AAE 511 Fall 2015
Problem Set 2
Due: Friday 9/11/2015
1.
(a) Starting from the vector form of the continuity equation,
+ (~u) = 0 ,
t
use the general formulations of the vector operators for orthogonal curvilinear
coordinates given in Appendix A of the t

in the file ps6 3 zprime.m. The first of the four equations is provided for you.
You will have to add the other three equations. Complete the program and turn
in a listing of your code.
(c) Set the circulations to +1 or 1 following the signs indicated in

AAE 511 Fall 2014
Problem Set 8
Due: Friday 10/31/2014
[5 pts.] 1. Consider an elliptical shaped airfoil, as shown below. Assume that the rear
stagnation point can be placed at the back of the ellipse along the major axis.
(This can be done by blowing tan

AAE 511 Fall 2014
Problem Set 3
Due: Friday 9/19/2014
(5 HW pts) 1.
(a) Derive an equation for the pressure in a constant density, incompressible flow
with no body force by taking the divergence of the momentum equation. Assume
viscosity is constant. Put

AAE 511 Fall 2014
Problem Set 10
Due: Friday 11/21/2014
(Note: There is no class Monday 11/24.)
(Late HW may be turned in on Monday 12/1.)
1. You are designing part of a new fountain to go on campus. Your section of the
fountain has water running over a f

AAE 511 Fall 2014
Problem Set 1
Due: Friday 9/5/2014
(5 HW pts) 1. Use index notation to show the vector identities in (a) - (d):
(a) = 0
(b) ( ~a) = 0
(c) () = +
(d) (~a) = ~a + ~a
(5 HW pts) 2. Given the tensor identity
ijk ipq = jp kq jq kp
,
show, u

AAE 511 Fall 2014
Problem Set 12
Due: Friday 12/12/2014
(NO LATE HOMEWORK ALLOWED)
(You should copy your HW before turning it in
so you will have it to study for the final exam.)
1. (This problem counts as two problems (10 HW pts.).)
Consider the boundary

AAE 511
Problem Set 7 Solution
1.
(a) The plots from running the Matlab programs cylinder1.m and cylinder2.m are shown in Figs. 1.1 and
1.2, respectively.
Figure 1.1. Streamlines for potential flow over a cylinder drawn as contour lines of the streamfunct

AAE 511 Fall 2014
Problem Set 4
Due: Friday 9/26/2014
(Note: No late homework allowed.)
(Note: Copy your homework before turning it in.)
(The midterm exam is Wednesday 10/1, 8:00-10:00 p.m., in PHYS 203.)
1. Consider the velocity field given by
u = (1 + t

AAE 511 Fall 2014
Problem Set 2
Due: Friday 9/12/2014
1.
(a) Starting from the vector form of the continuity equation,
+ (~u) = 0 ,
t
use the general formulations of the vector operators for orthogonal curvilinear
coordinates given in Appendix A, Section

AAE 511 Fall 2014
Problem Set 11
Due: Friday 12/5/2014
[10 HW pts.] 1. (This problem counts as two.)
Consider the two dimensional jet shown below. Far downstream the jet thickness will be thin compared to the distance downstream and the boundary layer
equ

AAE 511 Fall 2015
Problem Set 4
Due: Friday 9/25/2014
(Note: No late homework allowed.)
(Note: Copy your homework before turning it in.)
(The midterm exam is Tuesday 9/29, 8:00-10:00 p.m., in ARMS 1010.)
(4 HW pts) 1. Start with the dimensional form of th

AAE 511 Fall 2015
Problem Set 5
Due: Friday 10/9/2015
(Late HW accepted: Wednesday 10/14/2015)
(5 pts.) 1. Write the following in the form (z) = (x, y) + i(x, y) where z = x + iy.
(a) (z) = 1/z
(b) (z) = (z i)/(1 z)
(Note: z = the complex conjugate of z.)

Name:
AAE 511
Fall 2014 Final Exam
(Closed Book Exam)
(15 pts.) 1. Consider a Karman-Trefftz airfoil which has a non-zero included angle at the
trailing edge. This airfoil can be mapped from a circle using the following conformal mapping
c n
z nc
=
,
z +

AAE 511 Fall 2015
Problem Set 6
(This problem set is worth 15 homework points)
Due: Friday 10/16/2015
1.
(a) Consider a two-dimensional potential flow. Derive a formula for the complex
potential, F (z), for a new potential flow made by combining a doublet

AAE 511 Fall 2015
Problem Set 11
Due: Friday 12/4/2015
[10 HW pts.] 1. Consider the laminar viscous wake behind a two-dimensional (2-D) body, as
shown below. It is useful to work in terms of the velocity deficit, ud (x, y) =
U u(x, y). Also, let vd (x, y)

AAE 511 Fall 2015
Problem Set 3
Due: Friday 9/18/2015
(5 HW pts) 1.
(a) Derive an equation for the pressure in a constant density, incompressible flow
with no body force by taking the divergence of the momentum equation. Assume
viscosity is constant. Put

AAE 511 Fall 2015
Problem Set 10
Due: Friday 11/20/2015
(Note: There is no class Monday 11/23.)
(Late HW may be turned in on Monday 11/30.)
1. Consider a mixture of plane Couette and Poiseuille flow as shown below. A
plate, located a distance D above a so

AAE 511 Fall 2015
Problem Set 8
Due: Friday 10/30/2015
[5 pts.] 1. Consider a distorted elliptical shaped airfoil, as shown below. Assume that the
rear stagnation point can be placed at the back of the airfoil where it crosses the
real axis. We will call

AAE 511 Fall 2015
Problem Set 9
(NO LATE HOMEWORK ALLOWED)
Due: Friday 11/6/2015
(MAKE A COPY OF YOUR HW BEFORE TURNING IT IN)
(The 2nd midterm exam is Tuesday 11/10/2015,
8:0010:00 p.m. in ARMS 1010)
[10 HW pts.] 1. Consider potential flow in a channel o

5.
(a)
(i) Transition is the process of a flow going from laminar to turbulent. It is caused by instabilities in
which small disturbances grow or by large disturbances which by-pass the instability mechanism.
(ii) Separation of the boundary layer is when

AAE 511 Fall 2015
Problem Set 1
Due: Friday 9/4/2015
(5 HW pts) 1. Use index notation to show the vector identities in (a) - (d). (~a is a vector, and
and are scalars.)
(a) = 0
(b) ( ~a) = 0
(c) (~a) = ~a + ( ~a)
(d) 2 () = 2 + 2() () + 2
(4 HW pts) 2.

AAE 511 Fall 2015
Problem Set 7
Due: Friday 10/23/2015
[5 HW pts.] 1. Consider potential flow at a stagnation point as shown on the attached sheet.
Show that the velocity components are given by
u = cx
v = cy
.
Now consider potential flow over a circular

AAE 511 Fall 2015
Problem Set 12
Due: Friday 12/11/2015
(NO LATE HOMEWORK ALLOWED)
(You should copy your HW before turning it in
so you will have it to study for the final exam.)
[15 HW pts.] 1. You will use Thwaites method to solve for the boundary layer

Non-Cartesian Coordinates
We will sometimes use cylindrical or spherical
coordinates
See Currie, Appendix A
See curvilinear.pdf in Supplemental Material
AAE 511
Introduction to Fluid Mechanics