final_practice - 2.25 ADVANCED FLUID MECHANICS FINAL EXAM...

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2.25 ADVANCED FLUID MECHANICS Fall 2004 FINAL EXAM Tuesday, December 14, 2004, 1:30 – 4:30 P.M. OPEN EXAM WHEN INSTRUCTED AT 1:30 PM THERE ARE TWO PROBLEMS OF EQUAL WEIGHT (each graded out of 20) Please read each question in its entirety before starting Please answer each question in a SEPARATE book Be sure to write your name on each book No additional loose-leaf pages should be turned in (they will not be graded)
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2.25 Fall 2004 Final Examination PROBLEM 1 An Unmanned Helicopter A small unmanned reconnaissance helicopter is powered by jets attached to the tips of its two propeller blades. The idea is that a self-propelled rotor mounted on a torque-free bearing will minimize co-rotation of the helicopter’s body, making control (and reconnaissance) easier. In what follows, assume that the spherical body and its contents are not set in rotation. The lift and drag coefficients, L ± c L = 1 ² V 2 b 2 and D ± c D = 1 V 2 b 2 have values that are established by wind tunnel tests. L ± is the lift force per unit length of propeller blade, D ± is the drag force per unit length of propeller blade, is the density of the ambient air, and V denotes the local air velocity incident on rotor blade. b and R are the blade width and blade length, respectively. Also given are: M 0 , mass of each jet engine V m ± , mass per unit length of propeller blade M , mass of total helicopter system 0 , jet exhaust velocity 0 , jet exhaust density Assume that other masses are unimportant. 2
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2.25 Fall 2004 Final Examination A. Obtain an equation for the upward lift force provided by the rotor at a steady angular rotation rate ± (rad/s). Assume that the blades move through an essentially static fluid, i.e. that the propeller velocity is much higher than any induced angular rotation of the air.
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final_practice - 2.25 ADVANCED FLUID MECHANICS FINAL EXAM...

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