CHAPTER XI 

 SLOWLY VARIED FLOW 



Unsteady flow in which the changes with respect to time occur slowly, 

 so that dynamic effects are negligible, is very similar to steady flow. 

 With the exception of the law of continuity, which needs to be revised 

 to take into account any storing up or releasing of water, the same 

 equations that were used for steady flow will apply. Flow of this type 

 is frequently met in engineering practice, most commonly in connection 

 with the so-called " routing problems." 



Although there is no definite numerical criterion for the boundary 

 between slowly varied flow and unsteady flow, the status of most prob- 

 lems can be determined by the test described at the end of this chapter. 

 No satisfactory methods for solving problems in general unsteady flow 

 have yet been developed, though certain special cases have been found 

 to be amenable to mathematical solution.^ 



Level-pool routing with invariable stage-discharge relation. The 

 outlet from a reservoir or lake has an artificial or natural control, so 

 that for every possible value of the water-surface elevation in the lake, 

 there is a definite single value of the outflow. The water surface in the 

 lake is assumed to be level, and the area at each possible elevation to 

 be fixed, so that the elevation-storage relation is also single-valued 

 and invariable. The inflow hydrograph is given and it is required to 

 determine the outflow hydrograph. 



In passing, it should be noted that the assumption of slowly varied 

 flow is implicit in the assumption of a level pool. If the inflow rate 

 increased so rapidly that a large wave was started at the upper end of 

 the pool, and the wave took an appreciable length of time to travel to 

 the point of outflow, this assumption would not be valid. 



It should also be noted that the inflow is not the rate of discharge 

 relative to the (moving) section where the inflowing stream intersects 

 the pool level, but rather the rate of discharge relative to a fixed station. 

 Moreover, all of the water entering the reservoir above the point of 

 outlet must be considered. 



^ " The Hydraulics of Flood Movements in Rivers," Harold A. Thomas, Engi- 

 neering Bulletin, Carnegie Institute of Technology, Pittsburgh, Penna. 1937. 



133 



