Exam_final_2005_key_v2

Exam_final_2005_key_v2 - EAS 4101 Aerodynamics Spring 2005...

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EAS 4101 - Aerodynamics – Spring 2005 4/28/05, Final Exam Name: ____________key_ __________ 1/6 Short Answer Questions: (3 points each, unless otherwise marked) 1) Consider supersonic flow over a hump as sketched below (6 points total) 1 M 2 M a) Sketch the flow field for the picture shown below assuming . Clearly label the various wave phenomena that occur. 1 1 M > b) What is the qualitative relationship between 1 M and 2 M . c) For a thermally perfect gas , what is does the energy equation reduce to? The flow field consists of an oblique shock, followed by an expansion fan, followed by an oblique shock. Due to the shocks, 12 M M > . If the gas is only thermally perfect, then h . 0,1 0,2 h = 1 M 2 M 2) Give two examples studied in class where d’Alembert’s paradox is invalid for an inviscid aerodynamic flow and physically explain source of the drag. d’Alembert’s paradox is invalid for finite wings due to induced drag. It is invalid for compressible flow over an airfoil when cr M M such that wave drag occurs. 3) Consider supersonic flow over a shallow depression as sketched below (6 points total) 1 M 2 M a) Sketch the flow field for the picture shown below assuming . Clearly label the various wave phenomena that occur. 1 1 M > b) What is the qualitative relationship between 1 M and 2 M . c) What is the qualitative relationship between 1 s and 2 s . The flow field consists of isentropic expansion fans and compression waves, thus M M = and s s = 1 M 2 M

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EAS 4101 - Aerodynamics – Spring 2005 4/28/05, Final Exam Name: ____________key_ __________ 2/6 4) Describe the kinematic decomposition of a fluid flow as discussed in class. What are the four components and how do the assumptions of inviscid, but compressible flow possessing strong curved shocks affect their values? ( 4 points) 1) Pure translation: assumptions do not limit this component. 2) Pure rotational: entropy gradients will cause rotation 3) Dilation: compressibility results in this component being non-zero 4) Shear strain: the assumption of inviscid results in this component being zero 5) Consider a boundary layer of thickness δ possessing a velocity profile and an edge velocity . What is the () uy e U momentum deficit ?
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Exam_final_2005_key_v2 - EAS 4101 Aerodynamics Spring 2005...

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