Issue 006 · August 26, 2026

Your low-flow orifice is a weir half the time

Every detention-pond outlet opening has two personalities: it is a weir at low stage and an orifice once it submerges, and the handoff between the two happens exactly where your small-storm peaks live. The design manuals hand you both equations and, if you're lucky, a one-line note to use the lesser. Here is what the transition actually looks like on a real low-flow opening, and the two mistakes that put 20–40% error on a stamped release rate.

TL;DR. An outlet opening follows the weir equation until the water surface is roughly $1.2\times$ the opening height above the invert, then the orifice equation takes over — the governing discharge at any stage is $\min(Q_{weir}, Q_{orifice})$. On the 12″ × 9″ opening worked below, applying the orifice equation alone overpredicts low-stage discharge by 13–20%, applying the weir equation alone overpredicts high-stage discharge by 44–84%, and measuring orifice head to the invert instead of the centroid — the classic half-head mistake — inflates discharge by ~27% right at the top of the transition. On small openings the centroid offset is a large fraction of the head, so small ponds feel these errors hardest.

Two equations, one hole

Take the most ordinary outlet detail in land development: a rectangular low-flow opening cut into a riser wall or weir plate. While the water surface is below the top of the opening, flow spills over the opening's invert edge and the discharge is set by the weir equation. Once the opening submerges, the free surface detaches from the opening and the discharge is set by the orifice equation:

$$Q_{weir} = C_w \, b \, H^{3/2} \qquad\qquad Q_{orifice} = C_d \, A \sqrt{2 g \, H_c}$$

with $C_w \approx 3.0$ (US units, sharp-edged rectangular opening), $b$ the opening width, $H$ the head above the invert; $C_d \approx 0.6$, $A$ the opening area, and $H_c$ the head above the opening centroid — not the invert. Both coefficients are the textbook values (Brater & King; FHWA HEC-22 uses the same pair for storage outlets); check end-contraction and submergence corrections on a final design.

Neither equation is wrong. What goes wrong is the handoff. The weir equation grows as $H^{3/2}$; the orifice equation grows as $\sqrt{H}$. At low stage the weir value is the smaller of the two and physically governs; at high stage the orifice value is smaller and governs. In the band between — roughly one to two opening-heights above the invert — the flow is genuinely messy: partially submerged, air-entraining, neither derivation strictly valid. Standard practice, and what the routing programs (HydroCAD, ICPR, SWMM's outlet links, HydroComplete) do internally, is to compute both at every stage and take the minimum. It is not an approximation you should feel bad about; it is the only defensible move, and it happens to be conservative in the transition band.

The worked example

A dry detention pond's low-flow opening: rectangular, 12 inches wide, 9 inches tall ($b = 1.0$ ft, $D = 0.75$ ft, $A = 0.75$ ft², centroid $0.375$ ft above the invert). Invert at stage 0.00. $C_w = 3.0$, $C_d = 0.6$. Both equations at each stage, governing value in bold logic — minimum wins:

Stage above invert (ft)	Q_weir (cfs)	Q_orifice (cfs)	Governs
0.25	0.38	— (not submerged)	Weir
0.50	1.06	— (not submerged)	Weir
0.75	1.95	2.21	Weir
0.92	2.65	2.67	Crossover
1.00	3.00	2.85	Orifice
1.25	4.19	3.38	Orifice
1.50	5.51	3.83	Orifice
2.00	8.49	4.60	Orifice

Three things to read off that table:

The crossover lands at stage 0.92 ft — about $1.2\times$ the opening height. That ratio is not special to this geometry; run the algebra on other rectangular openings and the weir-to-orifice handoff keeps landing in the 1.0–1.8 $\times D$ band. Which is exactly the stage range where a small pond's water-quality and 1-year peaks sit, because we deliberately size low-flow openings small. The transition zone is not an edge case on small ponds. It is the operating point.
Orifice-only is a low-stage error. Treating the opening as an orifice from the invert up (a common spreadsheet shortcut) reads 2.21 cfs at stage 0.75 where the real, weir-controlled discharge is 1.95 — a 13% overprediction, growing to ~20% at mid-opening stages where the opening isn't even submerged yet.
Weir-only is a high-stage disaster. Carrying the weir equation past the crossover reads 5.51 cfs at stage 1.5 (real: 3.83, +44%) and 8.49 cfs at stage 2.0 (real: 4.60, +84%). Every foot of stage makes it worse, because $H^{3/2}$ outruns $\sqrt{H}$.

The half-head mistake

The subtler error hides inside the orifice equation itself: $H_c$ is measured to the centroid of the opening, not the invert. On a big opening under a lot of head the distinction hardly matters. On a small opening it is the whole game, because the centroid offset ($D/2 = 0.375$ ft here) is a large fraction of the total head at the stages that matter:

Stage (ft)	Correct: H_c to centroid	Wrong: H to invert	Overprediction
1.00	2.85 cfs	3.61 cfs	+27%
1.25	3.38 cfs	4.04 cfs	+19%
2.00	4.60 cfs	5.11 cfs	+11%

Twenty-seven percent, at the exact stage where the pond's compliance storm peaks, from a head measured to the wrong datum. The error decays as the pond fills — which means it is largest for the small storms regulators actually check release rates against. I keep a fuller version of this trap, with the routing consequences, in the free orifice detention-pond worked example on pe-calc, alongside the orifice calculator that measures head to the centroid so you don't have to remember.

Why an overpredicted outlet is not a conservative error

Every mistake above overpredicts outlet capacity, and it is tempting to file that under "conservative." It is the opposite. Overpredicted outlet capacity means the routing thinks the pond drains faster than it will: the modeled peak stage is too low, the modeled release rate meets the pre/post limit on paper while the real structure exceeds it, and the freeboard you certified is partly fictional. The stage-discharge curve is the one input the routing trusts absolutely — every cell of the modified-Puls table downstream of it inherits the error.

The fix costs nothing: build the composite rating by computing weir and orifice at every stage increment, take the minimum per device, sum the devices, and only then hand the curve to the routing. If your software builds outlet ratings for you, spot-check one stage in the transition band by hand — it is a two-line calculation, and it tells you immediately which convention the tool uses for orifice head.

Build the whole rating, not one point

HydroComplete's pond module composites weir, orifice, and outlet-barrel controls across the full stage range — min-per-device, centroid-referenced heads — and routes the result with every formula visible on the page, so the reviewer can audit the exact curve the peak stage came from.

Free 14-day trial See the tour

New since last issue: the curve-number workflow I use for the runoff side of these ponds is now a free, open-source QGIS plugin — HydroCN for QGIS fetches SSURGO soils, NLCD land cover, and 3DEP terrain and builds a composite CN for any watershed polygon, with the TR-55 tables cited in the output. GPL, on GitHub now, QGIS plugin-repository listing pending review.