**HEC-15 Section 6.1 – MANNING’S ROUGHNESS**

Manning’s roughness is a key parameter needed for determining the relationships between depth, velocity, and slope in a channel. However, for gravel and riprap linings, roughness has been shown to be a function of a variety of factors including flow depth, D_{50}, D_{84}, and friction slope, S_{f}. A partial list of roughness relationships includes Blodgett (1986a), Limerinos (1970), Anderson, et al. (1970), USACE (1994), Bathurst (1985), and Jarrett (1984). For the conditions encountered in roadside and other small channels, the relationships of Blodgett and Bathurst are adopted for this manual.

Blodgett (1986a) proposed a relationship for Manning’s roughness coefficient, n, that is a function of the flow depth and the relative flow depth (d_{a}/D_{50}) as follows (Equation 6.1):

n = α⋅d_{a}^{1/6}/(2.25 + 5.23⋅log(d_{a}/D_{50})) |
(6.1) |

where,

- n = Manning’s roughness coefficient, dimensionless
- d
_{a}= average flow depth in the channel, m (ft) - D
_{50}= median riprap/gravel size, m (ft) - α = unit conversion constant, 0.319 (SI) and 0.262 (CU)

Equation 6.1 is applicable for the range of conditions where 1.5 ≤ d_{a}/D_{50} ≤ 185. For small channel applications, relative flow depth should not exceed the upper end of this range.

Some channels may experience conditions below the lower end of this range where protrusion of individual riprap elements into the flow field significantly changes the roughness relationship. This condition may be experienced on steep channels, but also occurs on moderate slopes. The relationship described by Bathurst (1991) addresses these conditions and can be written as follows (See Appendix D for the original form of the equation):

n = α⋅d_{a}^{1/6} / (√g⋅f(Fr)⋅f(REG)⋅f(CG)) |
(6.2) |

where,

- d
_{a}= average flow depth in the channel, m (ft) - g = acceleration due to gravity, 9.81 m/s
^{2}(32.2 ft/s^{2}) - Fr = Froude number
- REG = roughness element geometry
- CG = channel geometry
- α = unit conversion constant, 1.0 (SI) and 1.49 (CU)

Equation 6.2 is a semi-empirical relationship applicable for the range of conditions where 0.3<d_{a}/D_{50}<8.0. The three terms in the denominator represent functions of Froude number, roughness element geometry, and channel geometry given by the following equations:

f(Fr) = (0.28⋅Fr/b)^{log(0.755/b)} |
(6.3) | |

f(REG) =13.434⋅(T/D_{50})^{0.492}b^{1.025⋅(T/D50)0.118} |
(6.4) | |

f(CG) = (T/d_{a})^{-b} |
(6.5) |

where,

- T = channel top width, m (ft)
- b = parameter describing the effective roughness concentration.

The parameter b describes the relationship between effective roughness concentration and relative submergence of the roughness bed. This relationship is given by:

b = 1.14⋅(D_{50}/T)^{0.453}(d_{a}/D_{50})^{0.814} |
(6.6) |

Equations 6.1 and 6.2 both apply in the overlapping range of 1.5 ≤ d_{a}/D_{50} ≤ 8. For consistency and ease of application over the widest range of potential design situations, use of the Blodgett equation (6.1) is recommended when 1.5 ≤ d_{a}/D_{50}. The Bathurst equation (6.2) is recommended for 0.3<d_{a}/D_{50}<1.5.

As a practical problem, both Equations 6.1 and 6.2 require depth to estimate n while n is needed to determine depth setting up an iterative process.

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