Energy Loss Coefficients

Several types of loss coefficients are utilized by the program to evaluate energy losses: (1) Manning’s n values or equivalent roughness “k” values for friction loss, (2) contraction and expansion coefficients to evaluate transition (shock) losses, and (3) bridge and culvert loss coefficients to evaluate losses related to weir shape, pier configuration, pressure flow, and entrance and exit conditions. Energy loss coefficients associated with bridges and culverts will be discussed in "Modeling Bridges" and "Modeling Culverts" of this manual.

Manning’s n. Selection of an appropriate value for Manning’s n is very significant to the accuracy of the computed water surface elevations. The value of Manning’s n is highly variable and depends on a number of factors including: surface roughness; vegetation; channel irregularities; channel alignment; scour and deposition; obstructions; size and shape of the channel; stage and discharge; seasonal changes; temperature; and suspended material and bedload.

In general, Manning’s n values should be calibrated whenever observed water surface elevation information (gaged data, as well as high water marks) is available. When gaged data are not available, values of n computed for similar stream conditions or values obtained from experimental data should be used as guides in selecting n values.

There are several references a user can access that show Manning's n values for typical channels. An extensive compilation of n values for streams and floodplains can be found in Chow’s book “Open-Channel Hydraulics” [Chow, 1959]. Excerpts from Chow’s book, for the most common types of channels, are shown in Table 3-1 below. Chow's book presents additional types of channels, as well as pictures of streams for which n values have been calibrated.

Table 3‑1 Manning's n Values

Type of Channel and Description	Minimum	Normal	Maximum
A. Natural Streams
1. Main Channels
a. Clean, straight, full, no rifts or deep pools	0.025	0.030	0.033
b. Same as above, but more stones and weeds	0.030	0.035	0.040
c. Clean, winding, some pools and shoals	0.033	0.040	0.045
d. Same as above, but some weeds and stones	0.035	0.045	0.050
e. Same as above, lower stages, more ineffective slopes and sections	0.040	0.048	0.055
f. Same as "d" but more stones	0.045	0.050	0.060
g. Sluggish reaches, weedy. deep pools	0.050	0.070	0.080
h. Very weedy reaches, deep pools, or floodways with heavy stands of timber and brush	0.070	0.100	0.150
2. Flood Plains
a. Pasture no brush
1. Short grass	0.025	0.030	0.035
2. High grass	0.030	0.035	0.050
b. Cultivated areas
1. No crop	0.020	0.030	0.040
2. Mature row crops	0.025	0.035	0.045
3. Mature field crops	0.030	0.040	0.050
c. Brush
1. Scattered brush, heavy weeds	0.035	0.050	0.070
2. Light brush and trees, in winter	0.035	0.050	0.060
3. Light brush and trees, in summer	0.040	0.060	0.080
4. Medium to dense brush, in winter	0.045	0.070	0.110
5. Medium to dense brush, in summer	0.070	0.100	0.160
d. Trees
1. Cleared land with tree stumps, no sprouts	0.030	0.040	0.050
2. Same as above, but heavy sprouts	0.050	0.060	0.080
3. Heavy stand of timber, few down trees, little undergrowth, flow below branches	0.080	0.100	0.120
4. Same as above, but with flow into branches	0.100	0.120	0.160
5. Dense willows, summer, straight	0.110	0.150	0.200
3. Mountain Streams, no vegetation in channel, banks usually steep, with trees and brush on banks submerged
a. Bottom: gravels, cobbles, and few boulders	0.030	0.040	0.050
b. Bottom: cobbles with large boulders	0.040	0.050	0.070
B. Lined or Built-Up Channels
1. Concrete
a. Trowel finish	0.011	0.013	0.015
b. Float Finish	0.013	0.015	0.016
c. Finished, with gravel bottom	0.015	0.017	0.020
d. Unfinished	0.014	0.017	0.020
e. Gunite, good section	0.016	0.019	0.023
f. Gunite, wavy section	0.018	0.022	0.025
g. On good excavated rock	0.017	0.020
h. On irregular excavated rock	0.022	0.027
2. Concrete bottom float finished with sides of:
a. Dressed stone in mortar	0.015	0.017	0.020
b. Random stone in mortar	0.017	0.020	0.024
c. Cement rubble masonry, plastered	0.016	0.020	0.024
d. Cement rubble masonry	0.020	0.025	0.030
e. Dry rubble on riprap	0.020	0.030	0.035
3. Gravel bottom with sides of:
a. Formed concrete	0.017	0.020	0.025
b. Random stone in mortar	0.020	0.023	0.026
c. Dry rubble or riprap	0.023	0.033	0.036
4. Brick
a. Glazed	0.011	0.013	0.015
b. In cement mortar	0.012	0.015	0.018
5. Metal
a. Smooth steel surfaces	0.011	0.012	0.014
b. Corrugated metal	0.021	0.025	0.030
6. Asphalt
a. Smooth	0.013	0.013
b. Rough	0.016	0.016
7. Vegetal lining	0.030		0.500
C. Excavated or Dredged Channels
1. Earth, straight and uniform
a. Clean, recently completed	0.016	0.018	0.020
b. Clean, after weathering	0.018	0.022	0.025
c. Gravel, uniform section, clean	0.022	0.025	0.030
d. With short grass, few weeds	0.022	0.027	0.033
2. Earth, winding and sluggish
a. No vegetation	0.023	0.025	0.030
b. Grass, some weeds	0.025	0.030	0.033
c. Dense weeds or aquatic plants in deep channels	0.030	0.035	0.040
d. Earth bottom and rubble side	0.028	0.030	0.035
e. Stony bottom and weedy banks	0.025	0.035	0.040
f. Cobble bottom and clean sides	0.030	0.040	0.050
3. Dragline-excavated or dredged
a. No vegetation	0.025	0.028	0.033
b. Light brush on banks	0.035	0.050	0.060
4. Rock cuts
a. Smooth and uniform	0.025	0.035	0.040
b. Jagged and irregular	0.035	0.040	0.050
5. Channels not maintained, weeds and brush
a. Clean bottom, brush on sides	0.040	0.050	0.080
b. Same as above, highest stage of flow	0.045	0.070	0.110
c. Dense weeds, high as flow depth	0.050	0.080	0.120
d. Dense brush, high stage	0.080	0.100	0.140

Other sources that include pictures of selected streams as a guide to n value determination are available (Fasken, 1963; Barnes, 1967; and Hicks and Mason, 1991). In general, these references provide color photos with tables of calibrated n values for a range of flows.

Although there are many factors that affect the selection of the n value for the channel, some of the most important factors are the type and size of materials that compose the bed and banks of a channel, and the shape of the channel. Cowan (1956) developed a procedure for estimating the effects of these factors to determine the value of Manning’s n of a channel. In Cowan's procedure, the value of n is computed by the following equation:

1)	$\begin{array}{l}\displaystyle n=(n_0+n_1+n_2+n_3+n_4)m\end{array}$

Symbol	Description	Units
$\begin{array}{l}n_b\end{array}$	Base value for n for a straight uniform, smooth channel in natural materials
$\begin{array}{l}n_1\end{array}$	Value added to correct for surface irregularities
$\begin{array}{l}n_2\end{array}$	Value for variations in shape and size of the channel
$\begin{array}{l}n_3\end{array}$	Value for obstructions
$\begin{array}{l}n_4\end{array}$	Value for vegetation and flow conditions
$\begin{array}{l}m\end{array}$	Correction factor to account for meandering of the channel

A detailed description of Cowan’s method can be found in “Guide for Selecting Manning’s Roughness Coefficients for Natural Channels and Flood Plains” (FHWA, 1984). This report was developed by the U.S. Geological Survey (Arcement, 1989) for the Federal Highway Administration. The report also presents a method similar to Cowan’s for developing Manning’s n values for flood plains, as well as some additional methods for densely vegetated flood plains.

Limerinos (1970) related n values to hydraulic radius and bed particle size based on samples from 11 stream channels having bed materials ranging from small gravel to medium size boulders. The Limerinos equation is as follows:

2)	$\begin{array}{l}\displaystyle \displaystyle n= \frac{(0.0926)R^{1/6}}{1.16 +201log \left( \frac{R}{d_{84}} \right)}\end{array}$

Symbol	Description	Units
$\begin{array}{l}R\end{array}$	Hydraulic radius, in feet (data range was 1.0 to 6.0 feet)
$\begin{array}{l}d_{84}\end{array}$	Particle diameter, in feet, that equals or exceeds that of 84 percent of the particles (data range was 1.5 mm to 250 mm)

The Limerinos (2) fit the data that he used very well, in that the coefficient of correlation $\begin{array}{l}\overline{R} ^2 = 0.88\end{array}$ and the standard error of estimates for values of $\begin{array}{l}n/R^{1/6} = 0.0087\end{array}$ . Limerinos selected reaches that had a minimum amount of roughness, other than that caused by the bed material. The Limerinos equation provides a good estimate of the base n value. The base n value should then be increased to account for other factors, as shown above in Cowen's method.

Jarrett (1984) developed an equation for high gradient streams (slopes greater than 0.002). Jarrett performed a regression analysis on 75 data sets that were surveyed from 21 different streams. Jarrett's equation for Manning's n is as follows:

3)	$\begin{array}{l}\displaystyle n=0.39S^{0.38}R^{-0.16}\end{array}$

Symbol	Description	Units
$\begin{array}{l}S\end{array}$	The friction slope. The slope of the water surface can be used when the friction slope is unknown.
$\begin{array}{l}R\end{array}$	The Hydraulic Radius of the main channel at bank full flow.

Jarrett (1984) states the following limitations for the use of his equation:

The equations are applicable to natural main channels having stable bed and bank materials (gravels, cobbles, and boulders) without backwater.
The equations can be used for slopes from 0.002 to 0.04 and for hydraulic radii from 0.5 to 7.0 feet (0.15 to 2.1 m). The upper limit on slope is due to a lack of verification data available for the slopes of high-gradient streams. Results of the regression analysis indicate that for hydraulic radius greater than 7.0 feet (2.1 m), n did not vary significantly with depth; thus extrapolating to larger flows should not be too much in error as long as the bed and bank material remain fairly stable.
During the analysis of the data, the energy loss coefficients for contraction and expansion were set to 0.0 and 0.5, respectively.
Hydraulic radius does not include the wetted perimeter of bed particles.
These equations are applicable to streams having relatively small amounts of suspended sediment.

Because Manning’s n depends on many factors such as the type and amount of vegetation, channel configuration, stage, etc., several options are available in HEC-RAS to vary n. When three n values are sufficient to describe the channel and overbanks, the user can enter the three n values directly onto the cross section editor for each cross section. Any of the n values may be changed at any cross section. Often three values are not enough to adequately describe the lateral roughness variation in the cross section; in this case the “Horizontal Variation of n Value” should be selected from the “Options” menu of the cross section editor. If n values change within the channel, the criterion described in "Theoretical Basis for One-Dimensional and Two-Dimensional Hydrodynamic Calculations", under composite n values, is used to determine whether the n values should be converted to a composite value using (.Cross Section Subdivision for Conveyance Calculations v6.0:2).

Equivalent Roughness “k”. An equivalent roughness parameter “k”, commonly used in the hydraulic design of channels, is provided as an option for describing boundary roughness in HEC‑RAS. Equivalent roughness, sometimes called “roughness height,” is a measure of the linear dimension of roughness elements, but is not necessarily equal to the actual, or even the average, height of these elements. In fact, two roughness elements with different linear dimensions may have the same “k” value because of differences in shape and orientation [Chow, 1959].

The advantage of using equivalent roughness “k” instead of Manning’s “n” is that “k” reflects changes in the friction factor due to stage, whereas Manning’s “n” alone does not. This influence can be seen in the definition of Chezy's “C” (English units) for a rough channel (Equation 2-6, USACE, 1991):

4)	$\begin{array}{l}\displaystyle \displaystyle C=32.6log_{10} \left[ \frac{12.2R}{k} \right]\end{array}$

Symbol	Description	Units
$\begin{array}{l}C\end{array}$	Chezy roughness coefficient
$\begin{array}{l}R\end{array}$	hydraulic radius	feet
$\begin{array}{l}k\end{array}$	equivalent roughness	feet

Note that as the hydraulic radius increases (which is equivalent to an increase in stage), the friction factor “C” increases. In HEC-RAS, “k” is converted to a Manning’s “n” by using the above equation and equating the Chezy and Manning’s equations (Equation 2-4, USACE, 1991) to obtain the following:

English Units:

5)	$\begin{array}{l}\displaystyle \displaystyle n = \frac{1.486 R^{1/6}}{32.6 log_{10} \right[ 12.2 \frac{R}{k} \right]}\end{array}$

6)	$\begin{array}{l}\displaystyle \displaystyle n = \frac{R^{1/6}}{18 log_{10} \right[ 12.2 \frac{R}{k} \right]}\end{array}$

Symbol	Description	Units
$\begin{array}{l}n\end{array}$	Manning’s roughness coefficient

Again, this equation is based on the assumption that all channels (even concrete-lined channels) are “hydraulically rough.” A graphical illustration of this conversion is available [USACE, 1991].

Horizontal variation of “k” values is described in the same manner as horizontal variation of Manning's “n” values. See "Modeling Culverts" of the HEC-RAS user’s manual, to learn how to enter k values into the program. Up to twenty values of “k” can be specified for each cross section.

Tables and charts for determining “k” values for concrete‑lined channels are provided in EM 1110-2-1601 [USACE, 1991]. Values for riprap-lined channels may be taken as the theoretical spherical diameter of the median stone size. Approximate “k” values [Chow, 1959] for a variety of bed materials, including those for natural rivers are shown in Table 3-2.

Table 3‑2 Equivalent Roughness Values of Various Bed Materials

	k (Feet)
Brass, Cooper, Lead, Glass Wrought Iron, Steel Asphalted Cast Iron Galvanized Iron Cast Iron Wood Stave Cement Concrete Drain Tile Riveted Steel Natural River Bed	0.0001 - 0.0030 0.0002 - 0.0080 0.0004 - 0.0070 0.0005 - 0.0150 0.0008 - 0.0180 0.0006 - 0.0030 0.0013 - 0.0040 0.0015 - 0.0100 0.0020 - 0.0100 0.0030 - 0.0300 0.1000 - 3.0000

The values of "k" (0.1 to 3.0 ft.) for natural river channels are normally much larger than the actual diameters of the bed materials to account for boundary irregularities and bed forms.

Contraction and Expansion Coefficients. Contraction or expansion of flow due to changes in the cross section is a common cause of energy losses within a reach (between two cross sections). Whenever this occurs, the loss is computed from the contraction and expansion coefficients specified on the cross section data editor. The coefficients, which are applied between cross sections, are specified as part of the data for the upstream cross section. The coefficients are multiplied by the absolute difference in velocity heads between the current cross section and the next cross section downstream, which gives the energy loss caused by the transition ((.Equations for Basic Profile Calculations v6.4:Energy Head Loss) of "Theoretical Basis for One-Dimensional and Two-Dimensional Hydrodynamic Calculations"). Where the change in river cross section is small, and the flow is subcritical, coefficients of contraction and expansion are typically on the order of 0.1 and 0.3, respectively. When the change in effective cross section area is abrupt such as at bridges, contraction and expansion coefficients of 0.3 and 0.5 are often used. On occasion, the coefficients of contraction and expansion around bridges and culverts may be as high as 0.6 and 0.8, respectively. These values may be changed at any cross section. For additional information concerning transition losses and for information on bridge loss coefficients, see "Modeling Bridges". Typical values for contraction and expansion coefficients, for subcritical flow, are shown in Table 3-3 below.

Table 3-3 Subcritical Flow Contraction and Expansion Coefficients

	Contraction	Expansion
No transition loss computed	0.0	0.0
Gradual transitions	0.1	0.3
Typical Bridge sections	0.3	0.5
Abrupt transitions	0.6	0.8

The maximum value for the contraction and expansion coefficient is one (1.0).

Note

In general, the empirical contraction and expansion coefficients should be lower for supercritical flow.

In supercritical flow the velocity heads are much greater, and small changes in depth can cause large changes in velocity head. Using contraction and expansion coefficients that would be typical for subcritical flow can result in over estimation of the energy losses and oscillations in the computed water surface profile. In constructed trapezoidal and rectangular channels, designed for supercritical flow, the user should set the contraction and expansion coefficients to zero in the reaches where the cross sectional geometry is not changing shape. In reaches where the flow is contracting and expanding, the user should select contraction and expansion coefficients carefully. Typical values for gradual transitions in supercritical flow would be around 0.01 for the contraction coefficient and 0.03 for the expansion coefficient. As the natural transitions begin to become more abrupt, it may be necessary to use higher values, such as 0.05 for the contraction coefficient and 0.2 for the expansion coefficient. If there is no contraction or expansion, the user may want to set the coefficients to zero for supercritical flow.