# nc2: Einstein and Banks method for composite Manning's n In iemisc: Irucka Embry's Miscellaneous Functions

## Description

This function computes the composite Manning's n using the Einstein and Banks method.

## Usage

 1 nc2(P, n) 

## Arguments

 P numeric vector that contains "wetted perimeter of any section i" n numeric vector that contains "Manning's n of any section i"

## Details

"A composite value of Manning's n for a single channel; that is, for the main channel only of a compound channel or a canal with laterally varying roughness." Source: Sturm page 118.

The equation to find Manning's composite n using the Einstein and Banks method is

n_c = ≤ft[\frac{∑ \limits_{i=1}^N P_i n_i^2}{P}\right] ^ \frac{1}{2}

n_c

Manning's composite n

P

"wetted perimeter of the entire cross section"

P_i

"wetted perimeter of any section i"

n_i

"Manning's n of any section i"

N

"total number of sections into which the wetted perimeter is divided"

Source: Sturm page 118.

## Value

numeric vector that contains nc2 as Manning's composite n.

## References

1. Terry W. Sturm, Open Channel Hydraulics, 2nd Edition, New York City, New York: The McGraw-Hill Companies, Inc., 2010, page 118-119.

2. Dan Moore, P.E., NRCS Water Quality and Quantity Technology Development Team, Portland Oregon, "Using Mannings Equation with Natural Streams", August 2011, http://www.wcc.nrcs.usda.gov/ftpref/wntsc/H&H/xsec/manningsNaturally.pdf.

n for Manning's n for natural channels, nc1 for Horton method for composite Manning's n, nc3 for Lotter method for composite Manning's n, and nc4 for Krishnamurthy and Christensen method for composite Manning's n.
 1 2 3 library("iemisc") # Example from the Moore Reference text nc2(n = c(0.05, 0.035, 0.05, 0.04), P = c(22.22, 34.78, 2.00, 6.08))