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15 sudden turbine or pump shutoff or a valve slamming shut. Pressure induced by the water hammer effect can be calculated from the Joukowsky equation: ∆𝑃=𝜎𝑎0 ∆𝑣 With: ΔP= Magnitude of the pressure wave ρ= Density of the water a0= Speed of sound in water Δv= Change in the fluid's velocity High pressure is induced into the system, creating noise and vibrations. It can result in severe damage to valves, gaskets, and any equipment exposed to water hammer. Systems involving a long length of pipe with high pressure are more exposed to water hammer effects. The valve must close slowly to minimize water hammer, and the safe closure rate can be calculated. If the fluid is assumed to be incompressible and the water column deceleration after closure is assumed constant, the resultant pressure can be calculated as follows: 𝑃=𝜎𝑣.𝐿 𝑡 With: P = Pressure (lb/ft2) ρ = Fluid density (lb/ft3) L = Pipe length (ft) v = Fluid velocity (ft/sec) t = Valve closure time (sec) To mitigate the pressure induced by the shock wave in the system, a surge tank can be added. Surge tanks will act as a “bumper” to provide a release for overpressure and level the overall pressure in the pipe. Summary Outlet control is a critical component of dam operation. Important parameters need to be considered during the design of the outlet, such as the flow, pressure, and frequency of use. Also, the type of power source and system will be influential in choosing the appropriate equipment. A variety of valves or gates can be used for outlet controls, each with particular characteristics. Although valves can accommodate any conduit size, they are used most often for conduits under 36 inches in diameter, with the butterfly valve suitable for most applications. The ball valve is recommended for high pressure applications and the Howell Bunger valve is used for discharge into free atmosphere. Gates are more suitable to control outlet conduits difficult to access, and any open channel outlet or spillway application. Tainter gates involve more specialized design, but are lightweight and widely used for surface water control applications. Fixed wheel gates are more robust and heavier; they can resist high pressure and rough conditions. Finally, sluice gates are also pressure resistant and very simple, but have high friction forces, requiring more power to operate. Sluice gates are typically used on low to medium flow rate outlets with low frequency of operation. Flow rate can be calculated with variable accuracy depending on the equipment used. Flow through valves or gates can easily be calculated using the associated coefficient. However, more complex outlet systems with several controls and long piping will require more developed calculations based on the Bernoulli equation. Gates and valves are specialized equipment that can have long lead times. Manufacturers should be consulted early in the design process. Useful References [1] Federal Emergency Management Agency (2005). Technical Manual: Conduits through Embankment Dams. [2] Tullis, B. P. and Larchar, J. (2009). Low-Level Outlet Works Air Vent Sizing Requirements for Small to Medium Size Dams. United States Geological Survey. [3] United States Department of the Army: US Army Corps of Engineers. (1980). EM 1110-2-1602: Hydraulic Design of Reservoir Outlet Works. [4] United States Department of the Interior: US Bureau of Reclamation. (1973). Design of Small Dams. [5] United States Department of the Interior: Bureau of Reclamation. (1990). Criteria and Guidelines for Evacuating Storage Reservoirs and Sizing Low-Level Outlet Works. [6] United States Department of the Interior: Bureau of Reclamation. (1984). Engineering Monograph No. 25: Hydraulic Design of Stilling Basins and Energy Dissipaters. [7] United States Department of the Interior: Bureau of Reclamation. (2011). Appurtenant Structures for Dams (Spillway and Outlet Works) Design Standards. [8] United States Department of the Interior: Bureau of Reclamation. (1980). Engineering Monograph No. 41: Air-Water Flow in Hydraulic Structures. [9] Walther, Martin (2004). Guidance for Air Vents for Drop Inlet Spillways. Washington State Department of Ecology: Water Resources Program/Dam Safety Office. [10] Control Valve Handbook – Emerson Control Management, 2005 [11] Nesbitt, Brian (2007). Handbook of Valves and Actuators [12] Erbisti, Paulo C.F (2014). Design of Hydraulic Gates