# Theory and Algorithm

How hydrologic and hydraulic calculations are worked out.

## Runoff Calculation

First, the potential maximum soil moisture retention (S) is computed with the user-defined curve number (CN) and used to calculate the initial abstraction (Ia).

S =
(1000) / CN
- 10
Ia = 0.2(S)

With the user-define total storm depth (P), computed maximum soil moisture retention, and initial abstraction, the resulting runoff depth is computed.

Runoff Depth =
(P-Ia)2 / (P-Ia+S)

## Hydrograph Calculation

With each runoff burst depth occurring at each time step, a small "burst" hydrograph is computed based on the dimensionless SCS (Soil Conservation Service) Unit Hydrograph. This dimensionless unit hydrograph was derived based on many hydrographs of varying size and geographic location and is made dimensionless by normalizing the flow with the peak flow (q/qpeak) and by normalizing the time with the time of peak (t/tpeak). The SCS Dimensionless Unit Hydographs is shown below in Figure 1. Figure 1: Dimensionless SCS Unit Hydrograph used to calculate runoff from each rainfall burst

In order to populate each burst hydrograph, the time to peak (tpeak) and peak flow (qpeak) are first calculated as follows:

tpeak = 0.667tc
qpeak =
(484)(Area)(Depthburst) / tpeak

where tc is the user-defined time of concentration (hours), "484" is the peaking factor, Area is the total contributing drainage area (square miles), and Depthburst is the depth of the runoff burst at a given time step (inches).

With the calculated tpeak and qpeak, the flow at each time step is solved for based on the shape of the Dimesionless SCS Unit Hydrograph shown in Figure 1 resulting in a burst hydrograph for the particular runoff depth.

Each burst hydrograph is then added together to form the runoff hydrograph for the overall storm.

## Stormwater Routing Calculations

Discharge and overflow from a basin resulting from inflow runoff (qinflow) is governed by a general continuity equation as follows:

qinflow = qoutflow - storage - seepage

where storage is dependent on the user-defined basin geometry parameters (area, void space, height) and seepage represents the volume of water lost to infiltration.

Outlflow from the basin (qoutflow) is can be broken down into orifice flow and weir flow as follows:

qoutflow = qorifice + qweir

Orifice flow is governed by the orifice equation which is essentially a rearrangment of the Bernoulli Equation

qorifice = CA2gh

where C is a coefficient (assumed to be 0.62), A is the cross-sectional area of the orifice based on the user-defined orifice diameter, g is the force of gravity, and h is the head on the orifice at a given point in time.

Similarly, weir flow is calculated as follows:

qweir =
2 / 3
CdB(2g)0.5h1.5

where Cd is the weir discharge coefficient, b is the width of the weir, g is the force of gravity, and h is the head on the weir at a given point in time.

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