Unified Quiz 2F Name________________ Unified Quiz 2F March 5, 2004 • Put your name on each page of the exam. • Read all questions carefully. • Do all work for each problem on the two pages provided. • Show intermediate results. • Explain your work --- don’t just write equations. • Partial credit will be given, but only when the intermediate results and explanations are clear. • Please be neat. It will be easier to identify correct or partially correct responses when the response is neat. • Show appropriate units with your final answers. • Calculators and a 2-sided sheet of paper are allowed • Box your final answers. Exam Scoring #1 ( 30 %) #2 ( 35%) #3 ( 35%) TotalUnified Engineering Spring 2004 Fluids Quiz 1 Page 1/3 1. (30 %) A thin airfoil of chord c is rotating with steady rate � so that its angle of attack is increasing in time. � = �t As a result, the airfoil trails a vortex sheet of constant strength α. The rotation rate � is slow enough so that the instantaneous flow and lift very nearly correspond to the instantaneous �. Both � and α are defined positive in the clockwise direction. V � �� , a) Determine the circulation �(t) about the smaller dotted-line circuit containing just the airfoil. b) The larger solid-line circuit contains both the airfoil and some part of the wake. Apply Kelvin’s theorem to this circuit at times t and t + �t, and thus determine the magnitude and sign of α. c) The flow is inviscid. What drag force D� do you expect? i) D� < 0 ii) D� = 0 iii) D� > 0 Explain your reasoning.Unified Fluids Quiz 1 (Q2F) Name________________ March 5, 2004 Problem #1 (continued)� Unified Engineering Spring 2004 Fluids Quiz 1 Page 2/3 2. (35 %) A sail-like airfoil of chord c consists of a membrane stretched between two thin rods at the leading and trailing edges. The membrane billows to a parabolic camberline shape whose height h is proportional to the lift per span h = L�/K where K is some effective stiffness of the membrane. V �� , h a) Use thin airfoil theory results to explicitly determine L� in terms of a given �. Note: Starting from known results is OK – no need to derive from scratch. Also determine the effective lift slope dc�/d� of this airfoil. 1b) What is the maximum safe operating dynamic pressure 2 ωV 2 for this airfoil? What do you expect to happen if this is exceeded?Unified Fluids Quiz 1 (Q2F) Name________________ March 5, 2004 Problem #2 (continued)� � � Unified Engineering Spring 2004 Fluids Quiz 1 Page 3/3 3. (35 %) An elliptic-planform wing with span b and chord c(y) = co 1 − (2y/b) is in slow steady rolling flight at roll rate p and velocity V . The wing has no geometric twist or camber, �geom = 0 �L=0 = 0 and the center chord line is lined up with the velocity vector (i.e. � = 0). V p y a) Draw a velocity triangle seen by the wing airfoil at typical spanwise station y and determine the local c�. Use small-angle approximations. b) The circulation distribution for this wing is known to be 1 V c c� � � = 2bV A2 sin 2� 2 � Combine this with your c� result from a), and determine the constant A2 in terms of the known parameters. c) In which direction is the rolling moment? The following identities may be useful: sin 2� = 2 sin � cos � cos 2� = cos 2 � − sin2 �Unified Fluids Quiz 1 (Q2F) Name________________ March 5, 2004 Problem #3
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