In an open uniform channel, mean velocity and flow depth are independent. In an open channel which is obstructed by a weir (i.e. in an obstructed channel), flow velocity is a function of the depth of flow and of the size and shape of the weir. Flows in fishways can be considered as flows over a chain of weirs. Flows over a weir with submergence are difficult to analyze purely theoretically, and even empirically. When there are several weirs in chain, each one affecting to the other, the hydraulic problems are even more difficult to solve. In these cases, dimensionless parameters are useful in evaluating beforehand the water depths and discharges. In this paper, a new scaling factor for creating dimensionless parameters for fishways has been established. The goal of this study has been mainly practical: the aim was to create a basis for practical design procedures. Empirical laws for flows over weirs were taken as the basis in addition to the assumptions that
fishways are hydraulically rough open channels,
flow is uniform and flow friction can be expressed with the channel width, distance between the weirs, and the slope of the channel, and
flow always runs over sharp-crested weirs.
The constant boundary conditions in a fishway are channel width, distance between weirs, bottom slope, weir height and possible roughness elements on the channel walls. Flow is determined by the depth of the flow over the weir. The use of scaling factors is based on the empirical equation for flows over weirs (Eq. (28)). In fishways, the main factors affecting the discharge coefficient C are
the contraction ratio, which depends on the ratio b/B, where b is the contracted channel width and B is the uncontracted approach channel width,
the longitudinal contraction ratio which depends on the ratio b/L, where b is the contracted channel width and L is the longitudinal distance between the contractions,
the Froude number at the contraction (approach section),
the submergence ratio.
Most fishway structures are characterized by sudden changes in the channel cross section, actually making the flow rapidly varied at every constriction. The rapid variation in flow regime often takes place in a relatively short reach. Accordingly, the boundary friction, which could play a primary role in a gradually varied flow, is comparatively small and in most cases insignificant. It can be said that boundary friction is replaced by ‘local roughness’ and local losses due to it.
In many studies on fishways, it has been observed that pool length is one essential factor that affects to the rate of flow (e.g. Veijalainen 1985, Rajaratnam et al. 1988, Sikora et al. 1996). Boiten (1990) stated that pool length is an important factor that affects the energy dissipation pattern, and through it the hydraulic operation of the fishway. When the discharge and, accordingly, depth of flow over the weir is low compared to the pool length, the flow could be classified as plunging, according to the definition of Clay (1961). Rajaratnam et al. (1988) stated that for the streaming flow, pool length is an important factor. They also stated that for the streaming mode, dimensionless discharge varied with the relation L/d where L is the pool length and d is the depth of flow.
In fishways, velocity distribution between the weirs is strongly affected by the flow over the upper weir. In pool-and-weir fishways, when the flow is over the weirs, the way the jet from the upper weir enters the pool makes a great difference in the velocity distribution in the pool. The higher the discharge and, accordingly, the depth of flow over the weir is compared to the pool length, the closer to the lower weir the jet from the upper weir hits the floor. When pools are long compared to the discharge (or the depth of flow), the jet plunges into the pool near the upper weir. In this case, the flow over the lower weir is not affected to a great extent by the flow over an upper weir. Below the jet there is an eddying region. This is the so-called plunging flow stage. When the depth of flow increases, the jet gradually hits the floor closer and closer to the lower weir, and finally streams over the lower weir almost without any mixing with the water mass in the pool. The eddying region fills the pool and the friction between the circulating water mass in the pool and the streaming flow above the weirs causes turbulence in the pools between. Between these two flow stages, there is a large variety of flow depths, which can be called as transitional flow depths. Weir height affects to the limits of the different flow stages, but the effect is not as clear as in the case of a single weir.
According to observations, pool-and-weir and Denil fishways are actually very similar in their hydraulic operation. If the pool length compared to the depth of flow is so large that the eddying region is fully developed and flow can be assumed to be uniform at least for a short distance, the weirs act as individuals. The same phenomenon can be seen in pool-and-weir fishways as well as in Denil fishways if the flow is low enough. If the eddying region in these fishway types reaches the next weir, this changes the hydraulic characteristics of the flow and actually, in this case, the weirs act as a chain. By choosing the right scaling factors, a variety of overflow fishways can be classified into the same category and a general dimensionless discharge equation can be created. In vertical slot fishways, the jet from the upper pool enters the lower pool through a narrow vertical slot (compared to the width of the channel). The energy dissipation scheme differs from that of the Denil and pool-and-weir fishways, as well as the overall hydraulic operation of the fishway. Thus, it was predictable that even in this analysis, the results would be different for vertical slot fishways. Despite of that, the developed model and procedure is applicable, but the model parameters differ more.
The basis of this study has been to create a general procedure and model to predict flows in fishways in several fishway structures for design purposes. The longitudinal distance between the weirs or baffles, L, is used for scaling distances and water depths. As a measure of discharge, the water depth at the weir was chosen instead of the head. In practice, in most cases the difference between the head at the weir and the depth of flow at the weir is not too large, and in field conditions the depth of flow at the weir is easier to measure. In addition, in most fishways the flow is submerged, which means that the flow is usually unstable with considerable surface undulations also at the weirs. In their studies on submerged weir flows, Wu and Rajaratnam (1996) noticed that in a transition flow state, the flow could be switched from one to the other by an external disturbance. Applied to fishway flows, this means that there always is ‘an external disturbance’ in the form of adjacent weirs making the flows unstable and making changes from plunging flow into a streaming flow unpredictable.
In this paper, a new scaling factor for dimensionless discharges was developed (Eq. 20). Equation (20) can be considered as a mean expression, which explains the differences in dimensionless discharges. Dimensionless discharge depends on several factors that are dependent on each other. For practical reasons (easiness of calculations), the power regression equation was selected as the form for the dimensionless discharge equation. This gives equations that are structurally similar to those of the conveyance factor and the general form of discharge rating curve. Equation (20) was applied to the author’s study results on different type fishways, and a general equation for dimensionless discharge in fishways (Eq. 22) was generated. For verification, the same procedure was applied to the results of several fishway types and studies reported in literature. It was noticed that dimensionless discharge-dimensionless depth –pairs fit quite well in the developed fitting curve. The regression was 0.96 for author’s data on pool-and-weir, Denil, and vertical slot fishways. Despite the high regression, the general model fails in predicting flow rates even with moderate accuracy. This can be seen from the results of the Student’s paired t-test, which gives reasonable mean percentage deviations, but far too high standard deviations. This can also be seen from the scatter in the results. The scatter is quite high with values of dimensionless depths yo/L being about 0.2, with y as the normal water depth at the weir and L as the pool length. The parameters in equation (22) are defined based on the measured data, which always includes inaccuracy. Due to this, the parameters are somewhat a matter of chance. This means that for a different data, the parameters would be different, as well as the regression. These model parameters would be basically as good and valid as the other parameters. The basic model and the procedure are still valid.
Basically, the created model is a dimensionless discharge rating curve for fishways based on the depth of flow inside the fishway, in the region of fully developed flow. In creating discharge rating curves from the data on discharge-water depth pairs, a logarithmic representation is commonly used. The logarithmic form of the rating curve may be described by a simple mathematical equation that is easily handled. A rating curve based on discharge-water depth –measurements is developed by balancing it through a scatter-plot of measurements. The measurements and observations of all kinds are invariably subject to error of observation. The error of observation is generally composed of several independent errors that may be considered independent of each other, and the associated errors may therefore be regarded as random variables. Thus, the composite error, i.e. the error of observation, may be regarded as normally distributed. The error of measurement is not independent but depends on the magnitude of the measured discharge. The absolute error of observation is proportional to the magnitude of the measured discharge over each range having the same station control. With proper measuring procedures it should be possible to keep the error of observation in the order of 3-5 % of the measured discharge. The basic assumption for a valid estimation of the standard deviation of the error of observation is that the error of observation is normally distributed and independent. For regression (i.e. the depth-discharge curve) this is achieved by a simple transformation to relative values.
The use of a general equation for different fishway types and different flow stages contains uncertainties. It should be noticed that it is not actually possible to create a precise equation for fishway flows which covers several fishway types and, in pool-and-weir fishways, both plunging and streaming flows. However, this procedure can be used to roughly estimate discharges and water depths in designing fishways. Caution should, however, be exercised when applying this procedure. The use of the general equation (22) would cause in mean an error of 50 % in the discharge with the same relative depth of flow inside the fishway. The general equation is best applicable for Denil fishways. It should not be used to estimate flows in pool-and-weir fishways with horizontal weir.
The use of special equations for different fishway types will give better results. The more homogenous the family of structures is in defining the model parameters, the better results will be received. Parameters given in this paper (Table 7) are based on a large variety of different structures, slopes and discharges. Parameters are subjects to changes when the data they are based on dates back to different observations. Of these three basic fishway types, changes in parameters in the equations for vertical slot fishways does not drastically change the values of dimensionless discharges in the normal operation range of dimensionless water depths yo/L = 0.15…1.5. In Denil fishways, for the low dimensionless water depths yo/L from about 0.5 to 1.2, the change in parameters does not affect the dimensionless discharge to an extremely large extend. The normal operation range in Denil fishways, however, extends to about 2.2. For the normal operation range from about 0.02 to 0.4 of dimensionless water depths in pool-and-weir fishways, even small changes in model parameters result in noticeable changes in dimensionless discharges.
The designer should take care that energy dissipation in the design stays in the limits of these procedures. This can be ensured, for example, by avoiding structures that differ to a great extent from the structures introduced in the literature. Some variation, however, can be done.
Discharge rating curves are usually based on changes in the upper water level above a control section. A control is any feature which determines the depth-discharge relationship. In pool-and-weir fishways, a weir inside is not an unequivocal control, but depending on the flow mode, the same depth of flow may be produced by several different rates of discharge. The same phenomenon is not present in vertical slot and Denil fishways, where vertical friction elements cause the greater part of the flow friction. Overall, a better measure for defining the discharge rate in fishways would be the upper water level instead of the depth of flow at the weir inside a fishway. This would eliminate the inconvenience of fluctuating water levels inside the fishway and the inaccuracy of measurements due to it. In addition, there would be no need to differentiate between different modes of flow. Because water depths in fishways, especially at weirs, are important for successful fish passage, there is still a clear need for equations that will generate water depths at weirs.