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13 Flow under these conditions is fully pressurized and a stage-discharge relationship can be developed based on Bernoulli’s Equation where discharge, 𝑄, is computed as follows: 𝑄=𝑎�2𝑔𝐻𝑇𝐾𝐿 where 𝑎 is the flow area, 𝑔 is the gravitational acceleration, 𝐻𝑇 is the total head needed to overcome various losses to produce discharge, and 𝐾𝐿 is a function of the head losses associated with trash racks, gates, valves, bends, transitions, friction and exit losses. See References [9] and [10], for more information. The stage-discharge relationship for the entire outlet works system is based on the minimum discharge of the inlet and outlet control relationships (see Figure 1). There are a number of commercial computer modeling tools available for evaluating outlet works hydraulics, but spreadsheets are commonly used for simple systems. See Reference [9] for more information. Figure 1: Combined stage-discharge curve of an outlet works Tailwater Effects – It is possible for tailwater in the downstream channel to impact the outlet works flow hydraulics, especially at high flow rates. For open channel flow systems, it is important to ensure the tailwater does not submerge the outlet and create mixed flow conditions within the outlet conduit. For pressurized systems, submergence of the outlet is acceptable; however, it reduces the capacity and must be considered in the analysis. For energy dissipation purposes, tailwater can be beneficial and may potentially reduce the required size of the energy dissipation structure. For simple downstream channel geometries, tailwater rating curves can be developed using Manning’s equation. For more complicated geometries, it may be necessary to model the tailwater using a program such as HEC-RAS. Cavitation and Venting – As flow passes through a gate or valve, the contraction produces separation downstream in which negative pressures may develop. When the pressure in the flow drops below the vapor pressure, cavitation, which is the formation of vapor bubbles within the water, may develop, causing damage to the control structures or conduits. When the water is subjected to higher pressures again, the bubbles implode, generating intense shock waves that can be extremely damaging to the outlet conduit. To maintain positive pressures in the flow, it is necessary to vent the region immediately downstream of a gate or valve located within the outlet conduit (See Figure 2). Vents typically consist of a pipe located within the embankment of the dam with an outlet near the dam crest. Vents must be sized appropriately to allow adequate airflow. See References [1], [7], and [14] and our previous article Design Considerations for Outlet Works Air Vents (Vol. 1 Issue 2) for more information. Figure 2: Air vent downstream of a slide gate Hydrologic Considerations The design flow rates for the outlet works are dictated by a variety of factors including downstream needs, storage considerations, power generation requirements, reservoir depletion requirements, and legal requirements. For outlet works that act as the only spillway, the capacity should be sufficient to pass the inflow design flood (IDF). A discussion about flood inflows was presented in Turning Rainfall to Runoff (Vol. 2 Issue 1). The outlet works design capacity for most low-level outlets is driven by the time required to drain the