Chapter 3 : Reservoir models - KU Leuven

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Although this is an unrealistic (artificial) situation, this state is most often a very good approximation of the situation at the end of an overflow event (figure 3.7). At least the maximum static storage in a sewer system can be assessed in this way, even if there is a flow in the system which creates an extra storage (this is most often the case). In the same way the static storage at any time can be assessed as the storage during the emptying of the system when no rainfall input is present. This means that the instantaneous static storage, for instance for the case of figure 3.6, must be very close to the storage during the falling branch of the storm (slightly smaller (see figure 3.15)). In figure 3.7 it can be seen that the storage at the end of the overflow event is a good indication of the maximum static storage in the system. If only the static storage is incorporated, the storage at the beginning of the smallest overflow event can also be a good estimation for the static storage (values near to 0 on the horizontal axis in figure 3.7). Although the maximum static storage can be easily obtained at the end of the overflow event, it is important to use the instantaneous relationship between storage and throughflow for the rising branch of the storm up to the moment the overflow starts spilling. This is necessary to obtain a good estimation of the start of the overflow. The primary objective should be to detect if an overflow occurs or not and when it starts. The emptying of the system after the overflow event only has a second order effect, because the storage in the system can have an influence on the following overflow event. This means that in the first instance the dynamic storage can be neglected. As for sewer system calculations in Flanders the composite storms are used, it is logical to use the composite storm that will just lead to an overflow event to determine this storage/throughflow-relationship in a first approach. This first approach has been applied to a number of different sewer systems and provides already a lot of information on the sewer systems behaviour. In figure 3.9 the ‘static’ storage/throughflow-relationship is shown for a small sewer system with a gravitary throughflow. 3.10 The influence of rainfall and model simplification on combined sewer system design
200 175 150 125 100 75 50 25 0 throughflow (l/s) real relationship linear 'static' approach storage (m 3 ) 0 20 40 60 80 100 120 140 Figure 3.9 : Storage/throughflow-relationships up to the moment the overflow starts spilling for a small sewer system with a gravitary throughflow. It can be seen in figure 3.9 that the relationship between storage and throughflow is almost linear. In that case the sewer system is labelled as ‘behaving linearly’. As the throughflow from the system is linearly varying with the volume in the system and the volume in the system is a function of the inflow through the continuity equation, a specific input hydrograph will be smoothed, but the antecedent condition in the reservoir will have only a limited influence. The system behaviour is then driven by the flow. In figure 3.10 the ‘static’ storage/throughflow-relationship is given for a small sewer system with a single pump for the throughflow. It can be seen that the relationship between storage and throughflow in this system is far from linear. If this relationship would be approximated with the best linear fit (as is shown in figure 3.10) large errors on the system behaviour are made. If a linear approximation is made based on the maximum storage and the maximum throughflow only, the error will be even larger. This clearly shows that it is not sufficient to determine the maximum storage and maximum throughflow only, but that the instantaneous relationship between storage and throughflow is equally important. When the relationship between the storage in the system and the throughflow is divergent from linearity, the system behaviour is labelled as non-linear. For this system (figure 3.10), the throughflow is even completely independent on the storage volume in the system. This means that the throughflow is hardly influenced by the immediate input into the system, but mainly by the antecedent rainfall over a longer time. The system behaviour is driven by the volume instead of the flow. The throughflow (and overflow) hydrograph can be completely different when the same input hydrograph is used, depending on the antecedent rainfall. Chapter 3 : Reservoir models 3.11
Page 1 and 2: Chapter 3 : Reservoir models 3.1 Hi
Page 3 and 4: In this figure 3.3 the constant thr
Page 5 and 6: 3.2.2 Concentration time As was alr
Page 7 and 8: (implemented) concentration time of
Page 9: In figure 3.7 the storage in the sy
Page 13 and 14: The influence of the simplification
Page 15 and 16: Figure 3.14 : Longitudinal profile
Page 17 and 18: 1.2 throughflow (m 3 /s) 1 0.8 0.6
Page 19 and 20: Also for combined sewer systems the
Page 21 and 22: 3.2.4 Runoff models After the calib
Page 23 and 24: instantaneous runoff coefficient 1
Page 25 and 26: Other more detailed runoff models c
Page 27 and 28: 3.3 The reservoir modelling system
Page 29 and 30: If the concentration time is not ta
Page 31 and 32: 200 throughflow Q (l/s) 175 real re
Page 33 and 34: 3.3.3 Other features The reservoir
Page 35 and 36: For emission modelling it is very i
Page 37 and 38: Figure 3.31 : Overflow frequencies
Page 39 and 40: Figure 3.33 : Overflow volumes (% o
Page 41 and 42: Not only the storage, the throughfl
Page 43 and 44: As the overflow events are strongly
Page 45 and 46: 16 peak overflow discharge (mm/h) 1

Chapter 3 : Reservoir models - KU Leuven

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