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Manning's Equation — 24-inch CMP vs RCP Capacity

A capacity check on an existing 24-inch corrugated metal pipe (CMP) ditch-relief crossing, and the single most under-appreciated number in small-pipe drainage: roughness. Annular corrugations put CMP at n ≈ 0.024 against concrete's 0.012 — and since Manning's capacity is inversely proportional to n, the same barrel on the same grade carries half the flow. Sources: FHWA HDS-5; Chow, Open-Channel Hydraulics; AISI/NCSPA corrugated pipe design data.

The crossing

A farm-road crossing carries roadside ditch flow through an existing 40-ft run of 24-inch annular CMP at 0.30% grade, flowing as an open channel (unsubmerged inlet at the flows of interest). The drainage study upstream now delivers a 10-yr peak of 10.5 cfs to the crossing.

Pipe	24-inch annular CMP, D = 2.0 ft
Manning's n (CMP, 2⅔ × ½ in corrugations)	0.024 (n reference)
Slope S	0.30% = 0.003
Design Q (10-yr)	10.5 cfs

Step 1 · Full-flow capacity, CMP

The barrel's ceiling at n = 0.024

Full circle, r = 1.0 ft: A = π ft² = 3.142, R = D/4 = 0.500 ft
Q_full = (1.486/0.024) · 3.142 · 0.500^2/3 · √0.003
= 61.9 · 3.142 · 0.630 · 0.0548 = 6.7 cfs
V_full = 6.7/3.142 = 2.1 ft/s

The crossing fails before the math gets subtle. Design flow 10.5 cfs against a 6.7-cfs barrel — the pipe surcharges, the ditch ponds, and the road overtops in events well short of the 10-year storm. No partial-flow iteration needed when demand exceeds the full-flow ceiling by 55%.

Step 2 · Same pipe in concrete

n = 0.012 doubles the capacity

Q_full,RCP = (1.486/0.012) · 3.142 · 0.630 · 0.0548 = 13.4 cfs
Ratio: 13.4/6.7 = 2.0 = n_CMP/n_RCP = 0.024/0.012
V_full = 13.4/3.142 = 4.3 ft/s

Capacity scales exactly with 1/n — everything else in Manning's equation is geometry and slope. This is why "replace in kind" is not a hydraulic no-op when the existing pipe is CMP and the replacement is RCP, or vice versa.

Step 3 · Upsizing options

Three ways to pass 10.5 cfs

Option	n	Q_full @ 0.30%	Verdict
Existing 24″ CMP	0.024	6.7 cfs	Fails
Replace with 24″ RCP	0.012	13.4 cfs	Passes (28% margin)
Replace with 30″ CMP	0.024	12.2 cfs	Passes (16% margin)
Spiral-rib metal pipe, 24″	≈ 0.012–0.013	≈ 12–13 cfs	Passes — smooth-interior metal

30″ CMP check: D = 2.5 ft, A = 4.909 ft², R = 0.625 ft
Q = 61.9 · 4.909 · 0.625^2/3 · 0.0548 = 61.9 · 4.909 · 0.731 · 0.0548 = 12.2 cfs

Helical/spiral-rib metal pipe with a smooth interior achieves concrete-like roughness in a metal product — the roughness belongs to the corrugation profile, not the material.

Step 4 · When this analysis is the wrong one

Inlet control and submergence

Submerged inlet → culvert hydraulics, not open-channel Manning's. Once headwater exceeds roughly 1.2× the rise, the crossing behaves as a culvert: inlet control may govern regardless of barrel roughness. Run the HDS-5 culvert tool for the full headwater rating.
Inlet control is roughness-blind. If the crossing is inlet-controlled at design flow, upsizing from CMP to RCP at the same size buys little — the entrance, not the barrel, is the bottleneck. Check both.
Tailwater matters. High tailwater pushes the crossing to outlet control, where barrel friction (and therefore n) matters most — the case analyzed here.
Abrasion and corrosion. Invert loss in old CMP raises effective n further and eventually perforates; inspect before rehabilitating around an assumed 0.024.

Tools used in this example

Reproduce every step: Manning's equation (full-flow circular mode) with n from the Manning's n card. For the submerged/headwater case, the culvert tool and the entrance loss card. Companion example: 24-inch RCP partial flow.