The physical laws evoked in derivation of the defining equations all apply to a system (e. g., recall that the First Law of Thermodynamics refers to a system). A system is

Figure 2.5. Fixed finite control volume.

Systema collection of fluid particles of fixed identity. Visualize a sealed plastic bag filled with liquid or gas that is proceeding downstream in a flow. The contents of the bag constitute a system. Note that if the flow is compressible, the density of the material inside the sealed bag may change. That is, the volume enclosed by the plastic bag may change but the mass of material contained within the bag must remain constant. A system may be finite in size or infinitesimal. An infinitesimal mass of fluid of fixed identity is termed a fluid particle.

Control Volume

The fundamental physical laws or principles expressing conservation of mass, momentum, and energy are expressed with respect to a system, as previously men­tioned. For example, the First Law of Thermodynamics states that the heat added to a system minus the work done by the system equals the change in internal energy of that system. In aerodynamics, however, it is more convenient to derive these conser­vation equations by applying the physical laws to a control volume rather than to a system.

A control volume is a volume fixed in space. Flow may pass into or out of the control volume through the control surface that surrounds the control volume. Con­sider a surface that encloses a volume of arbitrary shape. Imagine that this surface is made of wire screen and that it is fixed in space in a flowing medium. Fluid may pass in or out through the porous screen, as illustrated in Fig. 2.5. The wire screen constitutes a control surface enclosing a control volume. This control volume may be finite or infinitesimal in size.

Review the definition of a system; it is different than a control volume, and the two concepts must be clearly understood. Both have important applications because the mathematical tools needed for describing a flowing medium are derived in sub­sequent chapters.

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