336 



HYDRAULICS AND ITS APPLICATIONS 



tends to reduce them. The author's experiments however indicate that 

 for any such non-uniform flow as is likely to be experienced at a gauging 

 station, the influence of the sides is the all-important factor. 



This theory explains why, as is found in practice, the depth of the 

 filament of maximum velocity, and, as will be seen later, also that of 

 mean velocity in any vertical, 



(a) is greater as the influence of the sides increases and hence as the 

 ratio of depth to width of the stream increases. 



(b) is less as the roughness of the bottom increases, since this rough- 



ness retards the trans- 

 verse current without 

 having any compen- 

 sating effect. 



(c) in the case of a 

 rectangular channel, 

 is greater nearer the 

 sides. 



It also explains why, 

 on measuring the velo- 

 cities across a hori- 

 zontal in a stream, 

 two points of maxi- 

 mum velocity are often 

 found, these being one 



on each side of the centre as shown in Fig. 150, which is taken from a 



gauging of the Cornell channel. 1 



The effect of the wind on the curve of velocities in a vertical is indicated 



in Fig. 151, which shows the curves 



(a) with a strong up-stream wind. 



(b) with no wind. 



(c) with a strong down-stream wind. 



It is found that although both the magnitude and position of the 

 filament of maximum velocity is affected, that of the filament of mean 

 velocity (ra in Fig. 151) is sensibly independent of the state of the wind. 

 The probable explanation of this is that an up-stream wind banks up the 

 head waters and so increases the surface gradient of the stream, thereby 

 increasing the velocity of flow over its lower portions to an extent which 

 compensates for the reduced velocity of the surface layers. 



1 From U. S. Geol. Survey, Water Supply Papers, No. 95. pp. 73 and 74. 



