#### Date of Award:

6-1-2014

#### Document Type:

Dissertation

#### Degree Name:

Doctor of Philosophy (PhD)

#### Department:

Civil and Environmental Engineering

#### Advisor/Chair:

Blake P. Tullis

#### Abstract

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.

#### Recommended Citation

Allen, Tyler G., "A Study of the Variability Versus the Assumed Constancy of Manning's n" (2014). *All Graduate Theses and Dissertations.* Paper 2802.

http://digitalcommons.usu.edu/etd/2802

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