CHANNEL WITH LOWER END SUBMERGED 89 



critical, may actually be a mild slope, with depth of flow above the 

 critical. A comparatively small change in the roughness coefficient 

 may produce a marked change in the flow profile. 



The vertical scales in all the profiles shown in Fig. 801 are enor- 

 mously exaggerated. This makes the breaks in grade of the channel 

 bottom look sharp, and perhaps in need of rounding. Actually, few 

 such changes in grade need to be rounded. For high velocity flow 

 crossing a brink or a crest, a vertical curve may be needed in order to 

 prevent the formation of dangerously low pressures or excessive eddy 

 disturbances in the lee of the corner. If a crest is rounded, the cres^ 

 elevation is the actual elevation of the highest point on the curve, and 

 not the intersection of the straight grade lines from each side. Vertical 

 curves are sometimes used, though not needed for hydraulic reasons, 

 in order to save on construction costs. 



A treatment of all the possible cases of two breaks in grade sufficiently 

 close together to prevent the establishment of normal flow in the stretch 

 between them would be very lengthy, and, it is believed, unnecessary. 

 The student who can sketch, without reference to notes, all of the pro- 

 files shown in Fig. 801 should be qualified to solve the more complicated 

 profiles resulting from two or more changes of grade in the channel 

 bottom. 



PROBLEMS 



SOL A long portion of channel at mild slope is followed by a section at a still 

 flatter slope, and then by a steep section. The cross section is the same throughout. 

 Sketch the various possible water-surface profiles. 



802. A long steep portion of a channel is followed by a horizontal section, and 

 then a long section with mild slope. The cross section is constant. Sketch the 

 various possible profiles. 



803. A long rectangular concrete flume 12 feet wide has a change of grade from 

 0.004 to O.OOL If the flume is new and well finished, what will be the flow profile 

 across the change of grade when the discharge is 300 c.f.s.? What will be the 

 influence of increased roughness? 



804. A channel is to be built through a ridge to serve as the spillway for a reser- 

 voir. In order to save rock excavation the channel bottom will be built on a rising 

 grade of 2 per cent from the reservoir straight to the crest, a distance of 500 feet. 

 For 200 feet past the crest, the channel bottom will have a steep grade down the 

 hillside. What will be the discharge when the water level in the reservoir is 12 feet 

 above the elevation of the crest, if the channel is 200 feet wide? 



SOS. What would be the discharge, for the channel of problem 804, if the down- 

 ward grade past the crest was constant at 0.003 for a great distance? 



Uniform channel with lower end submerged in lake or reservoir. 

 The different conditions which may result in the formation of back- 

 water curves in a channel discharging into a pool are shown in Fig. 802. 



