RATIO OF MEAN TO GREATEST SURFACE VELOCITY. 217 



has formed the subject of much careful investigation. Put- 

 ting v for the greatest surface velocity, and v m for the 

 mean velocity of the whole cross-section, the following 



values have been found for : 



De Prony, experiments on small wooden channels, 0.8164 



Experiments on the Seine, 0.62 



Destrem and De Prony, experiments on the Neva, 0.78 



Boileau, experiments on canals, 0.82 



Baumgarten, experiments on the Garonne, . . . 0.80 



Brunings (mean), 0.85 



Cunningham, Solani aqueduct, 0.823 



Dubuat, experiments on small canals (mean), . . 0.83 

 Dupuit, from theoretical considerations, believes 

 the ratio to vary between 0.67 and 1.00. 



Various formulae have been proposed for determining the 

 ratio Bazin found from his experiments the following 

 empirical expression, 



Vm = v 25A\/rO, (1) 



where r is the hydraulic mean depth, and 6 the slope of the 

 stream (Art. 113). 



Prony found the following formula, 



v o (y o _}. 7.77) 

 Vm= \> + 10.33" 



The ratio of the mean velocity to the surface velocity in 

 one longitudinal section is better ascertained than the ratio 

 of the greatest surface velocity to the mean velocity of the 

 whole cross-section. Let the river be divided into a num- 

 ber of compartments by equidistant longitudinal planes, and 

 the surface velocity be observed in each compartment ; then 

 from this the mean velocity in each compartment and the 



