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.

PieceValues
Pond bottom100.0
Low-flow orifice in the riser wall4 in, invert 100.0, Cd 0.6
Riser box4 ft × 4 ft, crest 104.0
Crest weirL = 16 ft (full perimeter), Cw 3.0
Riser top as a horizontal orificeA = 16 ft², Cd 0.6
Barrel24 in RCP, L 80 ft, S 0.010, n 0.013, Ke 0.5
Barrel inverts98.50 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. Qbarrel 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 + Ke + 29 n² L / R1.33] 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

StageLow orifice + crest, cfsBarrel can carry, cfsOutlet passes, cfsControlsSum in parallel, cfs
104.000.832.20.8low orifice33.0
104.256.833.16.8crest weir40.0
104.5017.834.017.8crest weir51.9
104.7532.134.932.1crest weir67.0
105.0048.935.835.8barrel84.7
105.5089.237.537.5barrel126.6
106.00110.039.139.1barrel149.1
107.00134.542.242.2barrel176.7
108.00155.345.045.0barrel200.3

Three things in that table are worth a second look.

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:

BarrelBarrel takes over atStage to pass 60 cfs
24 in RCP104.80 (35.1 cfs)114.35
30 in RCP105.08 (54.5 cfs)106.11
36 in RCP105.37 (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.

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

Running it yourself

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.

— 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.

More from the Hydraulic Notebook

← Previous Issue 009 — A 300-metre snap and a 17 percent error: what automated watershed delineation gets wrong

← Issue 006 Your low-flow orifice is a weir half the time

← Issue 003 Why your Manning's n estimate is probably wrong (and why it matters more than you think)

Size the pieces: Culvert calculator · Orifice calculator · Sharp-crested weir calculator

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