Fundamental Equations for Compressible Flow

Consider a compressible flow passing through a rectangular control volume as shown in Fig. 4.1.1. The flow is one-dimensional and the properties change as a function of x , from the region ‘1' to ‘2' and they are velocity , pressure (p), temperature (T), density (ρ) and internal energy (e). The following assumptions are made to derive the fundamental equations;

• •  Flow is uniform over left and right side of control volume.

•  Both sides have equal area , perpendicular to the flow.

•  Flow is inviscid, steady and nobody forces are present.

•  No heat and work interaction takes place to/from the control volume.

Let us apply mass, momentum and energy equations for the one dimensional flow as shown in Fig. 4.1.1.

Conservation of Mass :

(4.1.14)

Conservation of Momentum :

(4.1.15)

Steady Flow Energy Conservation :

(4.1.16)

Here, the enthalpy is defined as another thermodynamic property of the gas.

Fig. 4.1.1: Schematic representation of one-dimensional flow.