Engineering
Rational Method Peak Stormwater Runoff (Q = C*i*A) & Composite C
Calculate an area-weighted runoff coefficient and Rational Method peak flow. Compare the customary Q≈CiA shortcut with the explicit acre-inch/hour conversion and validate the worksheet inputs.
Estimate peak flow, not a complete drainage design
The Rational Method estimates peak runoff using a coefficient, rainfall intensity and drainage area. It does not by itself size an inlet or culvert or generate a runoff hydrograph. Applicability and area limits depend on the governing guidance; a 200-acre limit is not universal.
Use rainfall intensity for the selected frequency and a duration equal to the catchment time of concentration. E2=3.2 in/hour is an illustrative input, not a location-specific 10-year design intensity. This sheet does not calculate time of concentration or retrieve IDF data.
Weight each coefficient by its area
Enter acres in B2:B4 and dimensionless runoff coefficients in C2:C4. All six entries are required, areas must be nonnegative, total area positive and coefficients between zero and one. A zero-area row is allowed but still needs a valid coefficient.
The example coefficients are illustrative rather than universal values for roof, lawn or gravel. With areas 4, 10 and 6, the weighted sum is 11 acres and the composite coefficient is 11/20=0.55. A simple unweighted average would give a different answer.
=IF(E6<>"OK",E6,SUMPRODUCT(B2:B4,C2:C4)/E9)Distinguish the unit shortcut from explicit conversion
E11 uses the common US customary approximation Q≈CiA. For the initial inputs it gives 35.2 cfs. One acre-inch/hour is actually 43,560/(12×3,600)=1.008333… cubic feet per second, so this shortcut is not an exact unit identity.
E12 applies the explicit conversion and gives 35.4933333 cfs. Both outputs are labeled so the convention is visible. More precise unit conversion does not make the empirical coefficient or rainfall estimate more accurate.
=IF(ISNUMBER(E11),E11*43560/12/3600,E11)Try a changed land-cover scenario
Change C3 from 0.35 to 0.90 while retaining the areas and intensity: E10 becomes 0.825, E11 becomes 52.8 cfs, and E12 becomes 53.24 cfs. In a real redevelopment study, time of concentration and therefore the selected intensity may change too.
Set intensity to zero: both flow outputs become zero while the composite coefficient stays unchanged. Negative or missing intensity produces a message. Set all areas to zero: the composite coefficient is undefined and the sheet requests positive total area instead of silently displaying zero.
The helper cells retain raw values. Use display formatting to shorten decimals without rounding intermediate calculations. This example assumes the same design intensity across the contributing areas.
Try the example
Use the original values or change them to test your understanding.