All methods are based on the continuity equation, in the form:
I OdV/dt (4.2)
whereIis the inflow, Othe outflow, and Vthe reservoir storage. In a finite
difference form, equation (4.2) can be written as
I ̄ O ̄∆V/∆t (4.3a)
or
. (4.3b)
In equation (4.3a), Orefers to the spillway outflow. If other regulated out-
flowsOR(bottom outlets, irrigation outlets, hydroelectric power, etc.) are
present then these should be included in the form O ̄R.
The solution of equation (4.3), which contains two unknowns, V 2 and
O 2 (∆tis chosen), is possible only because in reservoir routing there is a
unique relationship between water level and storage (this follows from the
assumption of a horizontal water level in the reservoir) as well as water
level and outflow; therefore there is also a unique relationship between
outflowOand storage volume V.
Denoting by hthe head above the spillway crest, and by Athe reser-
voir area at level h,
Af 1 (h) (4.4)
Vf 2 (h) (4.5a)
or
∆VA∆h (4.5b)
Of 3 (h) (4.6)
Of 4 (V). (4.7)
Equations (4.3a) and (4.7) together yield the solution in a numerical, graphical,
or semigraphical procedure. For example, by rewriting equation (4.3b) as
O 2 I 1 I 2 O 1 (4.8)
we have on the right-hand side of the equation only known quantities
enabling us to establish Of(t) from the relationship O(2V/∆tO), which
we can derive from equation (4.7) for a chosen ∆t(Worked example 4.1).
2 V 1
∆t
2 V 2
∆t
O 1 O 2
2
I 1 I 2
2
V 2 V 1
∆t
196 DAM OUTLET WORKS
