.
3.  Node Depths between yCrown and 1.25 * yCrown use the taper equation in which the node area decreases from the area at 0.96 Full Depth to a value of zero area at 1.25 yCrown.

If the current depth in the node is below 1.25 * yCrown

Where,  yCrown is the depth till the highest connecting conduit crown elevation

There is a tapered equation based on the sum of the  flow at the node and the surface area from the last non-surcharged condition which will influence dqdh if depth close to crown depth

F = yLast/yCrown – 1

Denom = Sum DQDH for all connecting links to the node

Denom = Denom + (Old Surface Area (at last non-surcharged condition) / dt (time step) – Sum DQDH term for connecting links ) * exp (-15*f)

This has the effect of quickly tapering the impact of the Old Surface Area between yCrown and 1.25 * yCrown (Figure 1 and Table 1).  It starts out at the value of Old Surface Area and by a depth of 1.25*yCrown the impact of Old Surface Area is zero.


Figure .  Values of the yCrown Taper from 1 to 1.25*yCrown in #SWMM5





Ycrown
exp(-15.0 * f)  Taper Value
            f = (yLast - yCrown) / yCrown or yLast/yCrown - 1
exp(-15.0 * f) Taper Value

1
1.0000
0
1.0000



1.01
0.8607
0.01
0.8607

1.02
0.7408
0.02
0.7408

1.03
0.6376
0.03
0.6376

1.04
0.5488
0.04
0.5488
1.05
0.4724
0.05
0.4724
1.06
0.4066
0.06
0.4066
1.07
0.3499
0.07
0.3499
1.08
0.3012
0.08
0.3012
1.09
0.2592
0.09
0.2592
1.1
0.2231
0.1
0.2231
1.11
0.1920
0.11
0.1920
1.12
0.1653
0.12
0.1653
1.13
0.1423
0.13
0.1423
1.14
0.1225
0.14
0.1225
1.15
0.1054
0.15
0.1054
1.16
0.0907
0.16
0.0907
1.17
0.0781
0.17
0.0781
1.18
0.0672
0.18
0.0672
1.19
0.0578
0.19
0.0578
1.2
0.0498
0.2
0.0498
1.21
0.0429
0.21
0.0429
1.22
0.0369
0.22
0.0369
1.24
0.0273
0.24
0.0273
1.25
0.0235
0.25
0.0235
 Table 1.  Values of the Taper Equation between 1 and 1.25*yCrown

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