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Mass Conservation Equation

Let us consider an infinitely small elemental control volume having dimensions dx, dy and dz as shown in Fig. 2.5.1. The flow through each side of the element may be treated as one-dimensional and continuum concept may be retained. It leads to the fact that the all the fluid properties can be considered to be varying uniformly as a function of time and position.

Fig. 2.5.1: Elemental control volume with inlet and outlet mass flow.

The basic control volume relations discussed earlier can be applied here and it takes in the following form.

(2.5.8)

The element being very small, the volume integral is reduced to the following differential form,

(2.5.9)

The mass flow terms appear in all six faces with three inlets and three outlets. As shown in Fig. 2.5.1, these terms can be summarized in the following table.

After substituting these terms in Eq. (2.5.8), one can get,

(2.5.10)