216 RATIO OF MEAN TO GREATEST SURFACE VELOCITY. 



surface, varying from point to point, and inclining alter- 

 nately from side to side.* 



116. Mean Velocity. The mean velocity of the water 

 in a cross-section is equal to the quotient arising from 

 dividing the discharge per second by the area of the trans- 

 verse section. 



When the discharge per second is not known, the mean 

 velocity may be determined by measuring the velocities in 

 all parts of the transverse section, and taking a mean of the 

 results. If the transverse section is irregular in form, the 

 only accurate manner of determining the mean velocity is 

 to divide this section into partial areas so small that the 

 velocity throughout each may be considered invariable. The 

 discharge is then equal to the sum of the products of these 

 partial areas by their velocities. 



Let flj, 8 , a 3 , etc., be the small partial areas into which 

 the transverse section is divided, and v lt v z , v 3 , etc., the 

 velocities in these small areas. Then the whole area is 



a = a l + 2 -t- 3 4- etc., (1) 



and the whole discharge is 



av = fljVj + 2 v g + a s v s + etc. ; (2) 



therefore the mean velocity is 



v _ a l v l +g > ty+g s t> 8 +etc. 



a i + a 2 + a 3 + 6 ^ C> 



117. Ratio of Mean to Greatest Surface Velocity. 



It is often very important to be able to deduce the mean 

 velocity from observation of the greatest surface velocity. 

 The greatest surface velocity may be determined by floats. 

 Unfortunately, however, the ratio of the maximum surface 

 velocity to the mean velocity is extremely variable ; and it 



* See Report on the Mississippi. 



