rational_formula: Modified Rational Method Equation

In iemisc: Irucka Embry's Miscellaneous Functions

Modified Rational Method Equation

Description

Computes the design peak runoff rate (Q) using the modified rational method equation.

Usage

rational_formula(
  C_F,
  C,
  i,
  A,
  area_units = c("acre", "square feet", "square mile", "hectare", "square kilometer")
)

Arguments

C_F	numeric vector that contains the "runoff coefficient adjustment factor to account for reduction of infiltration and other losses during high intensity storms" [Input a number between 2 and 10; 25; 50; or 100]
C	numeric vector that contains the dimensionless "runoff coefficient to reflect the ratio of rainfall to surface runoff"
i	numeric vector that contains the "rainfall intensity in inches per hour (in/hr)"
A	numeric vector that contains the drainage area in one of the area_units values.
area_units	character vector containing the units for area (default = "acre"). The other possible units are "square feet", "square mile", "hectare", or "square kilometer".

Value

the numeric vector Q, which is the "peak flow" in cubic feet per second (cfs or ft^3/s)

Note

Please note: Refer to the limitations of the Modified Rational Method equation for your particular jurisdiction. Notes are only included below for Oklahoma and Oregon, respectively.

for Oklahoma "The Rational Method, first introduced in 1889, is recommended for estimating the design storm peak runoff for areas up to 640 acres. The Rational Method was modified in the 1980's to include a runoff coefficient correction tied to the flood frequency. This Modified Rational Method is used by ODOT.

Some precautions should be considered when applying the Rational method: –The first step in applying the Rational method is to obtain a good topographic map and define the boundaries of the drainage area in question. A field inspection of the area should also be made to determine if the natural drainage divides have been altered. –In determining surface characteristics for the drainage area, consider any future changes in land use that might occur during the service life of the proposed facility that could result in an inadequate drainage system. Also, the effects of upstream detention facilities may be considered. –Restrictions to the natural flow (e.g., highway crossings and dams that exist in the drainage area) should be investigated to determine how they might affect the design flows. –The charts, graphs and tables included in this Section are not intended to replace reasonable and prudent engineering judgment that should permeate each step in the design process." [Oklahoma Department of Transportation Reference]

for Oregon: "Limitations and assumptions in the Rational Method are as follows: –The drainage area should not be larger than 200 acres. –The peak flow is assumed to occur when the entire watershed is contributing runoff. –The rainfall intensity is assumed to be uniform over a time duration equal to or greater than the time of concentration, Tc. –The peak flow recurrence interval is assumed to be equal to the rainfall intensity recurrence interval. In other words, the 10-year rainfall intensity is assumed to produce the 10-year flood." [Oregon Department of Transportation Reference]

The value of 1.008 is used for the unit conversion factor for English units. [Tennessee Design reference]

Author(s)

Irucka Embry

References

1. Design Principles for Erosion Prevention & Sediment Control for Construction Sites Level II EPSC Workshop, Fall 2017. Sponsored by The University of Tennessee Biosystems Engineering & Environmental Sciences Tennessee Water Resources Research Center, Tennessee Department of Environment and Conservation Division of Water Resources, and Tennessee Department of Transportation.

2. Oklahoma Department of Transportation (ODOT) Roadway Drainage Manual Chapter 7 Hydrology, November 2014, page 7.6-1, https://oklahoma.gov/content/dam/ok/en/odot/documents/chapter-7-hydrology.pdf.

3. Oregon Department of Transportation (ODOT) Geo-Environmental, ODOT Hydraulics Manual Appendix F – Rational Method, April 2014, page 7-F-1, https://www.oregon.gov/ODOT/GeoEnvironmental/Docs_Hydraulics_Manual/Hydraulics-07-F.pdf.

4. U.S. Department of Agriculture (USDA) Natural Resources Conservation Service (NRCS), Hydrology Training Series Module 206 D - Peak Discharge (Other Methods) Study Guide, page 18 (of the PDF document) and page 26 - 27 (of the PDF document), https://web.archive.org/web/20211018222532/https://www.nrcs.usda.gov/Internet/FSE_DOCUMENTS/stelprdb1083019.pdf. Retrieved thanks to the Internet Archive: Wayback Machine

Examples

# Example 1 from NRCS Reference

# Given
# Urban setting with a drainage area of 12 acres
# 6 acres = single family area
# 3 acres = park
# 3 acres = streets (concrete)
# Soil = clay loam
# Tc = 20 min (time of concentration)

# Find the instantaneous peak discharge for a 25-yr frequency flood at a
# road crossing in an urban/rural area located in the Kansas City, Missouri
# area.


library(iemisc)

area1 <- c(6, 3, 3)
C1 <- c(mean(c(0.30, 0.50)), 0.15, 0.90)
C1_w <- weighted_C(C = C1, area = area1)

i1 <- 5.1 # in/hr

rational_formula(C_F = 25, C = C1_w, i = i1, A = sum(area1), area_units = "acre")






# Example 2 from NRCS Reference

# Given
# Urban setting with a drainage area of 18 acres

# 1 ac = playground
# 10 ac = single family area
# 2 ac = streets (asphaltic)
# 5 ac = pasture (hilly)
# Soil = heavy clay
# Tc = 20 min

# Find the instantaneous 100-yr frequency peak discharge for design of a
# channel in a developing subdivision located in an area near Asheville,
# North Carolina.


library(iemisc)

area2 <- c(1, 10, 2, 5)
C2 <- c(0.35, 0.50, 0.90, 0.60)
C2_w <- weighted_C(C = C2, area = area2)

i2 <- 5.5 # in/hr

rational_formula(C_F = 100, C = C2_w, i = i2, A = sum(area2), area_units = "acre")

iemisc documentation built on Sept. 25, 2023, 5:09 p.m.