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Orifice Sizing for a Detention Pond — Drawdown Worked Example

Sizing the water-quality orifice on a dry detention pond riser: release the treatment volume over a target drawdown time (48 hours here; many manuals specify a 2–5 day window). The head falls as the pond drains, so the discharge falls with it — and the single most common sizing error is treating the average head as half the maximum. We work the exact falling-head solution and show where the shortcut goes wrong. Sources: standard orifice hydraulics (Brater & King); typical state stormwater design manuals.

The pond

Water-quality volume WQ_v	12,000 ft³
Depth of WQ pool above orifice, h₀	3.0 ft
Pond shape over that stage range	≈ prismatic (vertical-sided equivalent), A_s = 4,000 ft²
Target drawdown	48 hr = 172,800 s
Orifice coefficient C_d	0.60 (sharp-edged plate; see C_d card)

Step 1 · The falling-head equation

Drain time of a prismatic pond through an orifice

Orifice: Q(h) = C_d · a · √(2gh)
Continuity: A_s dh/dt = −Q(h) → integrate h₀ → 0:

T = 2 A_s √h₀ / (C_d · a · √(2g)) = 2V / Q_max

where V = A_sh₀ and Q_max = C_da√(2gh₀). The time-averaged release is therefore exactly half the maximum: V/T = Q_max/2.

Step 2 · Solve for the orifice area

T = 48 hr → a

Required: a = 2V / (T · C_d · √(2g h₀))
√(2gh₀) = √(64.4 · 3.0) = 13.90 ft/s
a = 2(12,000) / (172,800 · 0.60 · 13.90) = 24,000 / 1.441×10⁶ = 0.0167 ft²

d = √(4a/π) = √(0.0212) = 0.146 ft = 1.75 in

Check the 1.75-in plate: a = π/4 (1.75/12)² = 0.0167 ft²
Q_max = 0.60 · 0.0167 · 13.90 = 0.139 cfs
T = 2(12,000)/0.139 = 172,300 s = 47.9 hr ✓

Step 3 · The half-head mistake

Why "average head = h/2" undersizes the orifice

Shortcut (wrong): Q_req = V/T = 12,000/172,800 = 0.0694 cfs at h_avg = 1.5 ft
a = 0.0694 / (0.60 · √(64.4 · 1.5)) = 0.0694/5.90 = 0.0118 ft² → d = 1.5 in

Actual drain time of the 1.5-in plate: a = 0.0123 ft², Q_max = 0.102 cfs
T = 24,000/0.102 = 234,500 s = 65 hr — 36% over target

Because Q ∝ √h, the correct "average head" is h₀/4, not h₀/2. The time-average of √h over a linear drain is half of √h₀, so the average discharge is Q_max/2 — equivalent to evaluating the orifice at one-quarter of the starting head. The h/2 shortcut overstates the average release by 41% and delivers a pond that drains a day late. Whether 65 hours "fails" depends on the manual — a 2–5-day window forgives it; a 48-hour maximum does not.

Step 4 · Practical detailing

Beyond the diameter

Plate	Q_max (cfs)	Drain time	Note
1.5 in	0.102	65 hr	The h/2 shortcut's answer
1.75 in	0.139	48 hr	Target
2.0 in	0.182	37 hr	If the manual sets a 72-hr max and clogging governs

Clogging is the real enemy. Many manuals set a minimum orifice (commonly 1–3 in) and require a trash rack or internal skimmer/reverse-slope pipe. A 1.75-in hole needs protection to survive its first leaf season.
Pond geometry is rarely prismatic. With sloping banks, A_s shrinks as the pond drains and the tail of the drawdown slows further — a stage-storage routing (or the manual's method) refines the answer. The prismatic solution here is the standard first cut.
The WQ orifice is one opening on a multi-stage riser. The 2-, 10-, and 100-yr stages stack above it; each is sized against its own release target with the orifice/weir tools.

Tools used in this example

Reproduce every step: orifice flow tool with C_d from the discharge coefficient card, and reservoir routing for the multi-stage flood events. The treatment volume itself comes from the local manual's water-quality criteria with the runoff depth tool.