Evaluation of shear stress terms 



72. In the preceding sections, the friction slope was represented as 

 Sf, and the surface shear stress was designated as t^. The most coimnonly used 

 relation for computation of the bottom shear stress is Manning's formula. 

 According to this formula, if a channel of complex shape, consisting of sub- 

 areas with different roughnesses and depths, is subdivided into M elements, 

 the volume flow rate in the channel is given by Equation 40, 



where 



iC=C?-^^,V^3 (41) 



73. In Equation 41, iC is known as the conveyance . Aj is the area of 

 element i, i?hj is the hydraulic radius of element J, and n^ is the Manning's 

 friction factor of element J. If the composite channel is subdivided into a 

 number of nearly rectangular subchannels, the hydraulic radius of each sub- 

 channel would be practically the same as the depth in the subchannel, and the 

 depth in the element can be used as the hydraulic radius. 



74. Once the friction formula is selected, the values of the friction 

 slope and its derivatives with respect to the independent variables can be 

 calculated. Using Manning's formula as the friction formula, the value of the 

 friction slope and its derivatives at node i in the numerical model are given 

 in Equations 42 to 44, 



'■ m 



(42) 





^ = IRl (44) 



31 



