Chapter 3 : Reservoir models - KU Leuven

200
throughflow Q (l/s)
175
real relationship
150
125
Q 1
'static' approach
Q = Q 1 +
k 2 * (V-V 1 )
100
75
50
Q = k 1 * V
25
0
0 20 40 60 80 100 120 140
storage V (m 3 )
V 1
Figure 3.28 : Bi-linear ‘static’ approach (with slopes k 1 and k 2 ) for the
storage/throughflow-relationship of a small gravitary sewer system
(for the composite storm which will just lead to an overflow event).
If a linear relationship is used between the volume in the system and the inflow and
outflow, the differential equation (3.12) can be solved analytically (equation 3.13).
This has the advantage that a very fast and accurate calculation can be performed.
Calculation time and accuracy are both very important for long term simulations.
Using the piecewise linear relationships between storage and flow, these advantages
can be retained by applying the analytical solution in a subcoordinate system. The
transition from one linear relationship to another is made by a translation of the
coordinate system (figure 3.29). However, if the starting points of every linear
subrelationship between static storage and throughflow on the one hand and between
dynamic storage and inflow on the other hand are not situated at the same storage
values, the combined analytical solution of static and dynamic storage (equations 3.11
and 3.13) cannot be used anymore. Both relationships must be linear at the same time
in a subcoordinate system. Therefore, it is chosen to uncouple the dynamic storage
from the static storage module as shown in figure 3.26.
Chapter 3 : Reservoir models 3.31