34 



THE IMPROVEMENT OF RIVERS. 



conditions, but two will here be given, the latter of which is considered by many 

 engineers to be applicable to nearly all cases: 



D'Aubuisson attd Douming's : V=-ioo\/RSf, in which V is the velocity in feet JH r 

 second, R the hydraulic radius in feet (found by dividing the sectional area .1 }>y 

 the wetted perimeter), and 5 the slope of water-line. The discharge D, is found by 

 multiplying the velocity by the area, hence D VA. By wetted perimeter is meant 

 that portion of the profile of the section which Ik-s In-low the water-line. 



K utter's: 



16 

 ' 



N 



(, o.oo28i\ 

 41-6 + - 

 / 



VR 



in which Q= discharge in feet per second; 



A = sectional area of channel in square feet; 

 R=* hydraulic radius in feet; 

 S = slope per foot: 



W = coefficient of roughness, its value varying between 0.020 and 0.035 accord- 

 ing to the nature of the bed and condition of the channel. 



Mean velocities for any position may be deduced from the velocities given by the 

 rod-floats by the following formula of Francis: 



V' = r[i-o.n6(VX>-o.i)]; 



in which V = observed float velocity ; 



F'=mean velocity in the vertical; 



~ _ /depth of water minus immersion of rod 



\ 



depth of water 



) 



Humphreys and Abbot in their investigations on the Mississippi discovered that 

 the "ratio of the mid-depth velocity to the mean velocity in any vertical plane is 

 practically independent of the depth and width of the stream, of the mean velocity 

 of the river, of the mean velocity of the vertical curve, and of the locus of its maximum 

 velocity. In other words, it is a sensibly constant quantity for practical purposes." * 

 Later investigations, however, indicate that there is no constant ratio between mean 

 and mid-depth velocity. Neither is the numerical value of the ratio as given by them 

 (that at depths varying from 86 to 27 feet, the ratio has an extreme range only from 

 0.9868 to 0.9798), constant. These authorities suggested the taking of velocities at 

 mid-depth only, the quantity thus obtained to be reduced to the mean by using the 

 coefficients found. 



* Physics and Hydraulics of the Mississippi Kiver, p. 311. 



