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 velocityvector 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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 Spring '11
 Staff
 Fluid Dynamics, 2 K, Wind Tunnel, 50 m/s, 10 m/s

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