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Full Equations Utilities (FEQUTL) Model for the Approximation
of Hydraulic Characteristics of Open Channels and Control
Structures During Unsteady Flow

A generalization of the Ritter (1892) solution for the peak outflow following the instantaneous failure of a dam is computed with the GRITTER command (section 5.14). The reservoir cross section is assumed to be prismatic, horizontal, and frictionless. Furthermore, there can be an initial flow in the reservoir, and the cross section of the failure site need not match the cross section of the reservoir. Although restrictive, the assumptions for the generalized solution allow reasonable estimates to be made of the peak flows that are physically possible as a result of a variety of failures. These estimates can be used to assess the reasonableness of the results obtained through solution of the dam-break problem using the options available in FEQ.

The generalization to a nonrectangular channel cross section involves the introduction of the Escoffier stage variable, , defined as

where

The Escoffier stage variable transforms the characteristic form of the governing equations into a convenient form for solution. The details of this transformation and a derivation of the solution are presented in Franz (1977). The solution for the relation between the water-surface height and velocity at the dam site after the failure is

where

and

Equation 101 contains two unknowns: water-surface height and
water velocity at the dam site after the failure. If the dam
fails completely and the cross section at the dam is identical
to the cross section in the reservoir, the Ritter solution
indicates that the flow at the dam site is critical. Thus, it
is reasonable, as confirmed by test results, to assume that the
flow at the dam site will be critical for a partial failure
with perhaps some allowance made for the associated contraction
losses. The critical-flow relation at the dam site for the dam
breach provides another equation relating the velocity to
water-surface height at the dam site in the reservoir cross
section. Thus, a function, *f _{DB}* (

The depth and velocity in the reservoir at the dam site must be
the same for both equation 101 and for *f _{DB}* (

A modified false-position technique is applied to solve equation 102.

The command CRITQ (section 5.4) is designed to compute the
function *f _{DB}* (

where *a _{i}* and

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