352 HYDRAULICS AND ITS APPLICATIONS 



mean velocity being deduced from these readings as explained later ; 

 (2) at six-tenths, or at mid-depth in a series of equidistant verticals, the 

 mean velocity in each of these verticals then being found by applying a 

 factor ; (3) at the surface, bottom, and mid-depth in a series of verticals ; 

 (4) at the surface and bottom only, or at two-tenths and eight-tenths of the 

 depth in a series of verticals, in which case the mean of the two readings 

 is taken as the mean velocity in the vertical. While the first method is 

 likely to give the best results in a steady stream, yet, as previously 

 indicated, the length of time necessary to obtain the many observations 

 is a serious drawback in a stream of any considerable size. 



In a large stream where it is impossible to see the bottom, owing to the 

 impossibility of fixing the meter very near to the sides and bottom where 

 the velocities are least, the results tend to be too high. To obviate this 

 the meter should not be placed nearer to the surface than one foot. 



The mid-depth point is used because the factor, about '96, which is 

 used to obtain the mean velocity is more constant for it than for any 

 other point on the vertical ; while the six-tenths point gives very approxi- 

 mately the true mean velocity on the vertical. These factors are discussed 

 at further length on pp. 337 and 339. Observations taken at either of 

 these points are capable of giving excellent results. 



Method (3) was adopted by Moore in his gauging of the Thames. 1 

 Assuming the vertical velocity curve to be a parabola, its area is given 



by the formula A = 1 { v s + 4 v^ + v b } , h being the depth, v s and v b the 

 b 2 



surface and bottom velocities respectively. The discharge per second 

 flowing between the two end verticals is given by 



5 + )}c.f.s. 



where d is the breadth of the successive vertical strips ; the first term is 

 the sum of the areas of the first and last velocity curves ; the second term 

 is four times the sum of the even sections ; and the last term is twice the 

 sum of the odd sections excluding the first and last. The total discharge 

 is then obtained by adding the small volume flowing between each end sec- 

 tion and the shore. On account of the large variation in bottom velocity 

 with a given mean flow this method is, however, not to be recommended. 

 Method (4), in which the surface and bottom velocities are measured 

 is only advisable for very shallow steams. Experiments at Cornell 

 University show that the results thus obtained agree closely with those 

 given by a weir if the bed is smooth or gravelly, the depth from '4 to 



1 " Proc. Inst. C. E.," vol. 45, p. 220. 



