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14 0.64 0.66 0.68 0.7 0.72 0%10%20%30%40%50%60%70%Co e f f i c i e n t o f D i s c h a r g e , C d Gate Opening 𝑃=𝐶𝑣√P1 −P2 SG With: Q = Flow rate Cv = Valve coefficient SG= Specific gravity of water P1= Upstream pressure P2= Downstream pressure The lower the friction, the lower the CV coefficient, and thus the higher the flow rate through the valve. If the system includes other equipment and a long pipe length driving flow at high velocity, those elements should be included in the flow rate calculations by using the Bernoulli equation. Gate Discharge Discharge over a gate-controlled ogee crest: Q =2 3 √2g 𝐶𝑑𝐿(𝐻1 3/2 −𝐻2 3/2) With: Q = Flow rate (ft3/sec) g= Acceleration due to gravity (ft2/sec) Cd= Coefficient of discharge (see graph below) L= Gate crest length (ft) H1= Vertical distance between sill and reservoir level (ft) H2= Vertical distance between bottom of gate and reservoir level (ft) Figure 5: Coefficient of discharge for flow under gates – Reclamation, Design of Small Dams, 1973 See references [3] and [4]for more information Cavitation After fluid passes the narrowest point of the system, pressure decreases inversely as velocity increases. If the pressure drops below the vapor pressure of water at that particular condition, vapor bubbles start to form. As the fluid moves into a larger area of the vessel or downstream piping, the pressure stops dropping and increases over the vapor pressure, causing the vapor bubbles to collapse or implode. This two-step process is called cavitation and is a major factor in causing surface damage inside the pipe and valves and causing erosion on the pipe surfaces. The cavitation index “”, that was approved in 1995 by the Instrument Society of America, is a ratio of forces that resist cavitation to forces that promote cavitation and is written as: 𝜌=P2 −P𝑉 P1 −P2 With:  = Cavitation index P1= Upstream pressure P2= Downstream pressure PV= Liquid vapor pressure The cavitation potential is inversely proportional to the cavitation index; the lower the cavitation index, the higher the cavitation potential. It is typically recommended to keep σ above 2.5 to eliminate potential for cavitation. The following adaptations can reduce or suppress the risk of cavitation:  Venting (See references [2], and [8] and our previous article, Design Considerations for Outlet Works Air Vents (Vol. 1 Issue 2) for more information.)  Use of additional valves to reduce the pressure differential  Use of a bypass system. See reference [7] for more information. Water Hammer Effect Water hammer is generated when the flow is suddenly stopped in the hydraulic conduit, and a large shock wave is generated. This situation can be produced by a