4.6. A practical example of application
At the Sindi Dam, in the River Pärnu, Estonia, stands an old pool-and-weir fishway with alternating notches. The pools are 4 meters long and 3 meters wide with 1.3-meter-high weirs. The slope of the fishway is 5 % and the estimated drop between the pools is about 0.2 meters. Among the most important fish species in this river are whitefish and vimba, which are weak swimmers. Fish do not use the existing fishway and thus there are plans to improve it.
The structure is very massive having concrete sidewalls of 1.0 meters wide and the width of the weirs being 0.5 meters. The construction costs should be kept as low as possible, and thus dividing the pools into half is seen as the best option for improvement. Due to the poor swimming ability of the fishes for whom the fishway is meant, a vertical slot fishway would best fulfill the demands for the fishway. The new pool length would be 2.0 meters, the slot width should be at least 0.25 meters, and for reasonable energy dissipation, the slots should either alternate from side to side or be equipped with baffles below the slots.
It should be possible to estimate the fishway discharge in the changed situation. With the suggested energy dissipating schemes, it is estimated dimensionless analysis can be used. The procedures developed both the previously and for this study can be applied.
Rajaratnam et al. (1992) introduces a variety of possible vertical slot fishway modifications. One good choice for the present analysis is Design 6 (App. 4, Fig. A4.1). Uncertainties in this choice are caused by the width of the pool, which in this example is more than twice that of Design 6. Now, the scaling factor for dimensionless discharges Q* is
where Q is the discharge, So is the bottom slope and bo is free opening. Dimensionless discharge for Design 6 is expressed as
Q* = 3.77 yo/bo - 1.11 for yo/bo ≤10
where yo is the water depth at the slot. From these equations we get
=>
Q = 0.02 Q* = 0.02(3.77 yo/bo - 1.11).
For the water depth equal to the highest weir height 1.3 m we get with this procedure
Q = 0.410 m3/s and vm = 1.26 m/s.
According to the procedure developed in this study, the scaling factor for dimensionless discharges is
where Q is the discharge, So is the bottom slope, bo is free opening, and L is the pool length. Now
=> Q = 0.50 Q*.
The general dimensionless discharge equation is
where yo is the water depth at the slot. For the water depth equal to the highest weir height (1.3 m), this procedure yields (L = 2.0 m)
Q = 0.262 m3/s and vm = 0.80 m/s.
The dimensionless discharge equation for vertical slot fishways (from Table 7) is
For the water depth equal to the highest weir height (1.3 m), this procedure then yields
Q = 0.286 m3/s and vm = 0.88 m/s.
When approaching velocity is not taken into account, slot velocities with a drop of 0.1 meters can be estimated with the equation
v = (2gΔh)0.5 = (2*9.81*0.1)0.5 = 1.4 m/s.
According to the observations of Kamula (1995), a better estimate for the velocities would be
v = 0.7(2gΔh)0.5 = 0.7(2*9.81*0.1)0.5 = 0.98 m/s.
When these two values are compared, it can readily be seen that all the results reasonably well support the procedure used. The general equation (22) probably gave too low discharge values, which actually was predictable. The discharge value calculated by using the previously developed procedure probably gave slightly too high discharges. The best fit of these three is probably given by the equation for vertical slot fishways developed during this study. The real value of the procedure can be estimated only if the results are compared with measurements in actual structures and situations.