SCS Triangular Unit Hydrograph Peak

The curve number tells you the volume of runoff; this equation turns that volume into a peak. The SCS idealises the runoff hydrograph as a triangle whose base is 2.67 times the time to peak, so the peak of a triangle enclosing volume $V$ is $q_p = 2V/(2.67 T_p)$. Ten square kilometres shedding 25 mm of runoff hold 250,000 m³, and if the peak arrives three hours in, $q_p = 500000/28836 = 17.3$ m³/s. The tabulated coefficient form, $0.208 A Q / T_p$ with area in km², depth in mm and time in hours, gives 17.33 for the same watershed. It is the same equation with 2/2.67 rounded to 0.75.

The 2.67 is not arbitrary. It comes from the observed shape of hundreds of measured hydrographs, in which about 37.5 percent of the runoff volume arrives before the peak. The whole method is a claim that most watersheds are close enough to that shape, and the peaking factor of 484 in the imperial version is exactly the same claim written in different units. Flat, swampy, heavily storaged catchments are demonstrably flatter, and NRCS publishes peaking factors down to 300 for them, which lowers the peak by nearly forty percent. Coastal plain work in the US Southeast routinely uses 284.

The number that trips people is the time to peak, which is not the time of concentration. $T_p = D/2 + t_{lag}$, where D is the unit rainfall duration and the lag is 0.6 of the time of concentration. Feed the time of concentration straight in and the peak comes out low by a large margin. And once you have the peak, remember what a unit hydrograph really is: a linear response. Doubling the runoff depth doubles the peak, which is convenient and also known to be wrong at the extremes, where real catchments respond faster than proportionally.