"' Single Grid "': the-dependent non-linear equations of continuity and conservation of momentum are solved by implicit finite difference techniques with the variables defined on a space-staggered rectangular grid.

2.

Applying linearization techniques to the equation of motions for both species, to the equation of continuity, and Poisson's equation, and introducing the spatial and temporal harmonic operators \ partial _ t \ rightarrow-i \ omega, \ nabla \ rightarrow ik we can get the following expression:

3.

From the equation of continuity it is evident that for area of cross section being constant, discharge is maximum when the velocity of discharge is maximum . and from Ch�zy formula and Manning formula for a certain value of slope and surface roughness velocity is maximum when the hydraulic radius is maximum . and if we take area as constant hydraulic radius is maximum if the wetted perimeter is minimum.

4.

That is, viewing the motion through phase space as a'fluid flow'of system points, the theorem that the convective derivative of the density, d \ rho / dt, is zero follows from the equation of continuity by noting that the'velocity field'( \ dot p, \ dot q ) in phase space has zero divergence ( which follows from Hamilton's relations ).

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