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Culvert Sizing

8 min read

Size a culvert by computing the peak flow from the catchment and checking that the pipe passes it at the inlet and along the barrel. The rational method gives peak flow in cubic metres per second as C x i x A / 360, where C is a runoff coefficient from 0 to 1, i is rainfall intensity in mm per hour and A is catchment area in hectares, and the pipe diameter is the smallest one whose inlet-control and full-barrel capacities both exceed that flow. Compare the result with the rule of making the culvert at least twice the ditch’s flow area, and build to whichever is larger.

Part of Culverts

Culvert sizing is the calculation that turns a drainage catchment and a design rainfall into a pipe diameter. The rule of thumb in Flood Control and Drainage is a floor, not a replacement for this arithmetic.

The Twice-The-Ditch Rule Fails In Both Directions

The rule that a culvert should have at least twice the flow area of the ditch it replaces is easy to apply and safe for a field ditch. It has no connection to rainfall. A ditch dug small in a large catchment gives a culvert too small for the flow arriving, and a ditch dug generously in a small catchment gives a culvert larger than needed. The calculation below ties the pipe to the water that actually arrives.

The method has three parts: estimate the peak flow arriving, find out what the ditch and the pipe can pass, and compare. Each part has stated assumptions. A reader who cannot defend each assumption should round the pipe up, not down.

What You Need

  • A catchment boundary — the ridge lines draining to the crossing. See Water Flow Mapping.
  • A rainfall intensity — heavy rain in mm per hour for a storm as long as the water takes to cross the catchment. A straight-sided can or jar left in the open gives depth in mm for a known time.
  • A runoff coefficient C — a judgement from 0 to 1: close to 0 for deep sand under dense grass, and close to 1 for rock, roofs and packed clay.
  • The slope and length of the pipe, and its material.

Method: Size A Culvert In Five Steps

Step 1: Find the peak flow with the rational method. One millimetre of rain per hour on one hectare is 0.001 m x 10,000 m2 = 10 m3 per hour. Dividing by 3,600 s gives 0.002778 m3/s, which is 1/360. So Q = C x i x A / 360, in m3/s, with i in mm/h and A in hectares. The method assumes the whole catchment is contributing at once, so it suits small catchments, and the design storm should last at least as long as the water takes to flow from the farthest point to the crossing.

Step 2: Find what the approach ditch carries. Use Manning’s equation: V = (1/n) x R^(2/3) x S^(1/2), and Q = A x V. R is the flow area divided by the wetted perimeter, S is the slope as a fraction and n is the roughness. Typical n values from Chow’s Open-Channel Hydraulics: about 0.022 for a clean weathered earth ditch, about 0.013 for concrete pipe and about 0.024 for corrugated metal pipe.

Step 3: Find the inlet-control capacity. When the headwater is deep enough to cover the inlet, the opening works like an orifice: Q = Cd x A x sqrt(2 x g x H), with Cd about 0.6 for a sharp-edged opening, A the pipe’s flow area, g = 9.81 m/s2 and H the depth of headwater above the pipe centreline. Detailed charts are in FHWA’s culvert hydraulics manual (HDS-5); this is the screening version.

Step 4: Find the full-barrel capacity. For a round pipe running full, R = D/4 and A = pi x D^2 / 4. Apply Manning with the pipe’s slope.

Step 5: Take the smaller capacity. A culvert passes the lesser of its inlet and barrel capacities. Check that the headwater needed stays below the road surface, otherwise water overtops the road.

Worked Example: From Catchment To Pipe Diameter

Assumptions, each labelled: catchment 250 m x 200 m = 50,000 m2 = 5 ha; C = 0.4; i = 50 mm/h.

  • Peak flow: 0.4 x 50 x 5 / 360 = 100 / 360 = 0.278 m3/s.

Ditch check, taking the interceptor ditch in the parent article, 50 cm x 40 cm, as a trapezoid with an assumed 0.5 m bottom width, 0.4 m depth and 1:1 side slopes, n = 0.022, slope 0.5 percent (0.005):

  • Area: (0.5 + 1 x 0.4) x 0.4 = 0.36 m2.
  • Wetted perimeter: 0.5 + 2 x 0.4 x sqrt(1 + 1) = 0.5 + 1.131 = 1.631 m.
  • R = 0.36 / 1.631 = 0.221 m; R^(2/3) = 0.365; sqrt(0.005) = 0.0707.
  • V = (1 / 0.022) x 0.365 x 0.0707 = 1.17 m/s. Q = 0.36 x 1.17 = 0.42 m3/s brim-full.

The ditch holds more than the 0.278 m3/s arriving, as it should.

The twice-the-ditch rule gives a flow area of 2 x 0.36 = 0.72 m2, a pipe of diameter sqrt(4 x 0.72 / pi) = 0.96 m. The catchment calculation, tested on a 0.6 m pipe:

  • Pipe area: pi x 0.6^2 / 4 = 0.283 m2.
  • Inlet control with headwater H = 0.5 m: 0.6 x 0.283 x sqrt(2 x 9.81 x 0.5) = 0.6 x 0.283 x 3.13 = 0.53 m3/s.
  • Barrel, concrete (n = 0.013) at 1 percent: R = 0.15 m, R^(2/3) = 0.282, V = (1 / 0.013) x 0.282 x 0.1 = 2.17 m/s, Q = 0.283 x 2.17 = 0.61 m3/s.
  • Barrel, corrugated metal (n = 0.024): V = 1.18 m/s, Q = 0.33 m3/s.

The 0.6 m pipe passes 0.278 m3/s in all three checks. In this example the catchment calculation asks for a smaller pipe than the twice-the-ditch rule, and the larger one is the safe choice. Pipe flow scales with D^(8/3) at a fixed slope and n, so changing from concrete to corrugated metal at the same capacity needs a diameter larger by (0.024 / 0.013)^(3/8) = 1.26, about a quarter.

Headwater limit. Road surface above the pipe invert is the pipe diameter plus cover: 0.6 + 0.3 = 0.9 m, so the centreline headwater is at most 0.9 - 0.3 = 0.6 m before water reaches the road. At H = 0.6 m the inlet capacity is 0.6 x 0.283 x sqrt(2 x 9.81 x 0.6) = 0.58 m3/s, still above 0.278.

What The Figures Do Not Cover

  • Design storm — choosing how rare a storm to design for is a decision about risk, not arithmetic. Where failure would flood houses or endanger people, choose larger.
  • Debris and sediment — all the capacities above assume a clean pipe, which is why the parent article insists on oversizing. Assume the pipe is partly blocked.
  • Source of coefficients — the n values and the orifice coefficient are standard textbook values. They were written down here without access to the books, so check them against Chow and FHWA HDS-5 before relying on them for a crossing where failure would endanger life.

Common Mistakes

  • Using brim-full ditch flow as the design flow — it sets the minimum size for the ditch rule, but not the flow the catchment delivers.
  • Using ditch gradient for the barrel — the barrel capacity depends on the pipe’s own slope; a steeper barrel passes more at the barrel but the inlet still limits.
  • Forgetting the inlet — a large barrel with a small or partly blocked opening passes only what the inlet allows.
  • Dropping units in the rational method — mixing mm/h with square metres, or minutes with seconds, turns the answer wrong by orders of magnitude. Write units at every line.
  • Reading Q as a volume — Q is a rate. A flow of 0.278 m3/s lasts only as long as the storm.

Safety

A flow of 0.278 m3/s kills

0.278 m3/s is 278 litres every second. At 1 m/s in a ditch it is easily enough to sweep an adult off their feet, since about 15 cm of fast-moving water can do that, and a submerged culvert inlet can hold a body against the opening by the pressure difference across it (a 1 m head acting on 0.25 m2 is about 2,450 N). Never wade into a culvert inlet or channel carrying this flow. Do measurements before the storm, not during it, and keep people away from the crossing while it is running.

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