SPECIAL PROBLEMS
ME 303 FLUID DYNAMICS/ WESTPHAL/ WSU/ FALL 2000
These SPECIAL PROBLEMS are intended to supplement regular class lecture and homework
activities by providing an opportunity for in-depth study of some particular phenomena
related to our study of fluid flow. They are somewhat "open" in the sense that you
are left with considerable latitude to make assumptions and determine other particulars
of your study. The special problem is a REQUIRED element of the class.
Select ONE problem (that is, problem 1 OR 2 OR 3, etc). Complete and submit the "A" part by the first due date, and
the "B" part OF THE SAME PROBLEM by the second ("B") due date. Generally, the "A" part involves
mostly research and/or analysis, while the "B" part is more "hands-on", involving either an experiment
or more involved research/analysis/computation.
Follow the SPECIAL PROBLEM WRITE-UP REQUIREMENTS for your submission!
NOTE: You MAY work with other students on parts A and/or B of your selected special problem,
but your submission must be your own original version
of the collaboration--no photocopies or duplicate computer-generated submissions accepted.
A PART... Due: Oct. 24, worth 25 points
B PART... Due: Dec. 12, worth 25 points
INSTRUCTOR'S TIPS FOR PROBLEMS... POSTED AFTER OCT. 31
- V-NOTCH WEIR. Weirs are simply notches in a vertical wall
used to measure water flowrate in open channels;
flow depth above the weir
crest can be related to flowrate for a given weir geometry.
See pp. 542-546 of the text for some background on weirs.
PART A: Develop a dimensional analysis applicable to a V-notch weir, assuming that
volume flowrate is a function of graviational acceleration,
depth over crest, and V angle.
PART B: Conduct an experiment; measure depth over crest and flowrate
for a particular V-notch weir using your bathtub or backyard. You will need some
sort of water reservoir fitted with a weir.
You can measure flowrate with
a stopwatch and graduated container or bucket and bathroom scale.
- GOLF BALL FLIGHT. A ball in flight experiences forces due to
gravity, drag, and lift. The latter is strongly influenced by any spin imparted to the ball.
Conduct an analysis to evaluate the importance of air density in the flight of a golf ball.
PART A: From conservation of momentum principles, develop the equations governing the
ball flight. Measure ball diameter and weight. Find reference information concerning
lift and drag behavior of a golf ball. Solve for flight distance if lift and
drag are ignored ("ideal" flight), and plot ideal ball trajectories for selected initial
velocities for both Denver and Seattle (using homework problem 1-2 results for
air density at each location).
PART B: Check lift and drag data with instructor, and add these to your analysis. This
will require a numerical solution of the trajectory equations--you can solve this on
a spreadsheet or with a tool such as MATHCAD. Compare the computed trajectory and
distance of drive of a golf ball with and without lift and drag considered, just for Seattle and one
selected initial velocity. On your final graph, show "ideal", "lift only", "drag only",
and "lift + drag" trajectories. Consider only planar trajectories--that is, backspin only, no "hook"
or "slice" drives.
- CHANNEL FLOW OVER A BUMP. Consider the flow of water over a gentle
bump in a nearly level channel.
Will the elevation
of the water free surface above the bump be lower than, equal to, or above the free surface
elevation upstream of the bump?
PART A: Analyze the problem using
Bernoulli's equation and conservation of mass with upstream width,
depth, flow speed, and bump height as variables. Manipulate
the resulting equation involving the flow depth over the bump
into a dimensionless form and solve it. Present the solution graphically in
a dimensionless form (that is, in terms of dimensionless groups of variables).
PART B: Set up a small experiment
and measure upstream depth, flowrate, and depth over bump.
Compare your experimental results with the theory for one or
two depth and flow rate settings. Make a graph showing the solution
and your experimental data point(s); your discussion should summarize
both the experimental and analytical results in a few sentences.
- JET PUMP PERFORMANCE CURVE. The most-used description of a pump's capabilities
is typically called a "performance curve" and gives "head" vs. (volume) "flowrate" for
a particular pump. In this problem, you will examine the performance curve of a jet pump.
PART A: Develop a theoretical performance curve for a jet pump of the type used to drain
a water bed. See problem 6.83, page 224 of your text for hints on setting up the analysis.
PART B: Measure head vs. flowrate by timing the pumping of water from a bucket on a scale using a jet
pump connected to a sink faucet. To vary the head, you can change the elevation of the bucket
relative to the sink. You will need a pressure gauge to measure the inlet pressure. The pump
and pressure gauge can be borrowed from the instructor.
Compare theory and experiment on the graph... can you come up with a definition of
"efficiency" for this pump, and plot measured vs theoretical efficiency too?
- BUBBLE RISING IN A LIQUID. Small gas bubbles rising in a
liquid, such as CO2
in soda pop, are nearly spherical
in shape; they quickly achieve "terminal" velocity as they rise
because drag equals net bouyancy.
We wish to compare measured bubble velocity
to the terminal velocity, calculated from data
for a smooth, rigid sphere.
PART A: Develop the theory for terminal bubble rise velocity vs. diameter
and gas, liquid densities; use drag laws from references suggested by your instructor.
Make a graph showing the predicted terminal velocity of rise of a gas bubble
in water versus bubble diameter. Your graph will have at least two curves for different
assumed drag laws.
PART B: Develop an experimental apparatus using a notched wire suspended in the liquid
to provide reference marks.
Use a camcorder to record your observations of bubbles rising in a liquid column;
play back the tape slowly to measure bubble diameter and velocity. Then, compare
your theory to actual bubble velocity by adding the measured diameter and velocity
data points to the graph you made in part A. Which drag theory agreed with the
measured data?
- BOTTLE DRAINING FIXTURE. Develop a design for a fixture to assist in the rapid
draining of water from a vertically inverted 2 liter soda pop bottle.
The fixture may not protrude more than one foot from the top of the bottle;
also, the bottle may NOT be punctured or altered in any way.
No pump, fan, or any other powered assistance may be applied to the problem.
To get started, you can consider using a tube (a straw, say) that protrudes through
the mouth of the bottle. (Why not just invert the bottle? TRY IT!)
PART A: Following the classical approach of Toricelli, develop the theory
required to predict the liquid level in the bottle vs. time for the fixture
configuration you devise. Submit a graph showing
the predicted water level in the bottle vs. time.
PART B: Build your fixture and perform an experiment using a stopwatch and calibrated
markings on the side of a bottle. Plot your measured time vs. level on the same
graph as your theory of part A.
- WIND LOAD ON A FENCE. Wind loads are frequently responsible for destruction of residential
fences in southeastern Washington. Recently, my neighbor's fence--a simple cedar plank on
crossbar type--was blown over. He rebuilt it by mounting the panels alternately on opposite
sides of the crossmembers (sometimes called "good neighbor" style).
PART A: Search the literature for drag data for shapes similar to the plank fence configurations described.
Use the data you find to predict to moment at the base of one post for a 6 ft tall fence with posts on 8 ft centers; make
a graph showing base moment vs windspeed.
PART B: Do an experiment that will allow you to measure the drag, and moment on one post, for
both a simple plank fence and for the modified version with the good neighbor panels.
You will probably want to make a scale model using popsicle sticks... ask your instructor if you need ideas.
Compare your result to estimates obtained in part A.
- HILSCH TUBE COOLER. The vortex tube is a
device that can produce
air streams of comparatively hotter and cooler air, using compressed
air at normal room temperature as input. It contains no moving parts,
and may be considered adiabatic.
PART A: Using conservation of mass, energy,
and the second law of thermodynamics (we didn't study the latter, so you'll
need your thermodynamics here and can get help from the instructor), develop
equations to predict the hot and cold temperatures given the ratio of mass
flowrate in the hot vs. the cold stream.
PART B: Compare your performance prediction with experimental measurements
using a vortex tube provided by
the instructor. Make a graph of the hot vs. cold air temperature
from theory,
and plot a few experimental points on this graph. In addition to the
tube, you will need a temperature measuring device and a source of "shop"
air (at about 80-100 psig). You will NOT need to measure air flowrate.
- AIRFOIL/AILERON or WARPED WING PANEL CALCS
Aircraft must be fitted with systems that allow differing amounts of lift
to be obtained on each (right vs. left) wing panel to achieve roll control.
The Wright brothers used warping of flexible, variable-camber wings
to achieve roll control of their Flyer--in
contrast to (now considered conventional) ailerons,
which are rigid, pivoting pieces of the wing trailing edge.
PART A: Select one basic airfoil shape for study (suggestion: NACA 0012, see fig 11.20 of text page 451).
Using published data (from Abbott and von Doenhoff and/or other sources),
develop curves comparing drag and quarter-chord moment vs. lift for the basic section,
a cambered version (such as 2412 if the 0012 is the basic case), and a
version with a 20% chord trailing flap.
PART B:
Use the Virginia Tech program PANEL, or other
similar computational tool, for all
calculations.
Compare at least one calculation to data obtained for PART A.
Discuss your planned approach with instructor BEFORE starting any calculations!
- AUTOMOBILE AIR FLOW. Compare the flow of air around an automobile to the
flow around a simple shape.
PART A: Obtain a solution for the flow velocity around a simple shape such as an ellipse (2D) or a
sphere (3D), at a location 90 degrees from the stagnation point.
Plot the flow velocity as a function of distance from the surface in dimensionless
coordinates V/V_i vs. r/R, where V_i is the flow upstream velocity and R is the
sphere diameter or ellipse half-width.
PART B: Borrow a Pitot tube and pressure sensor from your instructor. While someone
else drives at a steady (LEGAL!) speed, sit in the passenger seat and use the Pitot probe to
measure the flow velocity at various locations perpendicular to the side of the automobile.
You can tape the Pitot tube to a stick, and put marks on the stick to indicate measurement
locations. Compare your measurements to the flow around a sphere by adding the measured
data to your graph from PART A.
- VORTEX SHEDDING IN A SOAP FILM WIND TUNNEL. Flow structures called "vortices" (an
individual structure is called a "vortex") are created downstream of the
flow around certain bluff bodies such as smooth cylinders.
Recently, some researchers have experimented with
flowing flat sheets of soap solution in the conduct of research on vortex phenomena.
However, it is not certain that such a "wind tunnel" can be used in the study of
such phenomena as vortex shedding when it occurs in the three-dimensional "real world".
PART A: Build the soap film wind tunnel apparatus described in the May 2000 column
"The Amateur Scientist" in the magazine "Scientific American" (pp 106-108). For more
information on the apparatus, click here and contact your instructor by email. Submit
a photo of your apparatus with your Part A write-up.
PART B: Using the smooth cylinder, attempt to measure the frequency with which the vortices
are created and "shed" downstream. Compare the Strouhal number for your measured conditions
of fluid velocity, shedding frequency, and diameter with the values given in
your textbook (see figure 11.10 p 436 of text).
- TURBULENT BOUNDARY LAYER SCALING CONTROVERSY. The variation of flow velocity
caused by viscosity when fluid flows near a flat surface occurs in a region
called a "boundary layer". Most flows of engineering interest involve turbulent
(time-varying, semi-chaotic) flow, but an average velocity distribution
(an average "profile") can still be defined and measured. There is no exact,
theoretical result that gives the shape of this profile, but in the 1960s it became
accepted that the shape followed a scaling law called "The Law of the Wall" (LotW).
Recently, the long-accepted functional LotW description has been challenged, with a new
form being proposed. A controversy has grown up as to whether the newly proposed or
the long-accepted LotW best represents physical reality.
PART A: Read two articles (email instructor for citations) to find the functions that define the "old" and "new" LotW.
Obtain measured velocity data from the instructor.
Make one graph showing the two competing versions of the LotW, and another
(separate) graph of the measured data.
PART B: Determine whether the new or old forms of the LotW best fit the
data you have through "least squares" analysis, and make a graph showing the measured
data on the same axes as both LotWs.
What influence would any measurement uncertainties have on the evaluation?
- PROPOSE YOUR OWN PROBLEM. Send email to the instructor (westphal@wsu.edu) with a
short description of the problem you wish to attack. We will then negotiate specific requirements
for your "A" and "B" part submissions.
