This document contains instructions for a semester project assignment involving analysis of a wind tunnel test. Students are asked to: 1) Calculate boundary layer thicknesses along the wind tunnel walls and over a model wing using provided tunnel geometry and an assumed test section velocity. 2) Determine where transition from laminar to turbulent flow would occur on the full-scale wing based on Reynolds number, and where it should be on the model wing. 3) Calculate what percentage of a minimum mounting height for the wing would be occupied by boundary layers on the wing and tunnel walls.

1. Sequence Number_ Name
EE 221 Spring 2015 Section 1 Prof. Barnes
Homework 9: Due Monday April 6
1) The circuit shown has been sitting with the switch closed for
a very long time. At time t=0 the switch is opened. Find the
differential equation needed to describe v(t) after the switch is
opened. You do
not need to solve the equation.
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2) The circuit shown has been sitting with the switch closed for
a very long time. At time t=0 the switch is opened. Find the
differential equation needed to describe vC(t) after the switch is
opened. You do not need to solve the equation.
3) The circuit shown has been sitting with the switch open for a
very long time. At time t=0 the switch is closed. Find a set of
equations needed to describe vC(t) after the switch is closed.
You do not need to solve the equations. I would use a node
analysis. If you choose to use a mesh
analysis specify how to get vC(t) from the mesh currents.
4) The circuit shown has been sitting with the switch open for a
very long time. At time t=0 the switch is closed. Find the
equation needed to describe iL(t) after the switch is closed. You
do
not need to solve the equation.
5) The circuit shown has been sitting with the switch closed for
a very long time. At time t=0 the switch is opened. Find the

3. equation needed to describe iL(t) after the switch is opened.
You do not need to solve the equation.
6) The circuit shown has been sitting with the switch closed for
a very long time. At time t=0 the switch is opened. Find the
equation needed to describe vC(t) after the switch is opened.
You do not need to solve the equation.
ENGR 3553 MECHANICS OF FLUIDS SPRING 2015
Prof. Peter Cavallo [email protected]
SEMESTER PROJECT – PART 4
BOUNDARY LAYER ASSESSMENT
In the final aspect of the project you will examine the boundary
layer characteristics for the
tunnel test section and the full scale wing and their implications
for a model scale test. The
model to be tested is a ½ scale model. The full scale vehicle is
expected to travel at a speed of
185 mph. The velocity at model scale is coming from your
calculations in Part 3 of the project.
The wind tunnel wall surfaces will enforce a no slip condition
and therefore a boundary layer is

4. expected to form starting from the inlet section, as depicted in
Figure 1. In addition, a separate
boundary layer will grow over the wing upper and lower
surfaces. Since the intent of our study
is to examine the wing in ground effect, the wing will be
mounted at different heights h above
the tunnel wall. Interference from the wing and tunnel
boundary layers is therefore a concern.
In the actual situation, the race car wing is moving relative to
the ground and while a boundary
layer develops on the wing, there is no boundary layer on the
ground plane.
Figure 1. Boundary layer growth on wind tunnel and wing wall
surfaces.
Of interest for test planning is the following:
1. Determine the boundary layer thicknes
layer displacement thickness
*
along the wind tunnel walls at the trailing edge of the wing.
Assume that the wing is
installed in the test section with the leading edge 3 ft from the
start of the test section

5. segment. Use tunnel and wing geometry data provided
previously. Assume the test
section velocity found in Part 3 of the project for a power input
of 80 hp.
2. Determine the full scale Reynolds number, assuming sea
level properties for air provided
previously. Assuming transition occurs at a Reynolds number
of 500,000, where will
transition occur on the full scale wing? Where should it occur
on the model if Reynolds
number is matched?
3. At model scale, if we are to consider a minimum height h c
of 0.125, what percentage of
this height will be occupied by the wing and tunnel wall
boundary layers?
ENGR 3553 MECHANICS OF FLUIDS SPRING 2015
Prof. Peter Cavallo [email protected]
SEMESTER PROJECT – PART 3
WIND TUNNEL POWER REQUIREMENTS

6. Figure 1 illustrates the wind tunnel we are considering in
greater detail. As the air passes
through the system and over the model, various losses are
encountered, which must be overcome
by the work input provided by the fan. In this segment of the
project you are to consider all
major and minor losses depicted in Figure 1 to develop a model
for predicting the velocity
obtained in the test section as a function of the fan power input.
Eventually this will be cast in
nondimensional terms.
Inlet segment
Test section segment
Diffuser segment
Exit segment
inlet
V
W
exit
V
Figure 1. Nominal open circuit wind tunnel with major and
minor losses.

7. Relevant data is provided in Table 1. Be sure to include these
in your analysis. You have four
(4) pipe segments to consider for major losses, and various
minor losses as depicted and
summarized in the figure and table. Assume the same surface
roughness height throughout the
system. For the sake of simplicity you may consider the
velocity at the start of each segment
when computing the major and minor losses. Be sure to
consider hydraulic diameter for any
non-circular segments.
Table 1. Tunnel losses and physical dimensions.
Dimensions (ft) Losses KL
Inlet height 9 Diffuser section height 3 Inlet entrance 1.0
Inlet width 10 Diffuser section width 4 Inlet contraction 0.2
Inlet length 10 Diffuser section length 30 Diffuser expansion
0.1
Test section height 3 Exit section diameter 6 Fan losses 1.5
Test section width 4 Exit section length 12 Exit 1.0
Test section length 8 (Only exit section is circular) Surface

8. NOTES:
1) This is a Class II problem and as such it is strongly
recommended that you set up a
spreadsheet to perform the calculations. You will need to
iterate (i.e. guess) on values for
volumetric flow rate through the system until this value is
consistent with other
parameters. You should set up your spreadsheet with all
relevant formulas, including
Equation (8.35b) of the text, to update the entire system with
just a few inputs.
2) Hint: rearrange the extended Bernoulli equation so all terms
are on one side. Iterate
on Q until the condition that all head additions/losses sum to
zero is met to within some
tolerance (within 0.1 ft, e.g.).
3) The fan power and volumetric flow rate are inputs. The inlet
and exit velocities are
unknown but nonzero.
4) Assume standard sea level properties for air in all
3 3

9. 2 3
7 2
5) As a sanity check, for a fan power of 80 hp, you should
obtain a volumetric flow rate of
about 1700 ft
3
/sec, producing a velocity of nearly 142 ft/sec in the test
section.