Hydrology and Hydraulics
Peak flow: the Rational Method
Q = C·i·A gives peak discharge in cfs when C is the runoff coefficient, i is rainfall intensity (in/hr) for a duration equal to the time of concentration at the design return period, and A is area in acres. It is limited to small, fairly homogeneous catchments - commonly 200 acres or less, and many jurisdictions cap it lower or require TR-55. Traps: pairing a 25-year intensity with a 2-year C, or using total storm depth where an intensity belongs.
Runoff depth: NRCS curve number
Q = (P − 0.2S)² / (P + 0.8S) with S = 1000/CN − 10 (inches). This yields runoff depth, not peak discharge - a unit hydrograph (TR-55) is needed for peak. Composite CN is area-weighted; check whether the jurisdiction allows the connected-impervious adjustment.
Open channel flow: Manning
Q = (1.49/n)·A·R^(2/3)·S^(1/2), with R = A/P (hydraulic radius, not depth) and S as a decimal. Traps: entering slope in percent rather than decimal, or confusing hydraulic radius with flow depth. Typical n: 0.03 for clean earth channels, higher for vegetated or rough channels.
Velocity and energy
Velocity drives transport and scour. Earth channels generally warrant attention above roughly 5–7 ft/s; either reduce velocity (flatten grade, widen, add roughness) or armor the channel. Outfalls need energy dissipation - riprap aprons, stilling basins, or flared end sections - because the failure point is almost always where concentrated flow leaves the pipe.
Worked example
C = 0.5, i = 4 in/hr, A = 3 acres → Q = 0.5 × 4 × 3 = 6 cfs. Handy check: 1 acre-inch per hour ≈ 1 cfs.