DISTRIBUTION OF VELOCITY 



213 



The mean velocity occurs at a radius x = '75 a. 



Messrs. Williams, Hubbell, and Fenkell found the surface velocity to be 

 practically one-half that at the centre, 1 in which case the mean velocity 

 is *83 times the maximum. The ratio was found to increase with the 

 mean velocity. Figs. 96 and 97 show velocity curves obtained on the 

 30-inch pipe respectively on the straight and at a bend in the*se 

 experiments. 



The results of Bazin's experiments can be represented very 

 approximately by the formula 



v = v - 



where k has a mean value, with the foot as unit, of 38, though a more 

 accurate formula is 



The mean results of these experiments gave u = '51 V ; v = *855 V ; and 

 showed the mean velocity to be attained at a radius "74 a. 



Assuming v = CVmi = '707 CVai, from Bazin's simpler formula 

 assuming x = "74 a, we have 



v = V - 1 



' v ~ C 



The value v = '855 V, thus corresponds to a value of C = 128. It is 

 indeed to be expected that as here indicated, the ratio of mean to 

 maximum velocity will vary with the diameter and surface conditions of 

 the pipe, both of which affect C. Experimentally the ratio is found 

 to range from '79 to *86, increasing with the diameter and smoothness of 

 the pipe, the following table indicating how, from Bazin's simple formula, 

 this ratio varies with C or with the value of /. 



1 Seethe discussion on surface velocity on p. 215. 



