Jarrett’s equation can be used to estimate an accurate Manning’s n value for steep streams. This is important because steep mountain streams should, in many cases, be assigned a higher Manning’s n value than what is shown in Chow’s Manning’s n value tables (which is a table many hydraulic engineers reference regularly). For example, Chow’s Manning’s n value table indicates that steep mountain streams should be assigned a Manning’s n value of 0.03 to 0.07, depending on how many boulders are in the stream bed. However, a much higher Manning’s n value (possibly as high as 0.25) should be assigned to steep mountain streams, especially when modeling lower discharges. If you are struggling with stabilizing an unsteady flow model, I recommend trying Jarrett’s equation.
Jarrett’s Equation for High Gradient Streams
n = 0.39 Sf0.38 R-0.16
where,
n is Manning’s roughness coefficient,
Sf is the energy gradient/friction slope of the stream (ft/ft), and
R is the hydraulic radius of the stream (ft2/ft).
Limitations of Jarrett’s Equation
- The equation is applicable to natural main channels comprised of stable bed and bank material (e.g., cobble and boulder-bed material).
- The equation applies to streams with slopes ranging from 0.002 to 0.04 ft/ft and hydraulic radii ranging from 0.5 to 7 feet. Jarrett did note that the results of his regression analyses indicated that Manning’s n did not vary significantly with depth for hydraulic radii greater than 7 feet. Therefore, extrapolation to large flow depths should not cause too much error as long as the channel’s bed and bank material remain fairly stable at those depths.
- The energy loss coefficients due to channel contraction and expansion were set to 0.0 and 0.5, respectively. However, Jarrett notes that the expansion coefficient should be increased in cases where there are moderate to several expansions.
- The equation should not be used for stream reaches affected by backwater from downstream obstructions.
Link to Jarrett’s Report
The following link will take you to Jarett’s full report, which is a 60-page document published on the United States Geological Survey’s website.