9.3 Hydraulics: Sizing Swales, Ditches & Storm Conduits

9.3 Hydraulics: Sizing Swales, Ditches & Storm Conduits

Section 9.2 produced a peak discharge. This section turns that number into a ditch section or a pipe diameter — the second half of the "level of hydrology and hydraulics necessary in the performance of incidental drainage" that the Board Guidelines permit inside a subdivision.

Keep the boundary in view throughout. Exclusion 5 removes any structure "requiring special or structural design," exclusion 7 removes conduit selection for highway loads other than residential streets, and exclusion 11 removes surcharged systems and pumping stations. Everything below assumes gravity flow, standard details, and residential loading.

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1. Manning's Equation

For steady uniform flow in an open channel or a conduit flowing under gravity:

$Q = \frac{1.486}{n} A R^{2/3} S^{1/2} \qquad\qquad V = \frac{1.486}{n} R^{2/3} S^{1/2}$

The constant 1.486 is the unit conversion from the metric form; in SI the coefficient is 1.0.

+-----------------------------------------------------------------------------+
|                    MANNING ROUGHNESS COEFFICIENTS (n)                       |
+----------------------------------------------+--------------------+---------+
| Conduit or channel                           | Typical n          | Use     |
+----------------------------------------------+--------------------+---------+
| Smooth reinforced concrete pipe (RCP)        | 0.012 - 0.013      | culverts|
| Smooth-interior corrugated HDPE (N-12)       | 0.012 - 0.013      | storm   |
| Corrugated metal pipe, annular               | 0.024 - 0.027      | driveway|
| Earth ditch, uniform and smoothly graded     | 0.020 - 0.025      | diversion|
| Vegetated grass swale (bermuda / fescue)     | 0.030 - 0.040      | roadside|
| Riprap-lined ditch                           | 0.040 - 0.060      | chute   |
+----------------------------------------------+--------------------+---------+

[!IMPORTANT] Corrugated HDPE comes in two very different products. Smooth-interior dual-wall pipe carries n of about 0.012; single-wall corrugated pipe carries n closer to 0.024. Doubling n halves the capacity at a given size and slope, so specifying "HDPE" without saying which is not a specification at all.

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2. Circular Pipe Flowing Full

For a circular pipe of internal diameter D (feet) flowing just full:

$A = \frac{\pi D^2}{4}, \qquad P = \pi D, \qquad R = \frac{A}{P} = \frac{\pi D^2/4}{\pi D} = \frac{D}{4}$

Substituting into Manning's equation collapses it to a single-variable form:

$Q_{full} = \frac{1.486}{n}\left(\frac{\pi D^2}{4}\right)\left(\frac{D}{4}\right)^{2/3} S^{1/2} = \frac{0.463}{n} D^{8/3} S^{1/2}$

Solved for diameter:

$D = \left(\frac{Q n}{0.463 \, S^{1/2}}\right)^{3/8}$

That R = D/4 identity is worth memorizing; it turns a two-unknown problem into a one-line solution and appears constantly on exams.

+-----------------------------------------------------------------------------+
|              WORKED CALCULATION - SIZING A SUBDIVISION CROSS PIPE           |
|                                                                             |
|   Required 25-year discharge ....................... Q = 18.5 cfs           |
|   Reinforced concrete pipe ......................... n = 0.013              |
|   Pipe slope ....................................... S = 0.010 ft/ft (1.0%) |
|                                                                             |
|   Q = (0.463 / n) D^(8/3) S^(1/2)                                           |
|   18.5 = (0.463 / 0.013) x D^(8/3) x (0.010)^(1/2)                          |
|   18.5 = 35.615 x D^(8/3) x 0.100 = 3.5615 D^(8/3)                          |
|   D^(8/3) = 18.5 / 3.5615 = 5.194                                           |
|   D = 5.194^(3/8) = 5.194^0.375 = 1.854 ft = 22.2 inches                    |
|                                                                             |
|   Select the next standard manufactured size: 24-inch RCP (D = 2.00 ft)     |
|   Check: Q = 3.5615 x 2.00^(8/3) = 3.5615 x 6.350 = 22.6 cfs > 18.5 cfs  OK |
|                                                                             |
|   Velocity check: A = pi(2.00)^2/4 = 3.14 sq ft                             |
|   V = Q/A at design flow = 18.5 / 3.14 = 5.9 ft/s -- within the usual       |
|   2.5 to 10 ft/s window, so no scour or siltation concern.                  |
+-----------------------------------------------------------------------------+

Two habits the worked example demonstrates. Always round up to a manufactured size, never down, and always re-check capacity at the selected size — the rounding gives you the margin. And always check velocity, because a pipe that satisfies capacity can still fail: too slow and it silts in, too fast and the outlet scours.

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3. Velocity Limits

Exceeding the channel limit is not just an erosion problem — it is a scope problem. An outlet needing an engineered energy dissipator, plunge pool, or structural apron slides into exclusion 5, "any major drainage ditch, storm culvert, branch, deep structure, catch basin, manhole, etc., requiring special or structural design."

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4. Open-Channel Sections

For a trapezoidal channel of bottom width b, depth d, and side slope z (horizontal to 1 vertical):

$A = bd + zd^2 \qquad P = b + 2d\sqrt{1+z^2} \qquad R = \frac{A}{P}$

For a triangular (V-ditch) section of depth d and side slope z:

$A = zd^2 \qquad P = 2d\sqrt{1+z^2}$

Design freeboard of roughly 0.5 foot above the design water surface is conventional in subdivision swales. Note also the erosion-control constraint in 15A NCAC 04B: ditches and channels used as erosion control measures shall be designed and constructed with side slopes no steeper than two horizontal to one vertical where vegetative cover is used for stabilization, unless soil conditions permit steeper slopes or mechanical or structural devices or ditch liners restrain accelerated erosion.

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5. The NCDOT Minimums That Govern Subdivision Drainage

Where a subdivision street is to be added to the state system, the NCDOT Subdivision Roads Minimum Construction Standards control the drainage details. Two dimensions are absolute floors:

The manual also fixes minimum cover for longitudinal pipe lines and electric power primary at 3 feet, requires that all pipe culverts, storm sewers, and appurtenances be free of debris and silt build-up at acceptance, and prohibits headwalls intended merely to shorten a drainage structure or reduce right-of-way requirements. Subsurface drainage must be adequate to maintain a stable subgrade.

[!CAUTION] A hydraulic calculation can return a 12-inch pipe and still be wrong. Minimum sizes exist for maintenance access and clogging resistance, not hydraulics. Where computation and minimum standard disagree, the minimum standard governs — and where a local ordinance is stricter than NCDOT, the local ordinance governs.

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6. Where the Hydraulics Stop

The pattern is consistent: uniform gravity flow with standard details is surveying; anything requiring structural analysis, pressurized behavior, or regulatory floodplain modeling is engineering.