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MAE 3241 Hmk 2

# MAE 3241 Hmk 2 - MAE 3241 Aerodynamics and Flight Mechanics...

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MAE 3241: Aerodynamics and Flight Mechanics Assigned: January 28, 2011 Homework #2 Due: February 11, 2011 Complete the following problems from the Fundamentals of Aerodynamics : 2.7 Comment: For part (a) of this question, which asks you to find the time rate of change of the volume of a fluid element per unit volume , note that this is nothing more than the physical meaning of the divergence of the velocity field ( 29 V as is discussed in Section 2.3.4 and shown mathematically in Equation 2.32. 2.11 2.12 The answer to this question is 4,822 N acting in the direction of the incoming flow. Problem 1: Examination of the acceleration of a given velocity field Given the Eulerian velocity-vector field: k ty j xz i t V ˆ ˆ ˆ 3 2 + + = 1.1 Find the acceleration of the particle. Problem 2: Calculation of the material (or particle, or substantial) derivative of a given flow field A velocity field and density field in Cartesian space are given as: i t L V ˆ = 2.1 ( 29 L x Kte - = ρ 2.2 Where L and K are constants, which must have the dimensions of length and density divided by

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MAE 3241 Hmk 2 - MAE 3241 Aerodynamics and Flight Mechanics...

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