PART II: THEORETICAL BACKGROUND 

 Review of Basic Equations 



19. The shallow-water hydrodynamic equations forming the basis of the 

 numerical model for one -dimensional depth -averaged flow consist of the 

 equations for the conservation of mass, momentum, and energy. Their deriva- 

 tions are given in standard reference works (for example, Chow 1959, Stoker 

 1957, Ippen 1966, French 1984). For most applications, the equations for the 

 conservation of momentum and energy provide identical information. A short 

 derivation of the equations for the conservation of mass and momentum is given 

 here to review concepts and introduce notation. 



20. Consider a short reach of a channel of length A7 with the flow 

 taking place from Section 1 to Section 2 as shown in Figure 1. A typical 

 channel cross section is shown in Figure 2. These figures introduce the 

 following notation*: 



A = cross-sectional area 



B = top width of the channel cross section 



g = acceleration due to gravity 



h = water depth from the channel bottom to the free surface 



P = wetted perimeter of channel cross section 



q = the lateral inflow or outflow per unit channel length per unit 

 time 



Q = the volume flow rate 



t = time 



At = small time increment 



V = average flow velocity 



X = distance across channel 



y = distance along channel 



z = water surface elevation 



Zb = channel bottom elevation 



z^ = water elevation at time t 



For convenience, symbols and abbreviations are listed in the Notation, 



Appendix C . 



10 



