Hydraulic geometry equations of alluvial channels

The prediction of the downstream hydraulic geometry of equilibrium alluvial channels is the main focus of this study. For any given water and sediment discharges in an alluvial channel, the depth, width, velocity and slope can be predicted by using 3 proposed sets of hydraulic geometry equations.; Two sets of semi-theoretical hydraulic geometry equations are proposed for predicting the downstream hydraulic geometry of alluvial channels. Both sets of equations are theoretically developed by using four fundamental hydraulic relationships: continuity, resistance to flow, sediment transport, and secondary flow. The independent variables of the first set of equations (Eqs. 5.5-5.8) are: flow discharge (Q in m{dollar}sp3{dollar}/s), mean sediment size (d{dollar}sb{lcub}50{rcub}{dollar} in m), and bed-load sediment in terms of Shields parameter {dollar}(tausb*).{dollar} The equations can be used for predicting the mean depth (D in m), surface width (W in m), mean flow velocity (V in m/s), and slope of alluvial channels (S). The independent variables of the second set of equations (Eqs. 5.9-5.12) are: flow discharge (Q), mean sediment size (d{dollar}sb{lcub}50{rcub}),{dollar} and channel slope (S). The equations can be used for predicting the mean depth (D), surface width (W), mean flow velocity (V), and Shields parameter {dollar}(tausb*).{dollar}; A third set of hydraulic geometry equations (Eqs. 5.1-5.4) has been determined by regression analysis and conceptually developed based on the qualitative morphologic principle as reported by Lane (1955) and Schumm (1969, 1971).; A large data set including hydraulic geometry measurements of 835 rivers and 45 laboratory channels has been used for calibration, verification, and validation of the proposed hydraulic geometry equations. From this data set, 382 observations, called river data "A", have been used for calibrating the proposed equations. Another 382 observations, called river data "B", verified the proposed equations. The verified equations were then validated with three extreme alluvial channel conditions: sand-bed rivers (28 observations), gravel-bed rivers (43 observations), and small scale laboratory channels (45 observations).; Both the verification and the validation show strong agreement between predictions and observations. At least 90 percent of the predicted values are within a factor two of the observed values, and the correlation coefficient usually exceeds 90 percent.