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United States Department of Agriculture

Agricultural Research Service

Title: Comparison of Constitutive FLOW RESISTANCE Equations Based on the MANNING AND CHEZY EQUATIONs Applied to Natural Rivers)

item Bjerklie, David
item Dingman, Lawrence
item Bolster, Carl

Submitted to: Water Resources Research
Publication Type: Peer reviewed journal
Publication Acceptance Date: 7/26/2005
Publication Date: 11/10/2005
Citation: Bjerklie, D.M., Dingman, L., Bolster, C.H. 2005. River discharge and general flow resistance in the manning and chezy equation revisited. Water Resources Research. 41, W11502.

Interpretive Summary: Stream flow is one of the most important parameters needed for watershed planning and conservation. Modeling of stream flow relies on the use of a general flow-resistance or constitutive equation that characterizes the relation between energy gradient and flow rate. The most commonly used constitutive equation is the Manning equation which requires measurement of bed slope, hydraulic radius, and an estimate of the resistance coefficient. Although the Manning equation is widely used, no studies have established a sound theoretical basis for the exponents on bed slope and hydraulic radius. A more significant limitation, however, is that there is no universally accepted way of determining the appropriate value of the resistance coefficient from measurable stream channel characteristics for a priori or a posteriori applications, especially considering that flow resistance varies with flow conditions. Estimation of the resistance coefficient often is the largest source of error in the application of the Manning equation to estimate velocity and discharge for various engineering problems. In this paper, values for the resistance coefficient and exponents on bed slope and hydraulic radius are developed for use in natural rivers using statistical and physical arguments. By modifying the Manning equation we were able to significantly reduce the variance associated with estimating flow resistance. This finding is especially important because it will free the modeler from the inherently subjective and highly uncertain process of estimating the value of the conductance coefficient. The study also provides insight into the physical interrelationship between flow resistance and channel geometry in rivers.

Technical Abstract: A set of rationally derived in-bank river discharge-estimating equations (models), based on the Manning and Chezy equations, are developed, calibrated and validated using a database of 1,037 discharge measurements in 103 rivers in the United States and New Zealand. The models are compared to a multiple-regression model and a general resistance equation. The comparison demonstrates that, in natural rivers, using an exponent on the slope variable of 0.33 rather than the traditional value of 0.5 reduces the variance associated with estimating flow resistance. Mean model uncertainty, assuming a constant value for the conductance coefficient, is less than 5% for a large number of estimates and 67% of the estimates would be accurate within 50%. The models have potential application where site-specific flow-resistance information is not available, and can be the basis for (1) a general approach to estimating discharge from remotely sensed hydraulic data, (2) comparison to slope-area discharge estimates, and (3) large-scale river-modeling.

Last Modified: 8/24/2016
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