Fluid acceleration

The equation of acceleration of a fluid mass is rather different from that of a vehicle, for example, and a note on fluid acceleration follows. Let a fluid particle move from P to Q in time 8t in a two-dimensional flow (Fig. 2.11). At the point P(x, y) the velocity components are и and v. At the adjacent point Q(x + 6x, у + 8y) the velocity components are и + би and v + 6v, i. e. in general the velocity component has changed in each direction by an increment 8u or 8v. This incremental change is the result of a spatial displacement, and as и and v are functions of x and у the velocity components at Q are

The component of acceleration in the Ox direction is thus

d(M + 8u)

and in the Oy direction

The change in other flow variables, such as pressure, between points P and Q may be dealt with in a similar way. Thus, if the pressure takes the value p at P, at Q it takes the value