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Full Equations (FEQ) Model for the Solution of the Full, Dynamic Equations of Motion for One-Dimensional Unsteady Flow in Open Channels and Through Control Structures

U.S. GEOLOGICAL SURVEY WATER-RESOURCES INVESTIGATIONS REPORT 96-4240

7.2 Approximation of the Equations of Motion in a Level-Pool Reservoir


A level-pool reservoir is similar to a dummy branch except that the storage relation is more complex and lateral inflows are possible. The elevation of the water surface in a level-pool reservoir is, by definition, the same at all points across the reservoir. However, it is useful to allow a small difference in elevation between the upstream and downstream flow-path end nodes, just as in a dummy branch. Thus, equation 87 applies as the relation between flow and elevation change for a level-pool reservoir. The conservation of mass equation is

(88)

Equation ,

where

Equation ;
Equation ; and
ST(zw) is storage capacity of the reservoir at water-surface elevation zw.

Again, the average water-surface elevation of the two nodes is used to define the storage so that all the partial derivatives will be nonzero for equation 88 in the nonlinear solution for the unknowns. The lateral inflow, IM, is computed for level-pool reservoirs in the same manner as for branches. One or more outflow relations can be associated with a level-pool reservoir. These relations are, however, viewed as internal boundary conditions for the stream system simulated with FEQ and not as part of the reservoir. The level-pool reservoir equations describe only the storage of water in the reservoir.


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