124 BENDS, TRANSITIONS, AND OBSTRUCTIONS 



(DSn&w) Transition from deeper than critical to shallower than 



critical. 

 (SDn&w) Transition from shallower than critical to deeper than 



critical. 



Not all of the possible cases are equally reliable in operation. De- 

 tailed comments follow. 



Operation of case DDn is predictable unless the downstream depth is 

 near the critical, when the flow may cross the critical in the transition 

 and come out below at the stage which is alternate to that desired. 



Vi^/2g 

 For example, consider where — — — = 0.06 and W2/W1 = 0.6. From 



"1 



. . V2^/2g 



Fig. 1003 It is seen that — — — should equal 0.35, but if the external 



D2 



flow conditions permitted it, a value of 0.75 would be likely. Theo- 

 retically, the value of 0.75 would not be possible unless the transition 

 narrowed down to 0.59 and then widened to 0.60, but actually the small 



deviation of the depth necessary to cross the critical would occur easily. 



72/2^ 



If W2/W1 equalled 0.8, ^ would be 0.11, with the flow still much 



D2 



deeper than the critical, so that the alternate value 1.9 would be very 



unlikely. When the depth approaches the critical in a DDn transition, 



there is always danger of the flow changing to DSn. This may occur 



even when the downstream flow must be at greater than critical depth 



to fit the tail water, with a hydraulic jump occurring in or below the 



transition. 



In the operation of case DDw, only one flow condition is possible. 

 The energy loss may be a large proportion of the diff'erence of the two 

 velocity heads if the angle of expansion is too great. 



Case SSn is predictable if the angle of contraction is less than the 

 wave angle, and if the depth does not approach the critical too closely. 

 If it does, the depth below the transition may rise above the critical, 

 starting a condition of flow (SDn) which is very unstable, and which 

 may give way to a hydraulic jump. 



Case SSw is stable. The angle of divergence of the walls should be 

 less than the wave angle, or transverse waves will be started which will 

 continue to disturb the water surface for some distance below the 

 transition. 



Case DSn forms occasionally when not expected, as noted in the dis- 

 cussion of case DDn. This form can be relied on when called for by the 

 general flow conditions, provided the downstream depth is only slightly 

 less than the critical. If the downstream depth is to be appreciably 



