Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 55

For simplicity we consider first the flow in the x-direction as in Figure 2.1. The mass flow balance contains the following quantities:

1 The elemental mass m=ρdV=ρA with A=dydz.

2 Mass flow into the volume (ρvxA)x.

3 Mass flow out of the volume (ρvxA)x+dx.

4 Mass input from external sources m˙.

Figure 2.1 Mass flow in x-direction through control volume. Source: Alexander Peiffer.

leading to equation

(2.1)

for mass conservation. Expanding the second term on the right hand side in a Taylor series gives

and finally

(2.2)

This one dimensional equation of mass conservation in x-direction can be extended to three dimensions:

(2.3)

The second term of (2.3) may be confusing, but it says that the change of density is not only determined by a gradient in the velocity field but also by a gradient of the density.