K = CAR^ (I) 



where K = conveyance 



C = a coefficient related to ttie roughness of the channel 



A = cross sectional area of flow 



R = hydraulic radius 



X = a fractional exponent 



The discharge is directly proportional to the conveyance with the proportion- 

 ality constant being the energy slope to a fractional power, usually i. 



The variation in the hydraulic geometry as a function of discharge 

 at a river cross section is an indicator of the shape of the channel cross 

 section. The shape primarily reflects the magnitude of the bank-full dis- 

 charge which typically has sufficient sediment carrying capacity to shape a 

 channel and occurs frequently enough to maintain the resulting shape. The 

 top width, hydraulic depth, and mean velocity at a cross section are often 

 expressed as a function of discharge in the form of power relations: 



W = a Q^ (2) 



D = c Q^ (3) 



V = k q"^ (4) 

 where W = top width 



D = hydr au I i c depth 



V = mean ve I oci ty 

 Q = di scharge 



a , c, k = coef f i c ients 

 b, f , m = exponents 



Typical relations for a hypothetical river are shown in Figure 30. Sub- 

 stituting the power relations for the hydraulic geometry variables into the 

 flow continuity equation illustrates the interdependence of the variables: 



Q=AV=WDV (5) 



= (a Q^) (c Q^ (k q"^) 



, > n 'b + f + m) ,^, 



= ( a c k ) Q (6) 



103 



