Rain falling on a town becomes runoff in proportion to how sealed each surface is. The rational method estimates the peak flow from a catchment as Q = C i A / 360 (Q in m3/s, i in mm/h, A in ha), where C is the area-weighted runoff coefficient and i is the design intensity for a storm as long as the time of concentration tc, the time for water from the farthest point to reach the pipe. Longer storms are less intense but collect from more of the catchment, so the peak comes at d = tc. Pipes are checked with Manning's equation for a full circular pipe, Q = (1/n) A R^(2/3) S^(1/2) with R = D/4.
i(d) = a T^0.2 (1 + climate) / (d + 10)^0.75 mm/h, d in min, a = 460 (illustrative IDF curve)
Q = C i A / 360, C = sum(C_s a_s)/A, C_s x 1.1 (25 yr), 1.2 (50 yr), 1.25 (100 yr), capped at 1
tc = inlet time (weighted by C a) + pipe length / full-flow velocity
Q_full = (1/n) (pi D^2/4) (D/4)^(2/3) sqrt(S), n = 0.013 (concrete)
simulation: effective rain C a max(0, P(t) - Ia) -> linear reservoir K = 0.5 tc -> pipe, min(supply, Q_full) -> street store
street depth = stored volume / (6 % of paved, road and permeable-paving area: the low points)
- Surfaces - roof 0.90, road 0.90, paving 0.85, permeable paving 0.35 (it also stores 10 mm in its stone layer), lawn 0.15, trees 0.10, extensive green roof 0.40 with 12 mm of substrate storage. Swapping a flat roof for a green roof or a car park for permeable paving lowers C and delays the peak.
- Rational vs simulation - the rational peak is a design estimate that ignores storage and the shape of the storm; the time-stepped simulation spreads the same rain over time, so its peak is usually lower, and the water that does not fit in a pipe is stored on the street until capacity returns.
- Same model in both pages - one shared module. The checks compare it with a unit identity, a numerical integration of the pipe, the IDF depth, a brute-force critical-duration scan, a mass balance and a time-step test.
- Honest simplifications - three fixed catchments and four pipes of fixed slope, no backwater or surcharge hydraulics, no overland flow routing between tiles, no groundwater, no inlet capacity, no pipe roughness ageing, runoff coefficients are typical textbook values (they change with soil, slope and storm), the IDF curve is invented, and the flood depth assumes the water collects at street low points. This is a teaching model, not a drainage design: use local design standards.