Hydraulic Engine & Theory

To build robust, reliable drainage models, it is essential to understand the underlying mathematics and physical principles the software uses to simulate flow. This platform relies on a sophisticated 1D hydrodynamic engine that solves the full Saint-Venant equations.

:::info Powered by EPA SWMM The core hydraulic calculations in this platform are executed using the Storm Water Management Model (SWMM) Version 5.2.4, originally developed by the US Environmental Protection Agency (EPA). SWMM is globally recognised as the gold standard for urban drainage and sewer modelling, providing industry-leading stability and accuracy for dynamic routing. :::

The Saint-Venant Equations

Unlike simplistic kinematic or steady-flow models (which assume uniform flow and cannot accurately simulate backwater effects or pressurised pipes), our engine uses Dynamic Wave Routing. This routing method solves the complete 1D Saint-Venant equations for conservation of mass (continuity) and momentum.

1. Continuity Equation (Conservation of Mass)

This equation ensures that the change in cross-sectional area (and thus volume) over time equals the net inflow minus outflow along the pipe segment.

$\frac{\partial A}{\partial t} + \frac{\partial Q}{\partial x} = 0$

Where:

• $A$ = Cross-sectional flow area ($m^2$)
• $Q$ = Flow rate ($m^3/s$)
• $t$ = Time ($s$)
• $x$ = Distance along the conduit ($m$)

2. Momentum Equation (Conservation of Momentum)

This equation balances the forces acting on the fluid, accounting for gravity, friction, and pressure differentials.

$\frac{\partial Q}{\partial t} + \frac{\partial \left( \frac{Q^2}{A} \right)}{\partial x} + gA \frac{\partial H}{\partial x} + gAS_f = 0$

Where:

• $H$ = Hydraulic head (water surface elevation, $m$)
• $g$ = Acceleration due to gravity ($9.81 m/s^2$)
• $S_f$ = Friction slope (head loss per unit length)

The terms in this equation represent:

1. Local Acceleration ($\partial Q / \partial t$): Change in momentum due to flow changing over time.
2. Convective Acceleration ($\partial(Q^2/A) / \partial x$): Change in momentum due to spatial changes in velocity (e.g., pipe narrowing).
3. Pressure Force ($gA \cdot \partial H / \partial x$): Driving force due to gravity and water surface slope.
4. Friction Force ($gAS_f$): Resistance to flow from the pipe walls.

Why Dynamic Wave Routing?

The primary advantage of solving the full momentum equation is the ability to accurately simulate complex hydraulic phenomena commonly found in urban drainage networks:

• Surcharging: When a pipe fills completely, it operates under pressure. The engine transitions seamlessly between open-channel flow and pressurised flow.
• Backwater Effects: High water levels at an outfall (e.g., a high tide) or behind a flow control structure (e.g., a Hydro-Brake) will propagate upstream, reducing the capacity of incoming pipes.
• Flow Reversal: If the downstream head exceeds the upstream head, water will flow backward up the pipe.
• Surface Flooding: When the hydraulic grade line (HGL) exceeds the cover level of a manhole, the excess water is calculated as flood volume.

Friction Losses (Colebrook-White)

To calculate the friction slope ($S_f$), the engine utilises the Colebrook-White equation, which is the standard methodology for pipe sizing in the UK.

$\frac{1}{\sqrt{\lambda}} = -2 \log_{10} \left( \frac{k_s}{3.7D} + \frac{2.51}{Re \sqrt{\lambda}} \right)$

Where:

• $\lambda$ = Darcy-Weisbach friction factor
• $k_s$ = Effective roughness height (e.g., $0.6 mm$ for standard concrete pipes)
• $D$ = Pipe diameter ($m$)
• $Re$ = Reynolds number

The $k_s$ value represents the physical roughness of the pipe material. Higher $k_s$ values increase resistance, slowing flow velocities and increasing depths.

Terminal Structures & Soakaways

In standard SWMM modeling, a network must typically route flow to an explicitly defined Outfall. However, in modern sustainable drainage systems (SuDS), a network may terminate entirely in a soakaway or infiltration basin without a piped outfall.

Our engine intelligently handles these Terminal Structures:

• If the lowest node in your network is defined as a soakaway or has a positive Infiltration Rate, the engine will not force an artificial outfall.
• The structure will act as a true terminal storage node. If the inflow volume exceeds the available tank storage and the infiltrated volume, the node will surcharge to the surface, and the excess volume is correctly reported as surface flooding.

Dynamic Side Infiltration

Physical soakaway design (such as BRE 365) relies on both the base area and the wetted side area of the structure for infiltration. As a tank fills, the surface area in contact with the surrounding soil increases, leading to a higher volumetric infiltration rate (L/s).

To perfectly mimic this physical behavior within a dynamic 1D model:

1. The engine calculates the footprint area (Base) and the perimeter of the structure.
2. It generates a custom Hydraulic Rating Curve ([OUTLET]) attached to the soakaway node.
3. This curve maps the exact depth of water in the tank to the corresponding combined wetted area (Base + Sides).
4. The engine converts the static infiltration rate ($mm/hr$) into a dynamic flow rate ($L/s$) that scales perfectly with the water depth during the storm event.

This approach ensures that side-infiltration is handled with mathematical precision at every time-step of the simulation, rather than relying on a simplified constant extraction rate.