15. Methods

This chapter says what StormSewer computes itself, with the equations and where they come from, and what it does not compute. The dividing line is simple: the SWMM engine does the simulation; StormSewer does the storm-sewer design arithmetic, the conversions in the mapping between the two, and nothing else. Every number below is worked by hand in VALIDATION.md and WORKED_EXAMPLE.md in the repository, and the tests that pin them run on every commit.

15.1 What the SWMM engine computes (and this manual does not re-explain)

Rainfall, evaporation and climate; surface runoff by the nonlinear reservoir; infiltration by Horton, modified Horton, Green-Ampt, modified Green-Ampt and Curve Number; groundwater; snowmelt; RDII; flow routing by steady, kinematic and dynamic wave; conduit geometry, storage geometry, critical and normal depth; pumps, orifices, weirs and outlets; minor losses, force mains, culverts, roadway weirs; water quality and LID; streets and inlets in 5.2. StormSewer runs the engine and reads what it wrote. Read the engine's own documents:

These are public-domain U.S. Government documents; the citations are the whole of what this manual says about the engine's physics.

15.2 Storm-sewer engine: overview

The design tool (chapter 12) is a peak-flow, steady pipe-network calculation of the kind a drainage manual describes:

1. Rational peak flow accumulated down a dendritic network, with the intensity at each pipe taken from an IDF curve at that pipe's own time of concentration.
2. Manning capacity, normal and critical depth, velocity and percent full per pipe.
3. A standard-step hydraulic grade line from the outfall upstream, with junction losses.
4. HEC-22 inlet interception at inlets, with bypass carried to the next inlet.
5. Catalog sizing and a design review.

Units are U.S. customary throughout (feet, acres, cfs, in/hr, minutes). Constants: Manning's K = 1.486 (3.280840^(1/3), the exact conversion, and the value Hydraflow Storm Sewers uses); g = 32.2 ft/s².

The network must be a tree draining to outfalls; loops and splits are rejected by the topological sort. Storage, pumps and diversions are not modelled here — that is the engine's job.

15.3 Hydrology

IDF curve.

i = a / (t + b)^c        i in in/hr, t in minutes

Coefficients come from the design basis, from a NOAA Atlas 14 PFDS CSV fitted by least squares per return period (storm-sewer workspace, File → Import NOAA Atlas 14 IDF), or from a Hydraflow .stm. A frequency factor Cf may raise the effective coefficient, min(C·Cf, 1), for the higher return periods, as HEC-22 and most DOT manuals require.

Rational method.

Q = ΣCA · i(t_c)        Q in cfs, ΣCA in acres, i in in/hr

The acre-inch-per-hour to cfs factor of 1.008 is taken as 1, the usual drainage-manual practice. ΣCA accumulates downstream; i falls as t_c grows, so Q rises less than proportionally with area.

Time of concentration. Each pipe's t_c is the larger of its own inlet time and the upstream t_c plus the travel time through the upstream pipe at its design velocity, L / V, floored at the project's minimum Tc. Inlet times are entered, or estimated:

• Kirpich (1940), l in ft, s in ft/ft;
• NRCS TR-55 (1986) Eq. 3-3 sheet flow, T_t = 0.42 (nL)^0.8 / (P_2^0.5 s^0.4) in minutes, with P_2 the 2-year 24-hour depth in inches;
• FAA (1970), T_c = 1.8 (1.1 − C) L^0.5 / S^(1/3), S in percent.

Tools → Tc Calculator… computes all three and a TR-55 multi-segment worksheet.

The C-from-%Imperv mapping (SWMM → design):

C = 0.20 + 0.75 · (%Imperv / 100)

A straight line from 0.20 (fully pervious) to 0.95 (fully impervious), the band the Rational-C tables give for lawns and pavement. Area-weighted when several subcatchments drain to one node. The inverse, %Imperv = 100 (C − 0.20) / 0.75 clamped to 0–100, is used on import. The inlet time for a subcatchment is Kirpich over the flow length Area / Width at %Slope. This is a stated assumption, not a derivation: a SWMM subcatchment has no C, and a C has to come from somewhere. Override it by editing the design basis or the imported project.

15.4 Hydraulics

Manning full-flow capacity.

Q_full = (K/n) · A · R^(2/3) · √S       A = πD²/4,  R = D/4 for a circle

Box, elliptical and arch sections use their exact geometry (no table lookups). The maximum open-channel capacity of a circular pipe is about 1.076 × Q_full, at y/D ≈ 0.938; flows above it are surcharged.

Slope is from the inverts, (inv_up − inv_dn) / L; a pipe's own end inverts, where the SWMM offsets give them, override the node inverts. A zero or adverse slope uses the basis's minimum slope for capacity and is flagged.

Normal depth is found by iteration on the section's A R^(2/3) at the design flow; critical depth by iteration on Q² T / (g A³) = 1. For a circular section at depth y:

θ = 2 arccos((r − y)/r),   A = r²(θ − sin θ)/2

Velocity is Q / A(y_n), the actual area at normal depth, not the full barrel. Percent full is a discharge ratio, Q / Q_full, not a depth ratio.

Hydraulic grade line. A backward pass from the outfall upstream, one pipe at a time:

• the outfall HGL is the tailwater when set, else the outfall invert (a free outfall);
• each pipe is classified by its normal depth against its critical depth, with a ±2 % dead band, and solved accordingly:
  • pressurised (design flow above the open-channel maximum, or the downstream HGL above the crown): full-pipe friction over the reach, S_f = (Q / K_conv)² with the full-section conveyance K_conv = (K/n) A R^(2/3);
  • supercritical (normal depth below critical) and not drowned from downstream: controlled from upstream; the upstream water surface is the reach's own normal depth and tailwater does not back up through it (no hydraulic-jump analysis);
  • subcritical: a true standard-step gradually-varied-flow profile from the downstream water surface (at least critical depth), the reach divided into sub-reaches, the friction slope S_f = (Q/K_conv)² evaluated at the actual local depth, and the energy balance EGL_up = EGL_dn + S_f,avg · Δx solved for the subcritical depth at each station; when no root exists the profile relaxes to normal depth;
  • adverse slope: the downstream HGL is recorded and no head loss is propagated upstream, since S_f is undefined;
• at each structure the entering flow loses H = K · V²/2g with the basis's junction K (plus a geometry-aware bend term for the deflection between the incoming and outgoing pipe when the workspace's bend-loss coefficient is non-zero); a supercritical reach is upstream-controlled, so a downstream structure loss does not raise its upstream HGL. When HEC-22 access-hole losses are switched on in the storm-sewer workspace, K_ah = K_o C_D C_d C_Q C_p C_B with K_o = 0.1 (b/D_o)(1 − sin θ) + 1.4 (b/D_o)^0.15 sin θ and the HEC-22 correction factors for relative diameter, flow depth and plunging, C_Q = 1 and benching C_B supplied (HEC-22 Ch. 7). The access-hole method is opt-in and is not yet pinned to a published FHWA worked example; the simple K is the default.

Freeboard is rim minus HGL at each structure; a negative freeboard is a surcharge to the surface.

VALIDATION.md §6 works this on a three-pipe trunk to six decimal places, and §8 runs a real Civil 3D network side by side with Hydraflow Storm Sewers, agreeing to 0.04 % on the terminal lines and 2.5 % on the outfall line with every difference explained.

15.5 Sizing and review

Catalog. RCP 8, 10, 12, 15, 18, 21, 24, 27, 30, 33, 36, 42, 48, 54, 60, 66, 72 in. (Metric sizes exist for the storm-sewer workspace's SI input mode: 300 to 1800 mm.)

Rule. For each pipe, the smallest catalog diameter for which, at the design flow and the pipe's slope:

• the flow does not exceed the open-channel maximum (no surcharge);
• velocity does not exceed the maximum (10 ft/s);
• percent full does not exceed the limit (85 %).

Minimum velocity (2 ft/s) is not a sizing filter: velocity falls as diameter grows, so rejecting a size for low velocity would reject every larger size too and report "no solution" on flat sewers. Low velocity is a review finding that says "steepen the pipe" instead. A pipe already meeting the criteria is reported as adequate at its current size. If no catalog size works, the largest is reported with its hydraulics as a diagnostic.

Review (§12.5): velocity band, percent full, surcharge, slope (adverse is an error), cover from rim to crown at each end using the section's real rise, size progression downstream, HGL freeboard.

15.6 HEC-22 inlets

On-grade inlets (HEC-22 Ch. 4, gutter flow and inlet interception):

• Gutter spread from Izzard's form of Manning for a triangular section, Q = (0.56/n) S_x^1.67 S_L^0.5 T^2.67, solved for T; gutter velocity V = Q / (½ S_x T²).
• Grate on grade: E = R_f E_o + R_s (1 − E_o), with E_o the frontal fraction, R_f the frontal capture (1 below the grate's splash-over velocity, which is grate-specific and is an input), R_s the side capture.
• Curb opening on grade: L_T = 0.6 Q^0.42 S_L^0.3 (1/(n S_x))^0.6, E = 1 − (1 − L/L_T)^1.8, or 1 when L ≥ L_T.
• Combination on grade is taken as the grate's efficiency; summing the two would count the same gutter flow twice.

Sag inlets: grate weir Q = 3.0 P d^1.5 with P = L + 2W (the curb side excluded), transitioning to orifice Q = 0.67 A √(2g d), the smaller governing; curb opening weir Q = 2.3 (L + 1.8W) d^1.5 for d ≤ h, orifice Q = 0.67 h L √(2g (d − h/2)) when submerged. A clogging fraction reduces open area and perimeter.

The flow arriving at an inlet is its local catchment's peak at the intensity for its own inlet time (floored at Min Tc), not the pipe system's accumulated Tc — HEC-22 §4 and Hydraflow's "i Inlet". Intercepted flow is E·Q on grade or the sag capacity capped at Q; the bypass is routed to the next designated inlet. The inlet pass is a surface check and does not change the pipe design flows, which assume everything reaches the system.

15.7 Design storms

Project → Design Storm… (§8.9) builds a hyetograph by one of six methods. All sources are public; the tables are checked in the tests against the cited figures. Depths are in the model's rain unit and nothing is converted.

NRCS (SCS) 24-hour Type I, IA, II, III. The cumulative mass curves are the NRCS TR-20 tabular rainfall distributions (Type IA and II from the 1982 tables, Type I and III from the 1992 tables shipped with TR-20 2/92) at 0.1-hour points (Type IA at 0.5-hour points), scaled by the 24-hour depth you enter and differenced at your time step. Their derivation and the hourly Type II ratios are in USDA-NRCS National Engineering Handbook Part 630, Chapter 4, §630.0403 and figure 4-36; the 0.1-hour tables are also reproduced in WSDOT Highway Runoff Manual M 31-16.04 Appendix 4C, tables 4C-3 and 4C-4. The Type II nested ratios of figure 4-31 (5 min 0.114, 10 min 0.201, 15 min 0.270, 30 min 0.380, 1 h 0.454, 2 h 0.538, 3 h 0.595, 6 h 0.707, 12 h 0.841) are kept as a check on the table.

NRCS NOAA Atlas 14 regional 24-hour, regions A–D. NEH 630 Chapter 4 §630.0408, figure 4-72: the ratio of the 5-minute … 12-hour depth to the 24-hour depth for each region, built into a curve by the chapter's nesting rule — every shorter duration's depth centred inside the longer one (§630.0403 A(9), §630.0407) — with log-linear interpolation between the tabulated durations. The handbook additionally smooths in WinTR-20; this does not.

Alternating block from an IDF curve. For blocks of Δt minutes over a duration D: the cumulative depth at each block boundary, P(t) = i(t) · t / 60 with i = a/(t+b)^c; the incremental depth of block k, P(kΔt) − P((k−1)Δt), never negative; the increments sorted descending, the largest at the centre block and the rest alternately right and left of it, spilling to the other side at an edge; each block's intensity depth / (Δt/60). The storm reproduces the curve's average intensity over every duration up to D. Chow, Maidment & Mays, Applied Hydrology (1988) §14.4. The same routine makes the storm when a storm-sewer project is imported (§13.1), with Δt = 5 min and D = 120 min.

Alternating block from a NOAA Atlas 14 PFDS row. The same placement, but the cumulative depths at the tabulated durations come straight from the pasted PFDS csv (5-min:,d1,d2,… under by duration for ARI (years):,1,2,5,…) for the chosen return period, interpolated between durations; no curve is fitted.

Chicago (Keifer & Chu 1957). From i = a/(t+b)^c, a duration D and a peak position r (the peak is at t_p = r·D). With P(t) = i(t)·t/60 the IDF depth over t minutes, the cumulative depth in the t_b minutes before the peak is r · P(t_b / r) and in the t_a minutes after it is (1 − r) · P(t_a / (1 − r)); the mass curve is r·P(D) − r·P((t_p − t)/r) before the peak and r·P(D) + (1 − r)·P((t − t_p)/(1 − r)) after it, and the total is P(D). Differenced at the time step, that gives the hyetograph whose average intensity over any interval centred on the peak equals the IDF curve. Chow, Maidment & Mays §14.4.

Uniform. The depth spread evenly over the duration.

15.8 Conduit lengths

Not automatic. A conduit drawn on the map is given its drawn length, in map units, once, at creation. Project → Compute Conduit Lengths… (§3.10) computes the geometric length through the vertices, L = Σ √(Δx² + Δy²) over the segments from the start node through each vertex to the end node, times a map-to-model factor from [MAP] Units and FLOW_UNITS (1 for feet→feet or metres→metres, 0.3048 for map feet in a metric model, 3.28084 for map metres in a US model, undefined for degrees), and writes the ticked ones. It is never run without being asked.

15.9 Units

SWMM. FLOW_UNITS decides the unit system of the whole model (RM I §1.5): CFS, GPM and MGD are U.S. customary (feet, acres, inches, in/hr), CMS, LPS and MLD are SI (metres, hectares, millimetres, mm/hr). The engine converts nothing when the keyword changes; it interprets every number in the declared system, so a weir coefficient of 3.33 in a CMS model is read as a metric coefficient. StormSewer labels fields by the keyword and, when you change it in the Options dialog, opens the unit-switch wizard (§8.2), which lists the groups of values the engine will misread and converts the ones you tick with

The checklist is §16.7.

Storm-sewer engine. Computes in U.S. customary. The storm-sewer workspace's SI input mode converts inputs on the way in:

Results (schedules, reports) remain U.S. customary; full SI output is on the roadmap. The SWMM design panel refuses metric models rather than convert silently (§12.2).

Offsets. With LINK_OFFSETS DEPTH a link's InOffset/OutOffset are heights above the node invert. With ELEVATION they are absolute elevations, and StormSewer converts them to depths as offset − node invert, never below zero, wherever it needs a pipe invert (profile, design mapping, CSV). Reading never writes anything back. Changing the keyword in the Options dialog offers to rewrite every offset with its node's invert in the same undo step (conduits from the from-node for InOffset and the to-node for OutOffset; orifices, weirs and outlets from their inlet node), so the geometry keeps its meaning; without that the pipes move. The engine's own silent corrections are in §16.6.

15.10 Result statistics

The Results views compute only: five-class breaks by equal interval or quantile over the frame's values; per-series min, max, mean, sum and the top-N local maxima; peak depth, inflow, flooding, flow, velocity and capacity per object over the run (the maximum of the reported values); and the difference and percent difference between two runs' peaks. Nothing is interpolated between reporting periods.