2.4. Basic concepts for modeling fishway flows
In modeling fishway flows, the basic assumptions are that
flow is uniform in mean,
flow is governed by the geometry of the structure,
flow friction can be estimated by general discharge formulas for sharp-crested weirs, and
flow is characterized as flow over a chain of weirs.
The last assumption might exclude vertical slot and pool-and-orifice fishways, because the flow in them is through the openings, not over the weirs. In fishways, the main factors affecting the discharge coefficient C are
the contraction ratio in the direction of breadth 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). If the Froude number at the approach section is greater than 0.8, nearly critical or supercritical velocities may occur in the approach section,
submergence ratio, that is, the ratio t/h where t is the depth of tailwater above the weir crest and h is head over the weir.
In creating empirical equations for discharge rating curves and water velocities in fishways, equations for continuos steady uniform flow have been used. The flow inside the fishway is continuos and, for a theoretical approach, it can be considered to be steady. Open channel flow is said to be uniform if the depth of flow is the same at every section of the channel (Chow 1959). Uniform flow requires a prismatic channel, i.e. a channel with an unvarying cross section and constant bottom slope. The flow is said to be uniform if the channel is prismatic, water velocity distribution is the same in every cross section, and the bottom slope, the slope of water surface, and the slope of energy line are the same.
In fishways, the channel is not prismatic because energy dissipation is created with vanes, baffles or weirs that form large-scale roughness elements inside the flume. If these elements are considered merely to be roughness, the flow in the fishway can be considered uniform because after a short distance the roughness elements create fast flow development. The flow is fully developed in the middle part of the fishway flume. In the region of fully developed flow, the mean slope of energy line, mean bottom slope and the slope of mean water surface profile are the same. Thus, flow in the fully developed region of the fishway can be considered uniform and the equations and procedures developed for uniform flow can be applied (Fig. 6). In experimental studies, it has been observed that after a short distance, the flow is fully developed and even in pool-and-weir fishways the flow depth is the same in adjacent pools when measured at equal points (Rajaratnam et al. 1992).
Strictly speaking, the flow in fishway is rapidly varied at every weir, baffle or vane. Even in Denil fishways, the flow is rapidly varied. Because flow in fishways is uniform only on the average, the equations and procedures created by assuming uniform flow can be applied only for solving of mean flow conditions or at certain cross sections. Empiric equations can, however, be created for discharges and mean velocities at weirs and cross sections, when there are enough measurements. In creating the equations, similarity analysis can be used.
It can be said that fishways are hydraulically very rough flumes, and it is possible to create theoretic total roughness coefficients and friction factors, which take into account all local frictional losses. Weirs and vanes can also be considered extremely large roughness elements.
Chow (1959) stated that when flow occurs in an open channel, resistance is encountered by the water as it flows downstream. This resistance is generally counteracted by the components of gravity forces acting on the body of the water in the direction of motion. A uniform flow will be developed if the resistance is balanced by the forces of gravity. The magnitude of the resistance, when other physical factors of the channel are kept unchanged, depends on the velocity of the flow. In a fishway that has been correctly designed, the flow in mean is neither accelerating nor decelerating – thus the force of gravity producing the flow is equal to the friction resisting the flow.