The rational method vs. the NRCS curve number on the PE Civil WRE exam

Most runoff problems on the Water Resources & Environmental exam start with one of two methods. The rational method returns a peak flow. The NRCS (SCS) curve-number method returns a runoff depth, which then feeds volumes, a peak by the TR-55-style peak discharge method, or a hydrograph. Most lost points come from treating one method's output as the other's.

What you actually need to own

• Rational method: Q = CiA. With C dimensionless, i in in./hr and A in acres, Q comes out in acre-in./hr. That is 1.008 cfs, so it is treated as cfs.
• Intensity comes from the IDF curve, entered at a duration equal to the time of concentration and at the design return period.
• Time of concentration is the travel time from the hydraulically most distant point. That means the longest time, which is not always the longest flow path. Build it from sheet, shallow concentrated and channel flow, or from the SCS lag formula (t_c = 5/3 × lag). Keep hours and minutes apart.
• Composite C is area-weighted: C_w = Σ(C_i·A_i)/ΣA_i. Only area inside the drainage divide counts.
• Curve number: S = 1,000/CN − 10 (in.), I_a = 0.2S, and Q = (P − 0.2S)² / (P + 0.8S) for P > I_a. When P ≤ I_a, runoff is zero. P is a storm depth in inches, and Q is a runoff depth in inches.
• CN comes from land use plus hydrologic soil group (A through D, from high infiltration to very low).
• Peak from runoff depth: q_p = q_u · A_m · Q. Here q_u is a unit peak flow per square mile per inch of runoff, and A_m is in square miles (640 acres per mi²).

When each applies

The rational method suits small, mostly developed catchments where only a peak is needed, such as storm-sewer inlets, gutters and small culverts. It assumes uniform rainfall that lasts at least t_c, and it returns a peak only. For detention, the Handbook turns it into an inflow volume, V_in = CiA·t, compared against the outflow volume. The curve-number method suits larger or mixed watersheds and any problem that needs a volume, such as detention, a unit hydrograph or a pre- vs. post-development comparison. When a problem names the method, use that method.

Where people lose points

• Two different Qs. In the rational method, Q is a flow in cfs. In the NRCS method, Q is a depth in inches. Runoff volume is Q × area, and the unit conversion is part of the answer.
• Intensity vs. depth. Q = CiA takes an intensity. A gauge depth over 30 minutes has to be divided by 0.5 hr first. The curve-number equation takes the depth directly.
• Order of operations in S. Divide 1,000 by CN first, then subtract 10. Also, I_a belongs to the watershed, not to the storm.
• Skipping the P > I_a check. A small storm on a low-CN watershed produces no runoff. Squaring hides the negative sign.
• Simple-averaging C or CN instead of area-weighting. Also using the pre-development C for the developed site.
• Area units. Rational area is in acres, and the TR-55-style peak uses square miles.
• Wrong IDF entry. Reading the curve at the storm's total duration instead of at t_c, or entering the exceedance probability where the curve needs the return period.

How to study it

Work one small developed site both ways: a rational peak, then a curve-number runoff depth and volume. Seeing the two outputs side by side fixes the difference. Then do t_c problems on their own until checking segment units is automatic. Rational volumes and curve-number depths are the inputs to detention pond sizing and routing. The peaks you compute here usually end up in a culvert or a channel sized by Manning's equation. The Handbook's Runoff Analysis and Time of Concentration sections hold both methods, so learn where they are before exam day.

Part of the Hydrology area of the PE Civil WRE exam. → Start practicing free — the whole practice bank, free with an account.