A Study of the Variability Versus the Assumed Constancy of Manning's n

• Main Author: Allen, Tyler G.
• Format: Others
• Published: DigitalCommons@USU 2014
• Subjects: Manning's n; Variability; Assumed Constancy; Civil and Environmental Engineering
• Online Access: https://digitalcommons.usu.edu/etd/2802; https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=3795&context=etd

Quantifying hydraulic roughness coefficients is commonly required in order to calculate flow rate in open channel applications. An assumption typically coupled with the use of Manning’s equation is that a roughness coefficient (n) that is solely dependent upon a boundary roughness characteristic (k) may be applied. Even though Manning reported unique values of n and x’ (the exponent of the hydraulic radius in Manning’s equation) for each of the different boundary roughness materials he tested, he chose x’ = 2/3 as representative, assumed a constant n value, and suggested that it was sufficiently accurate. More recent studies have suggested that in addition to k; Rh, Se, and Fr can influence n. While research points to situations where n may vary, it is always a temptation to simply apply the constant n assumption especially in the case of more complicated channels such as composite channels where different roughness materials line different parts of a channel cross section. This study evaluates the behavior of n as a function of Re, Rh, k, So, and Fr for four different boundary roughness materials ranging from smooth to relatively rough in a rectangular tilting flume. The results indicate that for the relatively rough materials n is best described by its relationship with Rh where it varies over a lower range of Rh but approaches and at a point maintains a constant value as Rh increases. The constant value of n is attributed to both the physically smooth boundary materials and a quasi-smooth flow condition in the rougher boundary materials. The study shows that an x’ = 2/3 (the basis of Manning’s equation) correlated to the assumption of a constant n value only applies to smooth boundary roughness materials and a quasi-smooth flow condition in the rougher boundary materials; otherwise, either n or x’ must vary. These findings are then applied to compare 16 published composite channel relationships. The results identify the importance of applying a varying n where applicable due to the potential for error in assuming and applying a constant n. They also indicate that the more complicated predictive methods do not produce more accurate results than the simpler methods of which the most consistent is the Horton method.