Giuseppe Gentili 
Q= 1m A R°°817 (1) 
Where 
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Q - discharge, in m's 
  
- . 2 
A =area of the section, in m” 
R =hydraulic radius, or ratio of A to P, the wetter perimeter , in m 
S =hydraulic slope, dimensionless 
i^n inan 
n —roughness coefficient of the section, in m 
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Longitudinal sectional view 
Figure 1 Definitions of hydraulic variables in fluvial sections 
Because of its simplicity and lacking something better it is assumed that Manning s equation is also applicable 
for non uniform sections as are invariably found in nature, if the hydraulic gradient is modified to reflect only the losses 
due to the roughness of the section. Thus, starting with Bernouilli s equation to calculate the hydraulic profile between 
sections (see figure 1) one can write (Bailey and Ray, 1966): 
ho + hío * hr t k(Ah,) — h; * hy (2) 
where 
h = water level at cross section, with subscritpt 0 for the downstream section and 1 for the upstream one 
h, - aV^(2g)! — velocity head at section, in m, where V is the average velocity, & is a coefficient which is 1 
for sections not subdivided and & = (EK;2/a;2)(Kq3/A T) for subdivided sections where 1 refers to each subdivision 
and T to the total section, and g is the gravity acceleration constant, 9.8, m s? 
hr7 Lo. 1( Qo * Qi Y 21 Ko K,)' = head loss between two sections because of friction, in m 
L(o-1) = distance between the sections, in m 
Q - discharge, in m! s' 
K = 1/n ( A R*” ) = total conveyance at a section (from Manning s formula) 
k(Ah,) — head loss , in m, due to expansion or contraction between the sections, where Ah, is the difference in 
velocity heads between the sections and k is a coefficient which is 0.5 for expanding sections and 0 for contracting ones 
Where constrictions exist on rivers, such as at bridges and culverts, there is a change in the water surface 
profiles caused by these constrictions. The general equation that holds under these circumstances is, (Matthai, 1967), 
  
Q- C A, V 2g [ Ah + o, (V, /2g) ... h] (3) 
336 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.