This equation accounts for the conservation of mass of the water. Consider the variation of the water volume contained between two sections at the abscissa x and x+Dx (see figure 23) during time Dt.

Figure 23

Inflow water mass:

r.Q(x,t).Dt + r.q.Dx.Dt

Outflow water mass:

r.Q(x+Dx,t).Dt

Change in storage:

r Vt+Dt - r Vt = r(A.Dx)t+Dt - r(A.Dx)t

The equation expressing the conservation of mass is written:

r(A.Dx)t+Dt - r(A.Dx)t = r(Q.Dt)x + rq.Dx.Dt - r(Q.Dt)x+Dx

At the limiting conditions, one obtains the equation [28]:

+ = q [28]