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By A. Roy

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In contrast to low speed or incompressible flow, these energy changes are substantial enough to strongly interact with other properties of the flow. Therefore energy concepts and consequently thermodynamics plays a major role in the study and understanding of compressible flow. 31) and energy equation as given below in its integral form. In the above equation ā€˜eā€™ stands for internal energy. The first term on the left hand side of the above equation stands for the amount of heat added to control volume, the second term stands for work done by pressure and third term stands for work done by body forces on the control volume.

The concept of compressibility can be explained using a simple example. Consider a small element of fluid of volume v. The pressure exerted on the surface of the element by the neighboring fluid is p. If the pressure acting on the element is now increased by an infinitesimal amount dp the volume of the element will be correspondingly compressed by the amount dv. The change would be accompanied by a negative sign because it is a reduction. 2 shows that the resulting change in density will be small for liquids due to their low values of compressibility, and large for gases due to their high values of compressibility.

This gave a very good approximation of the real flow field and the circulation distribution along the wing span was well modeled. Prandtl thus came up with the fundamental equation of his famous lifting line theory The wing spans from ā€“b/2 to b/2, which means its total span is b; c(yo) is the local sectional chord length of the wing. In physical terms the above equation simply states that the geometric angle of attack is equal to the sum of effective angle plus induced angle of attack. Note that the wing planform is in the x-y plane and line.

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