DR COLIN CLARK [2]
where IΔτ = change in inflow, OΔτ = change in outflow, Δs = change in storage during the time interval and Δt is the time interval in seconds.
The inflow and outflow discharges are the average of the values at the start and end of each time step. The change in storage is also over the same time period. Equation 2 can be rewritten in more detail, with subscripts 1 and 2, which refer to the start and end of each time period.
[3]
Equation 3 can be rearranged, making the solution of the outflow discharge possible. [4]
The relationship between the inflow and outflow terms in Equation 4 and the outflow discharge is shown in Table 11.
Table 11. Extract of the reservoir routeing
The routeing procedure can now proceed but the outflow discharges over the spillway must be reduced by up to 2.7m3/sec to take into account the effect of the bywash channel. Soon after the flood the author visited the bywash channel and it was clear from the trash line and disturbance to above bank vegetation that the channel had overflowed. The peak outflow is estimated as 22.1m3/sec, of which 2.7m3/sec passed down the bywash channel with spillage into the reservoir. Figure 7 shows the routed hydrograph as well as the model- based hydrograph just upstream of the reservoir. Balmforth[3] suggested that the reservoir would have needed to have been up to 5m higher in order to avoid overtopping of the auxiliary spillway. This volume equates to a run-off depth of 43mm. The inflow hydrograph shown in this paper compares well with the estimate here of 37mm. The flow of 19.4m3/sec
40 DAM ENGINEERING Vol XXXII Issue 1
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