**Subject:**How is the St Venant Equation Solved for in the Dynamic Wave Solution of SWMM 5?

**dq2**= Time Step * Awtd * (Head Downstream – Head Upstream) / Link Length or

**dq2**= Time Step * Awtd * (

**HGL**) / Link Length

**Qnew**= (Qold – dq2 + dq3 + dq4) / ( 1 + dq1)

**Qnew**= (Qold – dq2) / ( 1 + dq1)

**dq4**term in dynamic.c uses the area upstream (

**a1**) and area downstream (

**a2**), the midpoint velocity, the sigma factor (a function of the link Froude number), the link length and the time step or

**dq4**= Time Step * Velocity * Velocity * (a2 – a1) / Link Length * Sigma

**dq3**= 2 * Velocity * ( Amid(current iteration) – Amid (last time step) * Sigma

**dq1**= Time Step * RoughFactor / Rwtd^1.333 * |Velocity|

**Awtd**) is used in the dq2 term of the St. Venant equation:

**dq2**= Time Step * Awtd * (Head Downstream – Head Upstream) / Link Length

Figure 1. The four terms define the new flow at each iteration in the dynamic wave solution of SWMM5 |

Figure 2. The magnitude of the four terms determine the flow at the new iteration and ultimately the new Time Step. If the flow is constant then the value of the term is constant. |

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