Unit Steady-State Flow and Transient Flow
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发布时间：2022-05-21 06:00
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时间：2023-10-16 15:00
Steady-state flow occurs w hen at any point in a flow field the magnitude and direction of the flow velocity are constant w ith time. Transient flow ( or unsteady flow，or nonsteady flow) occurs w hen at any point in a flow field the magnitude or direction of the flow velocity changes w ith time.
Figure 7. 1 a show s a steady-state groundw ater flow pattern ( dashed equipotential line， solid flow line) through a permeable alluvial deposit beneath a concrete dam. Along the line AB，the hydraulic head hAB= 1000 m. It is equal to the elevation of the surface of the reservoir above AB. Similarly，hCD= 900 m ( the elevation of the tailrace pond above CD ) . The hydraulic head drop Δh across the system is 100 m. If the w ater level in the reservoir above AB and the w ater level in the tailrace pond above CD do not change w ith time，the flow net beneath the dam w ill not change w ith time. The hydraulic head at point E，for example，w ill be hE= 950 m and w ill remain constant. Under such circumstances the velocity v = － Kh / l w ill also remain constant through time. In a steady-state flow system the velocity may vary from point to point，but it w ill not vary w ith time at any given point.
Figure 7. 1 Steady-state and transient groundwater flow beneath a dam
Let us now consider the transient flow problem schematically show n in Figure 7. 1 b. At time t0the flow net beneath the dam w ill be identical to that of Figure 7. 1 a and hEw ill be 950 m. If the reservoir level is allow ed to drop over the period t0to t1，until the water levels above and below the dam are identical at time t1，the ultimate conditions under the dam will be static w ith no flow of w ater from the upstream to the dow nstream side. At point E the hydraulic head hEw ill undergo a time-dependent decline from hE= 950 m at time t0to its ultimate value of hE= 900 m. There may w ell be time lag in such a system so that hEw ill not necessarily reach the value hE= 900 m until some time after t = t1
One important difference betw een steady and transient systems lies in the relation betw een their flow lines and pathlines. Flowlines indicate the instantaneous directions of flow throughout a system ( at all times in a steady system，or at a given instant in time in a transient system) . They must be orthogonal to the equipotential lines throughout the region of flow at all times. Pathlines map the route that an indivial particle of water follows through a region of flow ring a steady or transient event. In a steady flow system a particle of water that enters the system at an inflow boundary will flow toward the outflow boundary along a pathline that coincides with a flowline such as that shown in Figure 7. 1 a. In a transient flow system，on the other hand，pathlines and flowlines do not coincide. Although a flow net can be constructed to describe the flow conditions at any given instant in time in a transient system，the flowlines shown in such a snapshot represent only the directions of movement at that instant in time. In that the configuration of flowlines changes with time，the flowlines cannot describe，in themselves，the complete path of a particle of water as it traverses the system. The delineation of transient pathlines has obvious importance in the study of groundwater contamination.
A groundw ater hydrologist must understand the techniques of analysis for both steady-state flow and transient flow. In the final sections of this chapter the equations of flow w ill be developed for each type of flow ，under both saturated and unsaturated conditions. The practical methodology that is presented in later chapters is often based on the theoretical equations，but it is not usually necessary for the practicing hydrogeologist to have the mathematics at his or her fingertips. The primary application of steady-state techniques in groundw ater hydrology is in the analysis of regional groundw ater flow. An understanding of transient flow is required for the analysis of w ell hydraulics， groundw ater recharge， and many of the geochemical and geotechnical applications. ( Source: Freeze et al. ，1979)
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