Computation of vertically averaged velocities in irregular sections of straight channels

Abstract

Abstract. Two new methods for vertically averaged velocity computation are presented, validated and compared with other available formulas. The first method derives from the well-known Huthoff algorithm, which is first shown to be dependent on the way the river cross section is discretized into several subsections. The second method assumes the vertically averaged longitudinal velocity to be a function only of the friction factor and of the so-called "local hydraulic radius", computed as the ratio between the integral of the elementary areas around a given vertical and the integral of the elementary solid boundaries around the same vertical. Both integrals are weighted with a linear shape function equal to zero at a distance from the integration variable which is proportional to the water depth according to an empirical coefficient β. Both formulas are validated against (1) laboratory experimental data, (2) discharge hydrographs measured in a real site, where the friction factor is estimated from an unsteady-state analysis of water levels recorded in two different river cross sections, and (3) the 3-D solution obtained using the commercial ANSYS CFX code, computing the steady-state uniform flow in a cross section of the Alzette River.

The FLO Diffusive 1D-2D Model for Simulation of River Flooding

“…The initial condition is η = 0, and L(h km ) in Equation (20) is the water surface width corresponding to h km . After some simple manipulations, it can be shown that Equations (18) and (19) are kinematic, with only one characteristic line passing through each (x, t) point [14,18]. The prediction PDE system is equivalent to a single non-linear convection equation, the function of the gradient of the piezometric head at time level t k , while the correction system has the functional characteristics of a pure diffusive problem.…”

“…In the present physical problem, an exact scalar potential of the flow field does exist (the water level), and this allows an easy ordering of the computational cells, from the highest to the lowest water levels. After integration in space, the differential form of the prediction Systems (18) and (19) for cell i is: where summation on the l.h.s. represents the leaving fluxes from cell i to any neighboring downstream (in the potential scale) cell j (with H k i ą H k j ) and summation on the r.h.s.…”

“…where Q sp is a function of h max , of the bed roughness and of the section geometry, called in the following conveyance and computed as a function of h max according to [19]. Equation (1) is the mass conservation equation, and Equation (2) is the momentum conservation equation where terms not proportional to acceleration due to gravity have been neglected according to the diffusive hypothesis.…”

Unsteady State Water Level Analysis for Discharge Hydrograph Estimation in Rivers with Torrential Regime: The Case Study of the February 2016 Flood Event in the Crati River, South Italy

“…Conveyance K is computed as function of the Manning coefficient n, the geometry of the river section and the water depth h, according to [6]. The investigated reach is discretized in N − 1 channels, linking N sections at the centre of N computational cells.…”

“…In the last years, some researchers have developed indirect methods for the discharge hydrograph estimation, based on the measure of two stage hydrographs at the ends of a selected reach of the river and on the use of unsteady-state hydraulic modeling [4][5][6][7]. The main advantage of the method is that it allows the simultaneous estimation of the unknown river bed parameters and discharge hydrographs.…”