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AA311.Homework3

# AA311.Homework3 - AA311 Homework 3 Due Give all your...

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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 Give all your...

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