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Unformatted text preview: Air Speed Theory Eugene M. Cliff January 22, 2001 1 Introduction The primary purpose of these notes is to develop the necessary mathematical machinery to understand pitotstatic airspeed indicators and several related notions of airspeed. In the next section we will begin with a model of onedimensional ow (along a streamline) and carry out the required devel opment for a compressibleow form of the Bernoulli equation. From there we will define a few notions of airspeed and discuss the relations among them. 2 One Dimensional Flow We consider steady ( no change with time ), frictionless ( no viscous forces ) ow along a streamline and so we have d P + d [ V 2 / 2] + g dz = 0 . (1) Our goal is to integrate this expression. Note that the real work is the integration of the first term; this requires that we introduce a P relation. 2.1 Case 1: Fluid at Rest In this case we have V 0 so that (1) takes the form d P = g dz, which we recognize as the hydrostatic equilibrium equation used in the inves tigation of the model atmosphere and altimeter theory. The required P relation came from the perfect gas law and the assumption of a temperature profile. 1 2.2 Case 2: Constant Density In this case we have ( i.e. a constant) and equn (1) can be simply integrated to yield P + V 2 / 2 + gz = C , where C is a constant along the given streamline. For most aircraft applica tions we neglect the last term ( gz ) and write P + V 2 / 2 = C . The constant ( C ) has a fixed value along the streamline; along the line P (the static pressure) and V (the airspeed) change, but in such a way that the combined term is constant. We can imagine a place along the (extended) line where the velocity is zero and at such a point ( p ) P ( p ) = C . This means that the constant of integration...
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 Fall '09

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