By A. Roy
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Additional resources for A First Course on Aerodynamics
7). It would be interesting to look at the differential form of the above equations. We would begin with the momentum equation in its differential form. Let us imagine that the control volume shrinks to an infinitesimal axial length dx. This leads to a control volume with cross sectional area A at station 1 and cross sectional area (A+dA) at station 2 respectively. , pressure changes from p to p+dp. 33) is the differential form of Euler’s equation. The reader is urged to explore the differential form of energy equation.
4) the expression becomes Speed of sound at standard sea level conditions is around 340 m/s. The Mach number of a flow is defined using ‘a’ as follows where ‘V’ is the velocity of the gas. When M<1 it is subsonic flow, when M=1 it is sonic flow and when M>1 it is supersonic flow respectively. Consider a point P in a flow field. Let us suppose that a fluid element instantaneously crosses this point with velocity V. Its Mach number, pressure and temperature are M, p and T respectively. , without heat addition or removal) slowed down to M=1 (if it was originally traveling at supersonic Mach number) or speeded up to M=1 (if it was originally traveling at subsonic Mach number).
Such flows are called as compressible flows. There are various flow regimes in compressible flow, namely subsonic compressible flow, transonic flow, supersonic and hypersonic flow. 7, the flow remains subsonic over the entire airfoil. It needs to be remembered that the local Mach number over the airfoil varies as a function of its shape and could well exceed the freestream Mach number in regions of high acceleration especially on the upper surface. 0, then there could well be a local pocket of supersonic flow on the upper surface of the airfoil.