120 BENDS, TRANSITIONS, AND OBSTRUCTIONS 



that theoretically required by the radius and average velocity, but it 

 must be introduced gradually. If it is increased linearly in a distance 

 L along the channel, a spiral wall transition should be used. The 

 required cross-slope should be obtained by depressing the bottom along 

 the inside wall rather than raising it along the outside wall. For this 

 reason the method is not as practical as the use of circular transition 

 curves. The minimum length of the transition should be 



Lt = \SWSc [1007] 



where Sc is the cross-slope 



The transition spiral should be constructed according to the equation 

 RL = RoLt = a constant [1008] 



The corrections are to be made for flow at maximum design capacity. 

 The flow pattern at lower flows might conceivably be unsatisfactory. 

 Ippen and Knapp state that the compound or transition curve method 

 is the best in this respect, with the flow pattern remaining remarkably 

 constant at all stages. 



Changes in cross section. The variable section connecting one uni- 

 form channel to another of different cross-sectional form is called a 

 transition. Let us first consider the simplest form of transition, that of 

 a change of width of a rectangular channel. The change is assumed to 

 be effected smoothly, and in a short distance, so that there is no addi- 

 tional contraction of the jet, beyond that guided by the walls, and no 

 appreciable friction loss. The bottom is level throughout. 



Let W\ = width of channel upstream from the contraction or enlarge- 

 ment, 



W2 = width of channel downstream from the contraction or en- 

 largement, 



£>i and Vi = upstream depth and velocity, 



D2 and V2 = downstream depth and velocity. 



A change in the width of the channel will result in a change in the 



ratio of velocity head to depth, so that unless Wi and W2 are equal 



Vi^/2g V2^/2g 



■ and will be unequal. If there is no loss of energy, as 



Di D^ 



assumed, 



