AA311.Homework3 - AA311 Homework 3. Due October 17, 2011...

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AA311 Homework 3. Due October 17, 2011 Give all your answers in SI units. Problem 1. Recall that, when developing the equations for the ISA and the notion of “geopotential height,” we assumed that g ( h G ) g 0 . The geopotential height h was then defined such that ΔPE( h ) = ΔPE( h G ) h = ± r earth r earth + h G ² h G This is a “zeroth order” approximation of the true acceleration due to gravity g ( h G ) = g 0 ± 1 1 + ( h G /r earth ) ² 2 A “first order” approximation is g ( h G ) g 0 ± 1 - 2 h G r earth ² 1. Verify the correctness of this first order approximation by expanding f ( ± ) = ± 1 1 + ± ² 2 in a Taylor series about ± = 0. Show the first three terms (i.e., to quadratic order in ± ). 2. Develop an expression for a new altitude ˜ h ( h G ) defined such that ΔPE( ˜ h ) = ΔPE( h G ) where ΔPE( ˜ h ) = Z ˜ h 0 m g 0 1 - 2 ˜ h r earth ! d ˜ h Problem 2. In a certain wind tunnel, the speed in the circular test section with radius 25 centimeters is 100 m/s. What is the speed upstream of the test section where the radius is 1 meter?
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AA311.Homework3 - AA311 Homework 3. Due October 17, 2011...

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