Oxbow River and Stream Inc. - Stream Ecology: Aquatic Hydraulics: Mannings

Aquatic Hydraulics: Manning's Coefficient

Manning's roughness coefficient, n, is commonly used to represent flow resistance for hydraulic computations in the flow of open channels. The selection of an n value requires judgment, skill, and subjectivity; it is a skill developed through experience. The best way to develop this skill is to study streams with known n values. Manning's roughness coefficients have been determined for 21 high-gradient streams in Colorado (Jarrett, 1985), 15 floodplains in the southeastern United States (Acement and Schneider, 1989), 78 rivers and canals in New Zealand (Hicks and Mason, 1991), 67 gravel-bed streams in Canada (Bray, 1979) and 21 perennial channels in New York State (Coon, 1995) (Phillips and Ingersoll).

More recently (September 2000), the United States Army Corps of Engineers used the Utah State University Water Research Laboratory to conduct 220 experiments using 20 plant species in order to correct for the 'near complete lack of hydraulic roughness values for shrubs and similar vegetation' (Copeland). They found that the modulus of plant stiffness is critical to the calculation of resistance because of the flexibility of the plants and the deformation of leaf masses due to the flow forces (Copeland). Equation (1) shows how to calculate the modulus of plant stiffness.


(Eq. 1)	Es = (F45*H²) / (3I)	Where Es = Modulus of plant stiffness, lb/ft² F45 = Horizontal force necessary to bend a plant stem 45 degrees, lb H = Average undeflected plant height I = Second moment of inertia of cross section of plant stem, ft^4

The Manning's roughness coefficient for vegetation is dependent on whether plants are submerged or not. Submerged vegetation can increase Manning's roughness coefficient twenty-fold while floating vegetation can double the value of n. During the growing season, the value of n can increase drastically, up to 300% (Fisher and Dawson). Equations (2) and (3) illustrate the difference in the calculations for the submerged plant (Eq. 2) and partially submerged plant (Eq. 3) n values. Note that these equations include the streambed roughness, which can be subtracted out in order to determine the Manning's roughness coefficient for the vegetation.

Eq. (2)
n = Kn*0.183[(EsAs)/(rAiV*²)]^0.183 * (H/Y0)^0.243 * (MAi)^0.273 * (v/(V*Rh))^0.115 * (1/V*)(Rh)^ * (S)^

Eq. (3)
n = Kn*3.487E-05[(EsAs)/(rAi*V²)]^0.150 * (MAi*)^0.166 * ((V*Rh)/v)^0.622 * (1/V)(Rh)^ * (S)^


		Where: Kn = Units conversion factor for Manning's equation, 1.4861 ft^ /sec Es = Modulus of plant stiffness, lb/ft² As = Total cross-sectional area of all the stem(s) of an individual plant, measured at H/4, ft² r = Fluid density, slugs/ft³ Ai = Frontal area of an individual plant blocking flow, approximated by the equivalent rectangular area of blockage H by We, ft² Ai* = Net submerged frontal area of a partially submerged plant, ft² V* = Shear velocity, (gRhS)^½, ft/sec H = Average undeflected plant height, ft Y0 = Flow depth, ft M = Relative plant density, number of plants per ft² v = Fluid dynamic viscosity, ft²/sec Rh = Hydraulic radius, flow area / wetted perimeter, ft S = Bed or energy slope, dimensionless

	Due to the varying values of Manning's roughness coefficient for vegetation in a stream, accurate estimation of channel capacity and water surface elevations is difficult at best (Copeland). There is a need for constant research in the area of Manning's roughness coefficients for vegetation. With the valuable information gained from this research, the field of river and stream restoration will be able to more accurately imitate nature.


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