338 



HYDRAULICS AND ITS APPLICATIONS 



abnormal cases, while the mean of the velocities at two-tenths and at 

 eight-tenths of the depth may also be relied upon as giving the mean 

 velocity within narrow limits. 



The velocity in a vertical is least at the bottom, the ratio of bottom 

 to mean velocity ranging from '6 to *9. It usually lies between '75 and 

 85, but varies widely in a short interval in the same stream. 



The ratio of the mean to the surface velocity in a vertical also varies 

 within somewhat wide limits and depends largely on the direction and 

 force of the wind. On a calm day it lies between *80 and '90, dimin- 

 ishing with the velocity of flow, with the roughness of the channel, 

 and with the ratio of breadth to depth. While usually inadvisable to 

 use the surface velocity in computing the discharge of a stream, it is 

 sometimes impossible, in time of flood to make any other measure- 

 ments. Under such circumstances the surface velocity, multiplied by 

 85 will give the mean velocity in a vertical with a fair degree of approxi- 

 mation. 



The ratio of the mean velocity over the whole section to the maximum 

 surface velocity varies considerably with the depth and state of the 

 channel and with the direction of the wind. On a calm day it usually 

 lies between '60 and '85, increasing with the depth of the stream. In 

 a gauging of the Pihine depth 6 to 19 feet its value was '73 while 

 Harlacher obtained the same value in gauging the Elbe depth 4 7 feet. 

 Gaugings of the Eger at Falkenau ('62 to 1*1 feet deep) gave a value of 

 *58. The following values of this ratio are deduced from Bazin's formula 

 (p. 342), by writing v mean = C V m sin. 6 and by giving C its appropriate 

 values. 



Material of Bed. 



