The Hydraulic Notebook

Terrain delineation from USGS 3DEP elevation data matched published drainage areas within −0.8% to +2.4% at three North Carolina gauges, from 2.6 to 49 mi². The biggest error had nothing to do with the terrain: at a 300 m pour-point snap, Cataloochee Creek's outlet jumped past a confluence and the area came out 17.2% high. Anywhere from 0 to 150 m gave −0.2%.

Couple a 2D surface to an EPA SWMM network and every cubic foot crosses the rim twice. On a surcharged test model the surface receives 5,360 ft³ against the engine's 0.040 MG of flooding, 1,454 ft³ drains back through open lids, and the surface balance closes to 0.0000%. The rim is not the depth you typed, and a coupled model can balance one ledger perfectly while wrecking the other by 667%.

The same four-line trunk through Hydraflow Storm Sewers and a from-scratch open-source engine: slopes, C·A, intensity, surcharge calls and the inlet schedule agree exactly, the outfall flow differs by 2.5% and the HGL by half a foot. Three decisions the Rational method leaves to the programmer, worked with the numbers: which velocity feeds travel time, how a surcharged reach loses head, and what K the last inlet gets.

A pond outlet opening is a weir at low stage and an orifice once it submerges — and the crossover lands at ~1.2× the opening height, exactly where small-storm peaks live. Worked example: orifice-only overpredicts low-stage discharge 13–20%, weir-only overpredicts high-stage discharge 44–84%, and the head-to-invert "half-head" mistake adds 27% right at the compliance storm. Build the composite rating; take the minimum.

Wahl (2004) showed the empirical breach regressions carry factor-of-two-to-four uncertainty on peak Q and recommended Monte Carlo. Twenty years later every breach memo still reports a single number. Teton calibration: deterministic estimate misses the observed peak by ~80%; the 5–95% ensemble brackets it. Built on the EMS-submitted swmm-breach Python package.

SWMM gives you a discharge at every node and almost nothing about local turbulence at a bridge pier or outfall. The gap between Manning's-class screening and full RANS CFD is forty years old. Built on the JWMM-submitted Adaptive Lagrangian Refinement post-processor — a 200-particle VPM that recovers 99.8% of a 6,000-particle baseline at 20× the speed.

A worked example showing why a 15% swing in Manning's roughness coefficient produces a 20% swing in design discharge — and a practical way to bound the real uncertainty before you sign and seal.

The two most-used Tc formulas can disagree by 2× on the same watershed. Kirpich was calibrated on rural Tennessee in 1940; NRCS lag is calibrated for modern urban/suburban work. Pick the wrong one and your peak flow is off by 30%.

Q = C·I·A is the simplest peak-runoff equation in civil engineering. The C is also the dirtiest number — varying by 4× for the same land cover depending on whose table you read. Why the disagreement exists, and what to actually use.