CHANGES IN CROSS SECTION 123 



Fi^/2p 

 Entering the diagram of Fig. 1003 with ^ = 0.0649 and W2/Wi = 



0.9, we find that 



Do 



= 0.085 or 2.25 



The total head at the downstream section is assumed to be the same as 

 that of the upstream section, and the depth of flow may therefore be 

 either 



6.389 

 ^^ = LOSS = '■'' 



or 



6.389 

 3.25 



= 1.97 



A check by computing the total head based on the velocities corre- 

 sponding to these depths shows that they are accurate to within less 

 than one per cent. 



Choice of the alternate depth which applies in any given situation 

 depends upon flow conditions in the transition and in the channels 

 upstream and downstream from the transition. Analysis of flow 

 conditions in the channels may be accomplished by the methods ex- 

 plained in Chapter VIII. This should be done before starting analysis 

 of flow conditions in the transition itself. For example, it would be 

 impossible for a transition to convert flow at greater than the critical 

 depth to flow at less than the critical depth if the downstream channel 

 was incapable of carrying the high-velocity flow away from the tran- 

 sition. 



Results of the analysis of flow conditions in the channels may indicate 

 that only one depth of flow in each channel is possible, or they may 

 indicate more than one possibility. In the former case the transition 

 may or may not cause local disturbances depending upon the details of 

 its design. In the latter, a detailed analysis of flow conditions in the 

 transition may show which alternative flow profile will exist. At times, 

 where a small difference in the total head seriously affects the possibili- 

 ties, the result is uncertain. 



In analyzing the flow conditions in the transition we recognize the 

 following possibilities : 



{DD) Flow deeper than critical throughout. 



{DDn) channel narrows in the downstream direction. 



(DDw) channel widens in the downstream direction. 

 (SSn&w) Flow shallower than critical throughout. 



