At ^ '■^^ 



^1*1/2] - Ay dlhz = 



(12) 



Ol*l/2 - Ci-H/2 + 



Afc 

 Ay 



At 

 Ay 



{Qi:i)' (or) 



.?'*1\2 





A/.i 



(1-6) 



+ g-j^ ALn (2/1 - z/) (1-6) 



+ gb.tA^\sV\% + gAt A/\S/ 1 (1-6) 

 2 » 2 2 



+ gAt A/;\s^;;^e + gAt a/^^^s/.^j^ d-s) 

 2 > 22 



- gAt <\Bf;\e - gAt ti^ ,B,,i(l-8) = 



(13) 



51. In the above equations, the value of a variable Q!(i+i/2) is, 



a . 1 = 

 ^*-2 yi.i - yi 



i { a(y, t)dy 



(14) 



where a represents any of the variables tj,, t^, A, Q, etc. A good approxima- 

 tion for 01(1+1/2) Is 



«i.A - T("i * "i*! 



(15) 



52. In Equations 12 and 13, all variables with superscripts J are 

 known, whereas all variables with superscript (J+1) are unknown. However, all 

 the unknowns are not independent because the water cross -sectional area and 

 the top width of the channel are functions of the water surface elevation at 

 grid points (i,J+l) and (i+1 ,J+1) . It should also be noted that the distance 

 increment Ay and the time increment At need not be constants in the solution 

 scheme and in DYNLETl. 



22 



