FLOW IN OPEN CHANNELS 



297 



The results obtained by tbis formula compare very well with those of 

 Fidler, the latter probably on the whole giving the better results. 



Prof. G. S. Williams, adopting this exponential formula, gives n and x 

 constant values respectively equal to 1'9 and 1*25. The formula then 



becomes h = , or v = C 



following values : 



m' 67 X 



.'54 

 I 



where K and C have the 



ART. 86. CRITICAL VELOCITY IN AN OPEN CHANNEL. 



So far it has been assumed that in channel flow the resistance to 

 motion is proportioned to some power of the mean velocity approximating 

 to the second, but while this is undoubtedly true in all natural streams 

 having a fairly rapid slope it is in all probability not the case where 

 velocities are very low. 



It might, in fact, be inferred from analogy with pipe flow that below 

 some " critical " velocity the resistance will be proportional to the first 

 power of the velocity. The clear glassy non-distortive reflecting surface 

 observed in any long straight reach of a deep and sluggish stream tends 

 to strengthen this inference, while the behaviour of small particles of 

 suspended matter appears to show almost conclusively that at low speeds 

 motion takes place in stream lines. 



