Fundamentals of Fluvial Geomorphology and Channel Processes
L = 1890 Qm0.34 M-0.74
where Qm is the average annual flow. The width to depth ratio (F) is also related to the
percentage silt and clay:
F = 255 M-1.08
Channel slope (S) was found to be related to the mean annual discharge (Qm) and percentage
silt and clay:
S = 60 M-0.38 Qm-0.32
Regime theory is an application of the idea that the width, depth, slope, and planform
of a river are adjusted to a channel-forming discharge. In his review of the history of regime
theory, Lane (1955) states that in 1895 Kennedy proposed the following relationship:
V = cDm
in which V is the mean channel velocity, D is the channel depth, and c and m are constants
developed for various channel locations. Much of the early work in developing regime
relationships was conducted in the irrigation canals of India, and since the early 1900s, many
relationships have been proposed.
Leopold and Maddock (1953) compiled a significant statistical data base using USGS
gauging records and developed hydraulic geometry relationships for the width, depth,
velocity, and other hydraulic characteristics for some streams in the United States. The
hydraulic geometry relationships are of the same general form as Kennedy (1895):
W = a Qb
D = c Qf
V = k Qm
in which W is channel width, Q is discharge, D is depth, and V is velocity.
All of the relationships presented, including the hydraulic geometry relationships, are
strictly empirical, i.e., the relationships describe observed physical correlations. As conditions
change from watershed to watershed, the relationships must be modified. For example,
stream width for sandy banks would be expected to be different from clay banks. Schumm's
relationship between width to depth ratio (F) and the weighted percent silt-clay in the channel
perimeter (M) is an empirical relationship that describes this observation. If Schumm's
relationship is correct, then is the hydraulic geometry relationship valid that predicts width
(W) based only as a function of discharge? Both relationships can be valid for the data set
used in developing the relationship.
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