6.4. Considerations of the velocity distribution at V-shaped sharp crested weirs
Velocity distribution at a weir was studied for a single weir with a sharp V-shaped crest and for a chain of weirs with almost similar crests. In the case of a single weir and zero bed slope, the approach velocity is nearly zero and only backwater and submergence affect to the flow over the weir. In the case of a chain of weirs, even though the approach velocity is higher, the chain of weirs more efficiently dissipates the energy of the flowing water.
The dimensionless velocity profiles of a chain of weirs were plotted into the same graph. It can be seen that the trend is mainly the same for all the curves: velocities are lower near the bottom of the opening for almost all the discharges and heads (Fig. 26). The only differences are for the lowest dimensionless discharges. With very low dimensionless discharges, the velocities at the weir are lowest at the surface and highest at the bottom. When the discharge increases, the velocity distribution gradually changes. At first, the velocities near the surface and near the bottom of the V are about the same, and with further increase in discharge, the velocities near the bottom of the V decrease and the highest velocities are found near the surface.
Velocities at a single weir are higher near the bottom of the V than near the surface (Fig. 25). The basic velocity distribution pattern does not change with the change of the head at the weir and the submergence ratio.
Velocity measurements at weirs are often included in studies on weirs and also in studies on fishways. These measurements are, however, occasional and not very precise, and the results are usually not included in the reports. However, some studies have been reported. According to Katopodis (1995), velocity distribution at a weir of a pool-and-weir fishway depends on the mode of flow, whether it is plunging or streaming. In the plunging mode, when the relative depth of flow is small, velocities near the weir crest are slightly higher than the velocities at the surface. In the streaming mode, velocities are highest at the middle of the flow depth of the weir, decreasing to the surface and to the weir crest (Fig. 27). Compared with the velocity distribution pattern in a pool-and-weir fishway with a V-shaped crest, the highest velocities are located higher in the opening.
Figure 27. Typical velocity profiles at the weir of a pool-and-weir fishway. y is the water depth measured from the bottom of the V-notch and d is the water depth perpendicular to the bottom (redrawn from Katopodis 1995).
Boiten (1989) studied a pool-and-weir fishway with a V-shaped crest (Appendix 6). In the studies, the pools were long and the depth of flow over the weir was so low compared to the pool length, that the weirs acted like separate/ local roughness elements. According to the measurements, the velocities were highest at the middle of the opening (Fig. 28). For comparison, the results were transformed into dimensionless values using equation (26) for scaling velocities and equation 20 for scaling discharges. Velocity distribution at the weir was similar to that of a single weir or that of a chain of weirs with very low dimensionless discharge (Fig. 29). The lower the discharge is, the closer to the mean velocity of the cross section the velocities at the mid-axis are. In this structure, however, the crest is so mildly sloping that it is almost horizontal. Actual water depths at the weir are very low, and because of this, flow friction at the sides is considerably high.
Figure 28. Velocity distribution at a weir for a pool-and-weir fishway with a V-shaped crest at a flow of 2 m3/s. Velocities in m/s (redrawn from Boiten 1990).
Figure 29. Dimensionless velocity distribution at the mid-axis of a pool-and-weir fishway with a V-shaped weir.
The velocity distribution with intermediate or high flows at the weirs in pool-and-weir fishways with a V-shaped crest resembles that of Denil fishways (Fig. 30 and 31). The velocity distribution is only more even in pool-and-weir fishways compared with Denil fishways. In Denil fishways, the energy dissipation rate is higher due to the strong inclination of baffles (45o to the bottom of the channel) and the wall baffles. Velocities near the bottom are directed upwards and velocities in the direction of flow are low near the bottom. Also in Denil fishways, when the flow depth increases, the energy dissipation rate and, accordingly, velocity distribution at the weir changes.
Figure 30. Centerplane velocity vector plots for a Denil fishway with large baffle spacing (Katopodis et al. 1997).
In vertical slot fishways, the velocity distribution is even almost from the bottom of the slot up to the surface, independent of the flow rate (Rajaratnam et al. 1986). The differences in velocity profiles indicate the differences in the energy dissipation patterns in vertical slot fishways compared with pool-and-weir and Denil fishways.
