On the Concept of Mean Hydraulic Radius

Abstract

By using the hydrodynamic analogy between the torsion of a uniform bar with arbitrary cross-section and viscous flow through a channel of the same shape, the flow rate through any channel may be predicted (1) Computation of the aspect ratio of the cross-section of the channel; (2) measurement of the area using a planimeter; (3) Measurement of the wetted perimeter of flow; and (4) Observation of the number of significant sides comprising the cross-section. The mean hydraulic radius may be obtained as the quotient of (2) and (3). This parameter is then modified by (1) and (4) to improve the accuracy of the prediction. For channels with variable shape and size along their length, the same concepts may be used. In such cases, an equivalent area is defined in the computation of hydraulic radius according to a method outlined in the appendix. Experimental support for the concepts proposed has been furnished from extensive tests by the author using plates with regular and random asperities. The validity of the mean hydraulic radius concept has led to the development of a scientific outflow instrument which is capable of predicting the drainage ability of road surfaces subjected to pneumatic tire traffic.