Hydraulic transients

Gas entrained in the fluid and the flexibiflty of the pipe wall both result in lowering of the wave speed. For deaerated water, the wave speed is about 1250 m/s. Detailed methods of analysis and evaluation of hydraulic transients may be found in the flterature (25). 

Many transient flows of liquids may be analyzed by using the full time-dependent equations of motion for incompressible flow. However, there are some phenomena that are controlled by the small compressibility of liquids. These phenomena are generally called hydraulic transients. 

Atomization = Eotvos numher, Eo Two-phase flows, free surface flows Compressible flow, hydraulic transients Cavitation... 

Software packages are commercially available for simulation of hydraulic transients. These may be used to analyze piping systems to reveal unsatisfactory behavior, and they allow the assessment of design changes such as increases in pipe-wall thickness, changes in valve actuation, and addition of check valves, surge tanks, and pulsation dampeners. 

Cavitation Loosely regarded as related to water hammer and hydraulic transients because it may cause similar vibration and equipment damage, cavitation is the phenomenon of collapse of vapor bubbles in flowing liquid. These bubbles may be formed anywhere the local liquid pressure drops below the vapor pressure, or they may be injected into the liquid, as when steam is sparged into water. Local low-pressure zones may be produced by local velocity increases (in accordance with the Bernoulli equation see the preceding Conservation Equations subsection) as in eddies or vortices, or near boundary contours by rapid vibration of a boundary by separation of liquid during water hammer or by an overall reduction in static pressure, as due to pressure drop in the suction line of a pump. 

Cauchy number C pV2 p inertial force compressibility force Compressible flow, hydraulic transients... 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considered incompressible, except for certain calculations involved in hydraulic transient analysis (see following) where compressibility effects are important even for nearly incompressible liquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compressible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (Gas Dynamics, vol. I and II, Wiley, New York [1976]). 

Li, W.H. 1972b. Differential equations of hydraulic transients, dispersion, and groundwater flow. Prentice-Hall, Inc., Englewood Cliffs, NJ. 

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