Issue 010 · November 1, 2026

Nine feet of headwater nobody drew: when the barrel takes over a pond outlet

A riser outlet has three ways to limit flow: the crest acts as a weir, the open top acts as an orifice, and the pipe out of the box acts as a culvert. Most outlet sheets check the first two carefully and give the third a single line. On the outlet below, the barrel takes over less than a foot above the crest, and from then on it's the only thing that matters.

TL;DR. A 4 ft × 4 ft riser with its crest at 104.0, draining through 80 ft of 24-inch RCP. The crest weir governs for the first 0.8 ft. At stage 104.80 (35.1 cfs) the barrel takes over, and the riser top never gets to act as an orifice. To pass 60 cfs, the riser alone would need stage 105.15. Behind the 24-inch barrel it needs 114.35, about nine feet higher. If you add the devices in parallel, the rating at stage 106 reads 149 cfs; the barrel lets through 39. The tell on a rating curve: plot stage against Q². Orifice flow plots as a straight line through the riser crest. Barrel flow plots as a straight line through a point below the crest.

The outlet

This is a typical small-pond outlet, made up for the example. Every number below comes from a script that rates each piece separately and takes the smaller flow at each stage. The barrel uses the FHWA HDS-5 culvert method, checking inlet and outlet control and taking the higher headwater.

Piece	Values
Pond bottom	100.0
Low-flow orifice in the riser wall	4 in, invert 100.0, Cd 0.6
Riser box	4 ft × 4 ft, crest 104.0
Crest weir	L = 16 ft (full perimeter), Cw 3.0
Riser top as a horizontal orifice	A = 16 ft², Cd 0.6
Barrel	24 in RCP, L 80 ft, S 0.010, n 0.013, Ke 0.5
Barrel inverts	98.50 in the box, 97.70 at a free outfall

Three devices in series, not side by side

Water gets into the box through the low-flow orifice and over the crest (or, at high stage, through the open top). It leaves through the barrel, and there is no other way out. So the riser openings and the barrel work in series. The outlet passes whichever is smaller: what the openings can deliver, or what the barrel can carry.

$$Q = \min\Big(Q_{\text{low}} + \min\big(\underbrace{C_w L H^{1.5}}_{\text{crest weir}},\ \underbrace{C_d A\sqrt{2gH}}_{\text{top orifice}}\big),\ \ Q_{\text{barrel}}(\text{stage})\Big)$$

Here H is the head above the crest. Q_barrel is the HDS-5 discharge at that headwater. With the barrel entrance submerged under inlet control, HDS-5 Appendix A gives:

$$\frac{HW}{D} = c\left(\frac{Q}{A D^{0.5}}\right)^2 + Y - 0.5\,S \qquad c = 0.0398,\ Y = 0.67\ \text{(square edge, Table A.1)}$$

Under outlet control, it's the full-flow energy equation, H = [1 + K_e + 29 n² L / R^1.33] V²/2g, plus the outlet depth, minus the fall of the barrel. The barrel's headwater is whichever of the two is higher.

The rating

Stage	Low orifice + crest, cfs	Barrel can carry, cfs	Outlet passes, cfs	Controls	Sum in parallel, cfs
104.00	0.8	32.2	0.8	low orifice	33.0
104.25	6.8	33.1	6.8	crest weir	40.0
104.50	17.8	34.0	17.8	crest weir	51.9
104.75	32.1	34.9	32.1	crest weir	67.0
105.00	48.9	35.8	35.8	barrel	84.7
105.50	89.2	37.5	37.5	barrel	126.6
106.00	110.0	39.1	39.1	barrel	149.1
107.00	134.5	42.2	42.2	barrel	176.7
108.00	155.3	45.0	45.0	barrel	200.3

Three things in that table are worth a second look.

The barrel takes over at 104.80, only 0.8 ft above the crest, at 35.1 cfs. The crest weir would have handed off to the riser-top orifice at 105.61, but the outlet never gets there.
Above the handoff, the riser hardly matters. Between stages 105 and 108 the crest could pass three times what the barrel takes. You could double the riser and the pond would rise exactly the same.
The parallel column is the classic mistake. Enter the riser and the barrel as two separate outlets in any tool that adds device flows, and that column is your rating: 149 cfs at stage 106 instead of 39. The pond routes far too low, and the emergency spillway goes unchecked.

What it costs

Take a design flow of 60 cfs. The riser alone would pass it at stage 105.15. Here is the stage the pond needs with each barrel, all with the same riser, length and slope:

Barrel	Barrel takes over at	Stage to pass 60 cfs
24 in RCP	104.80 (35.1 cfs)	114.35
30 in RCP	105.08 (54.5 cfs)	106.11
36 in RCP	105.37 (78.3 cfs)	105.15 (riser controls)

Nine feet of headwater from one pipe size. In practice the 24-inch pond overtops the embankment long before 114, which is the point: the outlet sheet says the riser handles it, and the barrel says otherwise.

Telling them apart from the curve alone

Sometimes all you have is someone else's stage-discharge table and you need to know what controls it. Plot stage against Q².

Weir control curves. Q goes as H^1.5, so stage goes as Q^2/3 and the plot bends. Over 104.1 to 104.6, a straight-line fit only reaches R² = 0.89.
Orifice control is a straight line through the crest. Fitting 104.5 to 105.5 for the riser top alone gives an intercept of 104.00 and a slope of 0.000168 ft/cfs². The intercept is the crest, because that's where the orifice head is measured from.
Barrel control is a straight line through a point below the crest. Fitting 105 to 108 for the barrel gives an intercept of 99.83 and a slope of 0.00403 ft/cfs², 24 times steeper. That intercept isn't arbitrary. It's the barrel invert plus D(Y − 0.5S) from the submerged inlet equation: 98.50 + 2 × (0.67 − 0.005) = 99.83.

A shortcut that works on a log plot: measure head from the crest and find the slope of log Q against log H. A weir gives 1.50 and an orifice gives 0.50. On the barrel-controlled stretch here it's 0.16 to 0.23. An exponent below one half means the head is measured from the wrong datum. The real one is below the crest, and the only thing down there is the pipe.

At stage 107 this barrel is in inlet control, but only just: the headwater is 8.50 ft for inlet control and 8.13 ft for outlet control. Make the barrel longer or flatter, or put tailwater on the outfall, and outlet control takes over. The Q² plot stays close to straight, but its intercept moves toward the outlet's hydraulic grade line. Either way it sits well below the crest.

Two honest caveats

The box doesn't always fill to pond level. Taking the smaller of the two flows assumes that once the barrel controls, the box water surface rises to the pond level and the openings drown. That's the usual simplification for a rating table. In reality, near the handoff the box level is somewhere in between and the openings act as submerged orifices driven by the pond-minus-box difference. A dynamic model solves for the box level directly.
HDS-5 doesn't have a "riser box" entrance. I used the square-edge headwall constants (Ke 0.5), the closest tabulated case. A barrel entrance in the floor of a box with water dropping onto it is rougher than that, so treat the barrel capacity here as on the generous side.

Running it yourself

Each device alone, free: the culvert calculator (HDS-5 inlet and outlet control), the orifice calculator and the sharp-crested weir calculator on pe-calc.
The barrel rating, with every step shown: HydroComplete's culvert outlet rates a barrel with HDS-5 inlet and outlet control, using its real length, slope, n and Ke. The barrel column above came from that routine. The worked 48-inch CMP inlet/outlet control example walks through one. When the riser and barrel are in series, rate the barrel separately and cap the riser rating with it.
The whole outlet, with the box level solved: in AquaSWMM, build it as it's built in the field. The pond is a storage unit, with an orifice and a weir into a small storage node for the box, and a conduit with an HDS-5 culvert code from the box to the outfall. Run dynamic wave, and the barrel backs water up into the box exactly when it should. The model shows the handoff on the box's depth plot instead of hiding it in a min() function.

Check the barrel before the riser

HydroComplete rates culvert barrels with HDS-5 inlet and outlet control and puts every equation on the report, with the numbers that went into it. AquaSWMM models the whole riser box in the SWMM engine, dynamic wave included.

Open HydroComplete (free trial) See AquaSWMM

— Michael Flynn, PE
Next issue: the far end of that 24-inch barrel. At stage 107 it runs at 13.4 ft/s, and three common riprap sizing methods disagree about what it takes to keep that jet from digging a hole.