Transportation Learning HubTransportation Learning Hub · PE Civil Transportation · Area 10 of 10
Drainage — PE Civil Transportation
Every road is a drainage structure whether it was designed as one or not. This area runs the full chain: estimate the runoff, collect it, convey it, and let the energy out safely — the hydrology and hydraulics end of the Transportation exam.
Take the free 3-question mini-quiz ↓
Hydrology: how much water arrives
The rational method treats peak runoff as the share of rainfall that runs off, falling on the whole drainage area at the design intensity:
\[Q = C\,i\,A\]
| Q | peak discharge, cfs |
|---|---|
| C | runoff coefficient — the fraction of rainfall that becomes runoff, entered as a decimal (0.80, not 80) |
| i | rainfall intensity, in/hr, for the design storm and duration given in the problem |
| A | drainage area, acres — with \(i\) in in/hr and \(A\) in acres, \(Q\) comes out in cfs |
All three inputs are givens in an exam problem: the surface description selects \(C\), the design storm sets \(i\), and the catchment map sets \(A\). The calculation itself is a single multiplication — the marks are in matching each input to the right part of the problem. Water quality mitigation sits in the same specification line: capturing and treating runoff, not just moving it.
Worked example Peak runoff by the rational method
Given: A drainage area of \(A = 12\) acres has a runoff coefficient \(C = 0.80\). The design rainfall intensity is given as \(i = 5.0\) in/hr. Find the peak discharge.
Solution:
- Substitute directly: \(Q = C\,i\,A = 0.80 \times 5.0 \times 12\).
- \(Q = 48\) cfs.
Answer: \(Q = 48\) cfs — the flow the collection and conveyance system must now be checked against.
Hydraulics: can the system carry it
Conveyance is checked element by element, because the weakest element controls. An inlet that cannot capture the gutter flow starves a pipe that could have carried it; a pipe laid too flat cannot deliver what its diameter promises. For full circular pipe flow, Manning’s equation gives the velocity, and discharge follows from the cross-sectional area:
\[V = \frac{1.486}{n} R^{2/3} S^{1/2} \qquad Q = V A\]
| V | mean velocity, ft/s |
|---|---|
| n | Manning roughness coefficient for the pipe material, given in the problem |
| R | hydraulic radius, ft — for a circular pipe flowing full, \(R = D/4\) |
| S | pipe slope, ft/ft, entered as a decimal (1% = 0.01) |
| A | full cross-sectional area, \(\pi D^{2}/4\), ft² |
The same Manning relationship, with the channel’s own \(R\) and \(A\), is what runs open-channel flow — ditches and channels are checked the same way, with the geometry of the channel section in place of the pipe circle.
Worked example Full-flow capacity of a 24-in. pipe
Given: A 24-in. reinforced concrete pipe (\(n = 0.013\) given) is laid at \(S = 1\%\). Check its full-flow capacity against the design flow of 48 cfs from the previous example.
Solution:
- Convert the diameter: \(D = 24\) in \(= 2.0\) ft. Hydraulic radius flowing full: \(R = D/4 = 0.5\) ft.
- Full area: \(A = \pi D^{2}/4 = \pi (2.0)^{2}/4 = 3.14\) ft².
- Velocity: \(V = \frac{1.486}{0.013} (0.5)^{2/3} (0.01)^{1/2} = 7.20\) ft/s.
- Discharge: \(Q = V A = 7.20 \times 3.14 = 22.6\) cfs.
- Compare: \(22.6\) cfs \(< 48\) cfs.
Answer: \(V \approx 7.20\) ft/s and \(Q \approx 22.6\) cfs — the single pipe is undersized for the 48 cfs design flow; the design needs a larger pipe, a steeper slope, or multiple barrels.
Culverts, inlets, detention and energy dissipation
The remaining specification items are about control points and consequences:
| Inlets | Capture gutter and surface flow into the storm sewer. Inlet capacity can govern the whole system — water that never enters the pipe cannot be conveyed by it |
|---|---|
| Culverts | Carry flow under the road. Capacity is set by whichever controls: the entrance (inlet control) or the barrel, tailwater and losses along it (outlet control) |
| Detention | Stores runoff temporarily and releases it at a controlled rate — a volume-and-time device, not a peak-flow formula. Sizing starts from the storage volume the release limit requires |
| Energy dissipation | Slows high-velocity outflow at culvert and pipe exits so it does not erode the receiving channel or embankment |
| Open channels | Ditches and channels checked with Manning, using the channel section’s own area and hydraulic radius |
This is the area where the Transportation hub meets the hydrology and hydraulics foundations head-on — runoff, pipe flow and open-channel flow are the same physics the water topics are built on, applied here to the road corridor. Work this page after Geotechnical and Pavement, and use the study plan to place it in the full route.