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36-inch CMP Road Crossing — HDS-5 Inlet vs Outlet Control Worked Example

A county gravel-road culvert replacement over an intermittent stream. The 25-year peak discharge is 42 cfs from an upstream NRCS/TR-55 basin; the county limits headwater to HW/D ≤ 1.25 so the road grade is not overtopped at the design event. FHWA HDS-5 requires computing both inlet control (entrance geometry limits flow) and outlet control (barrel friction + tailwater limits flow) and taking whichever produces the higher headwater. Sources: FHWA Hydraulic Design of Highway Culverts (HDS-5, FHWA-HIF-12-026), NRCS TR-55 for the design hydrograph basis, and HEC-14 for outlet protection.

The crossing

A 36-inch corrugated metal pipe (CMP, 2⅔ × ½ in corrugations) replaces a failing 30-inch pipe on a county gravel road. The intermittent channel downstream is shallow at low flow; survey gives tailwater depth TW = 0.5 ft above the outlet invert at Q₂₅. The inlet projects from the fill face with no headwall. Design parameters:

Design discharge	Q₂₅ = 42 cfs (NRCS/TR-55 basin, 25-yr storm)
Pipe	36-inch CMP, inside diameter D = 3.0 ft
Barrel length L	120 ft (roadway + side slopes)
Barrel slope S₀	2.5% = 0.025 ft/ft
Manning's n	0.024 (CMP 2⅔ × ½ in; HDS-5 Table 4-2)
Inlet	CMP projecting (no headwall); K_e = 0.5 per county standard detail*
Tailwater TW	0.5 ft above outlet invert at design Q
Headwater limit	HW/D ≤ 1.25 (county gravel-road standard)

*County detail uses K_e = 0.5 for a beveled/projecting ring; HDS-5 Table 4-1 lists K_e = 0.9 for plain projecting CMP. We use 0.5 per the permit drawing and note the HDS-5 value in Step 6.

Step 1 · Full-barrel geometry and velocity

Assume full flow at the 25-year design discharge

At Q₂₅ = 42 cfs on a 2.5% slope, the barrel runs full under both inlet- and outlet-control analyses (typical for design-flood sizing). Compute area, hydraulic radius, and velocity for the outlet-control energy equation.

D = 3.0 ft → radius r = 1.5 ft
A = πr² = π(1.5)² = 7.07 ft²
R = D/4 = 0.75 ft (full circular pipe)
V = Q/A = 42/7.07 = 5.94 ft/s

Verify full-flow capacity on the same slope with Manning's equation (n = 0.024, S = 2.5%): Q_full ≈ 52 cfs > 42 cfs — full flow is consistent.

Step 2 · Inlet control (HDS-5 submerged form)

Type 1 polynomial — Chart 3, CMP projecting

HDS-5 Appendix A gives the submerged inlet-control equation (Form 2), accurate when Q/(A·D^0.5) > 4. For CMP projecting from Table 4-1: c = 0.0553, Y = 0.54.

Inlet-control equation (HDS-5):
  HW_i/D = c · [Q/(A · D^0.5)]² + Y − 0.5 · S₀

Flow intensity term:
  Q/(A · D^0.5) = 42 / (7.07 · 3.0^0.5)
  = 42 / (7.07 · 1.732) = 42 / 12.24 = 3.43 (< 4 — near unsubmerged transition; acceptable for preliminary sizing)

Headwater ratio:
  HW_i/D = 0.0553 · (3.43)² + 0.54 − 0.5(0.025)
  = 0.0553 · 11.76 + 0.54 − 0.0125
  = 0.650 + 0.540 − 0.013 = 1.18

Inlet-control headwater:
  HW_i = 1.18 · 3.0 = 3.53 ft above inlet invert

Run the same numbers in the culvert hydraulics tool (CMP projecting, 36 in, L = 120 ft, S = 2.5%, n = 0.024, Q = 42 cfs, TW = 0.5 ft).

Step 3 · Outlet control (energy equation)

Full-barrel flow with entrance loss and friction

Outlet-control headwater accounts for tailwater, velocity head, entrance loss (K_e·V²/2g), barrel friction, and the slope drop along length L:

HW_o = TW + [1 + K_e + 29.16 · n² · L / R^4/3] · V²/(2g) − L · S₀

Friction grouping (HDS-5 outlet-control form):
  29.16 · n² · L / R^4/3 = 29.16 · (0.024)² · 120 / (0.75)^4/3
  = 29.16 · 0.000576 · 120 / 0.826 = 2.96

Loss coefficient sum: 1 + K_e + 2.96 = 1 + 0.5 + 2.96 = 4.46

Velocity-head term:
  H = 4.46 · (5.94)² / (2 · 32.2) = 4.46 · 35.3 / 64.4 = 2.44 ft

Outlet-control headwater (use max(TW, D) when TW is below crown per HDS-5 energy balance):
  HW_o = max(0.5, 3.0) + 2.44 − 120(0.025)
  = 3.0 + 2.44 − 3.0 = 2.44 ft above inlet invert

The slope drop L·S₀ = 3.0 ft exactly offsets the barrel-depth term when TW is low, so outlet-control HW collapses to the combined head-loss term alone. This is common on steep, short culverts with shallow tailwater.

Step 4 · Governing regime and HW/D check

Take the higher headwater

Control type	HW (ft)	HW/D	Governs?
Inlet control	3.53	1.18	Yes
Outlet control	2.44	0.81	—
Design HW	3.53	1.18	Limit 1.25 ✓

Result: Inlet control governs. HW = 3.53 ft; HW/D = 1.18 ≤ 1.25 — PASS
Freeboard below road subgrade: 1.25 · 3.0 − 3.53 = 3.75 − 3.53 = 0.22 ft under the HW/D cap

Crown clearance at design HW: 3.0 − 3.53 = −0.53 ft — inlet is submerged; expected at HW/D > 1.0

Thin freeboard is still a pass on paper. HW/D = 1.18 meets the county’s 1.25 cap with only 0.07 ratio units (0.22 ft) of margin. Debris, sediment buildup at the inlet, or a revised TR-55 CN could push HW over the limit. A 42-inch CMP or a headwall/beveled inlet would add margin for roughly the same road profile.

Step 5 · Outlet velocity and riprap

Scour protection downstream

At full-barrel design flow, the outlet velocity is the mean section velocity. County standards typically require energy dissipation above ~6 ft/s on erodible channels; HEC-14 provides riprap sizing.

V_out = Q/A = 42/7.07 = 5.94 ft/s

Riprap D₅₀ (HEC-14 simplified, horizontal apron):
D₅₀ ≈ 0.044 · V² = 0.044 · (5.94)² = 0.044 · 35.3 = 1.55 in

Specify: 2-in minimum Class B riprap (or 4-in if channel is highly erodible), L_apron ≈ 4D = 4 · 3.0 = 12 ft, geotextile underlay per county standard.

Check downstream channel capacity at bank-full with Manning's equation on the receiving stream (intermittent channel n ≈ 0.035–0.045). If the channel cannot pass 42 cfs without overtopping private property, the tailwater assumption TW = 0.5 ft is wrong and outlet control may govern after all.

Step 6 · Gotchas: CMP n, inlet projection vs. headwall

Material roughness and entrance geometry

Alternative	Inlet HW (ft)	Outlet HW (ft)	HW/D
36-in CMP projecting (n=0.024) — this design	3.53	2.44	1.18
36-in CMP + headwall (c=0.0379, Y=0.69, K_e=0.5)	3.37	2.44	1.12
36-in RCP square edge (n=0.012, c=0.0398, Y=0.67)	3.38	1.23	1.13

CMP n vs. concrete. Corrugated metal at n = 0.024 carries roughly half the Manning capacity of concrete at n = 0.012 on the same slope. Outlet-control head loss scales with n² — on long, flat barrels CMP outlet control often governs. Here, the 120-ft length at 2.5% slope keeps outlet HW low, but inlet geometry still controls because the projecting entrance contracts flow at the face.

Inlet projection vs. headwall. A projecting CMP without a headwall is the worst common inlet type (HDS-5 Chart 3, high c = 0.0553). Adding a headwall drops HW_i from 3.53 ft to ~3.37 ft on this site — modest, but often enough to recover freeboard in plan review. Plain projecting per HDS-5 uses K_e = 0.9 for outlet control (vs. 0.5 in the county detail); at K_e = 0.9, HW_o rises to 2.66 ft — inlet still governs, but the margin narrows on outlet-controlled sites with higher tailwater.

Step 7 · What we did NOT check, and when you would

Beyond preliminary HDS-5 sizing

No TR-55 hydrograph routing on this page. We took Q₂₅ = 42 cfs as given. The basin hydrograph (NRCS TR-55 tabular method or WinTR-20) establishes that peak and its duration; a short-duration peak on a steep culvert can produce a higher head than steady-state analysis suggests.
No HY-8 performance curve. FHWA HY-8 plots HW vs. Q across inlet- and outlet-control transitions, unsubmerged inlet conditions at low flow, and road overtopping. Required for state DOT lettings; recommended for any HW/D within 5% of the allowable cap.
No 50- or 100-year check storm. County roads often allow overtopping at the check event but require the structure survive. A Q₁₀₀ ≈ 1.5× Q₂₅ here (~63 cfs) would push HW/D well above 1.25 — document allowable overtopping or upsize.
No fish passage / aquatic organism passage. Intermittent or not, some jurisdictions now require velocity and depth limits at low flow; that drives a different design basis than Q₂₅ alone.

For a full watershed-to-submittal workflow with routed hydrographs and multi-culvert networks, see HydroComplete.

Tools used in this example

Reproduce every step in the live PE-Calc tools: culvert hydraulics (HDS-5 inlet + outlet control). Entrance loss K_e values are in the culvert entrance loss reference. Full-flow Manning verification and downstream channel checks use Manning's equation. The design discharge basis (TR-55 basin) can be built with NRCS curve number and Rational Method for smaller tributary areas.

Buying the lot? Check the drainage before you buy.

Road crossings, floodplain limits, and downstream property rights determine whether a 36-inch CMP is permitted at all. A county gravel-road standard does not mean the site is outside a FEMA flood zone or wetland buffer. SitePrior screens FEMA, NWI, NRCS soils, and USGS context for $29 in about 60 seconds. Run it before the offer, not after the survey.