Forest Reference Stream
Hydraulic Geometry Equations and Coefficients
Samuel H. Austin March 2, 2006
Hydraulic geometry describes the way in which channel properties change with stream flow. Reference hydraulic geometry describes the normal range of channel properties for each type of forest reference stream, serving as a useful guide.
Mean water depth (D), water width (W), and mean water velocity (V) all vary with stream discharge (Q). The interrelationships among these variables, termed hydraulic geometry are described by the following equations:
W = aQb D = cQd V = eQf
The coefficients a, c, and e, and the exponents b, d, and f are empirically derived. The hydraulic geometry equations are power functions. When plotted on log-log paper the slopes of the curves, described by the exponents b, d, and f indicate the average change in width, depth, and velocity respectively, with changes in water discharge, and do not vary with the units used (i.e. metric or English units).
Since, by the continuity equation:
Q = velocity (V) • cross-sectional area (A) = WDV (with D the hydraulic
depth, A/W),
it follows that WDV = aQb • cQd • eQf =
Q
and thus, theoretically perfect relationships result in
b + d + f = 1 and a • c • e = 1.
Our reference hydraulic geometry relationships are measured, empirical, and “dimensionless” meaning they have been developed as ratios related to forest reference stream bankfull values of width, depth, velocity, and discharge. Since the geometric relationships in stream channels remain consistent as scale changes, our dimensionless hydraulic geometry relationships are applicable to streams of most sizes, small to large.
The following table lists dimensionless values and coefficients of forest reference stream geometry, organized by Rosgen stream type. Values are for bankfull conditions.
Reference Hydraulic Geometry
Dimensionless Width, Depth and Velocity Ratios and Coefficients
Organized by Rosgen Stream Type
| Rosgen Stream Type | W | D | V | a | c | e | b | d | f |
|---|---|---|---|---|---|---|---|---|---|
| A2 | 1.024 | 0.963 | 1.009 | 1.024 | 0.963 | 1.009 | 0.216 | 0.208 | 0.574 |
| B2 | 0.997 | 0.897 | 1.001 | 0.997 | 0.897 | 1.001 | 0.073 | 0.156 | 0.681 |
| B3 | 1.174 | 0.915 | 1.000 | 1.174 | 0.915 | 1.000 | 0.216 | 0.344 | 0.531 |
| C4 | 1.000 | 0.882 | 1.002 | 1.000 | 0.882 | 1.002 | 0.023 | 0.223 | 0.698 |
| C5 | 0.872 | 1.000 | 1.001 | 0.872 | 1.000 | 1.001 | 0.248 | 0.409 | 0.307 |
Note: W, D, and V represent dimensionless ratios such that:
W = w/WBKF, D=d/dBKF, V = v/vBKF. B3 e, C4 a, and C5 c values are assumed.
Last modified: Monday, 10-Mar-2008 19:32:09 UTC