The continuity equation

For a small length of channel, Ax, (Fig. 14.15) and considering a small time interval, At, the mass balance or continuity equation can be written in discrete form as:

where AS is the increment of storage during At, Q is the inflow and (Q + AQ) is the outflow.

Fig. 14.15 Changes in flow over a short increment of time, At, in a short river reach of length Ax.

If A is the average cross-section in the reach then S = AAx, so that

and dividing by AxAt

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