Breaking Down the St Venant Terms in SWMM5 🌊💧

 Deciphering the Non-Linear Term in SWMM 5's Saint Venant Equation 🌊📐

Understanding the flow dynamics within SWMM 5 requires diving into the Saint Venant equation's intricate elements. Here's a breakdown:

1. Unsteady Flow Term (dQ/dt): 🔄
This represents the change in flow rate with respect to time. As water moves, its rate doesn't remain constant, and this term captures those variations over time.

2. Friction Loss Term: 🌪️
Primarily based on Manning's equation (except when dealing with full force mains), it captures the resistance or frictional loss as water flows over the channel surface.

3. Bed Slope Term (dz/dx): ⛰️
The natural inclination or gradient of the riverbed or channel affects how water flows. This term addresses the contribution of that slope to the flow dynamics.

4. Water Surface Slope Term (dy/dx): 🌊
As water moves, its surface doesn't remain flat. The differences in water surface elevations, or the water surface slope, significantly influence flow behavior.

5. Non-Linear Term (d(Q^2/A)/dx): 🌀
Perhaps the most complex, this term captures the non-linear aspects of flow, which can't be described by a simple linear relationship. The flow's intensity and area play crucial roles here.

6. Loss Terms (Entrance, Exit, and Others): 🚪
These terms account for the losses as water enters or exits a section and any other associated loss mechanisms.

For a balanced system, these components must net out to zero at every time step. However, when the water surface slope becomes non-positive, flow reduction becomes the only way to maintain this balance. Spikes typically arise due to variations in downstream versus upstream heads. Such spikes can lead to a temporary flow reduction (as the water surface slope goes flat or turns negative), followed by a flow surge as the upstream head starts dominating.

Interestingly, the flow often exceeds what's predicted solely based on head differences. Why? Because the non-linear terms, represented as dq3 and dq4 in some analyses, provide an additional "push" to the flow. This amplifies the flow beyond what's expected, showcasing the intricate dance of factors at play in SWMM 5's hydrodynamic modeling. 🌐🌊🔍

Breaking Down the St Venant Terms in SWMM5 🌊💧

Overview: 📖
The St Venant equations, foundational to the world of hydrodynamics, find their application in SWMM5. Today, we aim to unveil the mystery behind them. By deploying a QA/QC version of SWMM 5, we gain access to a plethora of link, node, system, and Subcatchment variables that go beyond the offerings of the default SWMM 5 GUI and engine. This treasure of knowledge extends to both #InfoSWMM and ICM SWMM, and any software deploying the #SWMM5 engine. 🚀🔍

St Venant Terms in Action: 🎬
Our illustrative Figure 1 📊 unfurls the terms for you. Meanwhile, Figure 2 and Figure 3 transport you into the SWMM5 universe, showcasing these terms within the framework of a SWMM5 table and graph. 📈📉

Dive into the equations: 🧮

• For a full force main:

  • dq2 = Time Step * Area wtd * (Head Downstream – Head Upstream) / Link Length
  • Qnew = (Qold – dq2 + dq3 + dq4) / ( 1 + dq1)

• But, when it's not full, dq3 and dq4 take a break and you get:

  • Qnew = (Qold – dq2) / ( 1 + dq1)

• The dynamics at play: ⚖️

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

Dive deeper into the SWMM 5 intricacies with the QA/QC report. 📘🔍

St Venant Units in the SWMM5 Limelight: 🌟
When a new flow (Q) arises during each time step iteration, the formula:
(1) Q for the new iteration = (Q at the Old Time Step – DQ2 + DQ3 + DQ4 ) / ( 1.0 + DQ1 + DQ5)
takes center stage. The spotlight then shifts to DQ2, DQ3, and DQ4, all of which boast flow units. SWMM 5, the backstage hero, works in CFS units, seamlessly transitioning to user-specific units for output clarity.

• DQ2, DQ3 & DQ4 are measured in CFS (feet^3/second). 📏
• DQ1 & DQ5 are dimensionless. ✨

Conclusion: 🌟
The world of SWMM5, with its intricate equations and units, is vast and profound. But, with the right understanding, the St Venant terms become less intimidating, paving the way for more accurate and efficient hydrodynamic modeling. 🌐🌊🌟