HYDRAULIC-RESISTANCE TERMS MODIFIED FOR THE DRESSLER CURVED-FLOW EQUATIONS

Abstract

The well-known empirical hydraulic-resistance terms, in common use with the Saint-Venant equations, are here modified to the specific functional form necessary for their use with the Dressier equations for curved open-channel two-dimensional flow in rectangular channels. From the general resistance term three cases are considered for three regimes of turbulent flow: the Blasius “smooth” flow; the Chezy “transitional” flow; and the Manning “rough” flow. These new functions are compared with the analogous terms in common use with the Saint-Venant equations. The modifications needed for the Dressier equations for the Chezy and Manning regimes are incorporated in two extra factors, a_m and a_v. The a_m factor is a given function of channel bottom curvature κ and of flow perpendicular thickness N, expressing the mass change affected by a boundary drag when flow is over a convex or concave bottom. The av factor is a given function of κ, N, and channel width w, expressing the modification required in bottom velocity C to adjust for the variable velocity profile in curved flow. For the Blasius regime, an additional function aq is required to adjust the velocity near the bed to the average velocity over the profile. Each of the three functions a_i reduces to unity when κ = 0. An example is presented showing their numerical values for κN = -0.4 (convex) and +0.4 (concave). Their behavior shows that the hydraulic resistance effect is decreased when the channel bottom is convex, but increased when concave, and these changes are greater in narrow channels than in wide channels.