Why...nobody gets in to see the Wizard, not nobody, not no how !
Eight Time Winner of the Prestigious
"Crying Towel Award"
Bestowed annually by the students in the civil engineering
program on the faculty member responsible for inflicting
the most mental anguish during the Year
Course
Materials
and
MathCad File
Distribution Page(s)
page
last
modified 8/22/2009, 3:30 pm
Resume : Resume
Current attractions
2/22/07 - Chemistry problems can often exhibit convergence problems, depending on how the equations are writtem, in the CVEN 314 section
2/11/06 - Are minor losses really minor ? In the fluids section
2/21/06 - The potential effect on clarifier size when laminar flow around a settling particle is assumed....but isn't occurring
3/11/06 - Determining the operating point, brake hp and efficiency of a cetrifugal pump.
3/19/06 - The concept of Net Positive Suction Head, NPSH, and how to determine it
5/18/06 - Sensitivity analysis of Green Ampt infiltration procedure - in the student section
5/29/06 - A discussion of the vector product as a tool in dynamics, in the dynamics section
6/4/06 - An application of the vector cross product with explanation and several schematics.
8/2/06 - A neat little chemistry problem exploring calcite solubility, excellent application of a solve block
8/6/06 - File demonstrating use of a "parameterized" solve block for solving a chemistry problem
8/13/06 - An interesting file for a nonchemist showing what happens when the salt of a weak acid is added to water
8/13/06 - The strong acid in water problem
8/15/06 - Species distribution in a CO2/water system open to the atmosphere
8/15/06
- Water containing soluble calcium and solid calcite, subject
to partial pressure of CO2
You can access various problem topics by clicking on the following targets :
Course
Materials for Contaminant Transport
Notes,
Derivations,
Discussions for Contaminant Transport
Materials
for undergraduate environmental engineering (314) class
Air
Pollution
Chemistry
Probability
and Statistics
Civil
Engineering
Misc.
Problems
Numerical
Methods
Fluid
Mechanics
Dynamics
Water
Resources I and II - CE 310 and 411
Mathcad
Procedures
Files developed by former students
| FILE | FILE DESCRIPTION AND DEVELOPER |
| A File from Katrina | Developed by Rel Gray, currently with Hunt-Guillot and Associates, Ruston, La This was done in response to a contract from development of temporary living quarters for victims of hurricane Katrina, posted Nov. 1, 2005 |
| Drainage and Detention Basin Design | This file is several years old. It was done by Michael Foster. "Foster" did not like hydraulics/hydrology or Mathcad and said he wasn't going to work in the hydraulics area or with Mathcad after he left school, "he was going to do structures". He went to work for a firm that does structural work in the electrical power industry. Unknown to Foster, the firm also has responsibilty for drainage around their structures. This was Foster's first assignment. Moral of the story "In private industry you do what comes through the door" |
| Sizing of Culverts - Minimum Performance Approach | This file was produced by Lance Tyson in CVEN 411 (Fall 2005). It uses the minimum performance approach (FHWA) to size culverts. Posted Nov. 5, 2005. Nice use of conditional statements with text strings as output. |
| Sensitivity Analysis of the Green Ampt Infiltration Procedure | This file was produced by Joseph Bramande. He uses an "iterative input" into an Excel component to do a sensitivity analysis of the Green- Ampt infiltration procedure. Posted May 18, 2006, 9 am |
| Detention
Basin Simulation |
This file models the performance of a detention basin, it actually consists of 5 files. Very nicely done. Developed by a current student Keith Stagg, PDF version, posted 2/5/09, 3:30 pm |
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version 1 - solve block |
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development
of the titration curve for a strong acid/strong base system.
This file uses the
"root
function" rather than a solve block and
results in
a very general template
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This problem arose as a result of the need to predict the pH and alkalinity resulting from the addition of sodium bicarbonate to a low alkalinity well water. We defined a function, fct(Na), which calls a solve block for each dosage. Resulting pH and alkalinity plotted vs dosage. |
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calculations dealing with pollutants in fog vapor |
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A neat applied problem using a little chemistry and a little thermodynamics. From the Environmental Organic Chemistry text by Schwarzenbach et al. |
| Another neat problem
from
Environmental Organic Chemistry by Schwartzenbach, et.al , posted 5/1/03, 4:40
p.m. |
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Methyl Bromide on lettuce leaves |
A very practical little problem from Schwartzenbach et al. but I'm not sure if my solution is correct. Anyone seeing a mistake is asked to email me. Posted 2/25/00 8:30 am |
| Stumm&Morgan/7-1_solubility_of_FeCO3.mcd | Solving for the soluble Fe +2 concentration when the system contains a buffer system. Posted 12/15/01, 8:41 am. |
9-6_iron_oxidation_kinetics.mcd |
Problem illustrates that equilibrium calculations don't tell the whole story, posted 12/20/01, 7:15 am |
| 8_1_biochemical_calculations_M@E.mc |
A neat little problem from Metcalf and Eddy which draws together material from different areas to compute the oxygen requirement for metabolism of casein, posted 1/18/02, 1:45pm |
| Engineers are not
chemists - this
is a very simple little problem where I examine an often used
approximation in acid-base chemistry. The use of Mathcad
solve
blocks does not require many of the assumptions made when solving
chemistry problems manually or graphically. |
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| Open
system with solid phase |
Here I solve an "open
system" in
contact with a solid phase for a range of the independent variable.
I used a "solve block function" . This is an
iterative form
of a solve block not documented in Mathcad literature, at least not
very well. Posted 4/6/03, 11:05 am |
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A problem from Stumm
and Morgan's
Text, posted 4/14/03, 12 noon
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| Shows how to
determine if CaCO3
precipitation will occur and how much
, posted 4/29/03,
3:30 pm |
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A kinetics problem
dealing with
chlorine residuals.
Posted 5/14/03, 10:24 am |
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Reverse Osmosis Fouling Calculations |
A Problem
from "Water
Treatment" 2nd edition by MWH Global (GREAT BOOK).
I tried
to add a little chemistry explanation as well as a drawing, posted
7/25/05, 3:30 pm |
| CaCO3 Solubility | A neat little problem exploring the solubility of calcite in an open system with the presence of a solid phase. Much written explanation. These types of problems are an excellent application of solve blocks, posted 8/2/06, 7:15 am |
| Use of a parameterized solve block for weak base addition | This is a slick little problem showing how to use a solve block as a function with 2 independent variables that has ranges. The equations defined in the solve block are solved for each value of the independent variable(s), posted 8/6/06, 10:20 am |
| Adding strong acid to salt of weak base | File illustrates the effect a small amount of weak base has on pH reduction when a strong acid is added. Nice use of a solve block function, posted 8/6/06, 4 pm |
| Solubility of Silver Acetate in Water and the resulting pH | Interesting file for a non-chemist. I was surprised that adding AgAc changed the pH of water. It's because Ac- is the anion of the weak acid HAc. Posted 8/13/06, 9:05 am |
| Numerical Solution of the strong acid - water problem with explanation | Here I "beat to death" the strong acid in water problem. Both a numerical and analytical solution are provided as well as chemistry and Mathcad explanations, posted 8/13/06, 2:45 pm |
| CO2 - water open system - alkalinity zero | Species distribution in a CO2 water system open to the atmosphere - key point is that in such a system the alkalinity is zero, posted 8/15/06, 7:05 am |
| water containing solid calcite subject to p.p. of CO2 | What effect does the soluble Ca concentration on partial pressure of CO2 (or vice versa), posted 8/15/06, 4:30 pm |
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Based on a file from a Mathsoft E-book on statistics. Illustrates the Kruskal-Wallis procedure and explains some of the more esoteric Mathcad statements used. The test is a nonparametric version of ANOVA. A PDF file, reads external data sets. Posted 6/21/00 7:05 am |
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Based on file from Mathcad ebook. Nonparametric version of the t test. A PDF file. Posted 6/21/00 7:40 am |
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Based on a file taken from the Mathcad Treasury. I tried to dress it up a little and add some explanation and a possible application so that the user can learn a little statistics as well as Mathcad. posted 11/24/00, 12:55 pm |
| This
illustrates the fact that sample means are normally
distributed even when the underlying population is not. However you
must collect alot of samples with a few observations per sample or
fewer samples with many observations per sample. Posted 11/28/03, 10:30
am. This is repost of a (hopefully) better version of an
earlier
file. |
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| A hydrologic example of the use of the binomial distribution, posted 3/5/01, 5:10 pm | |
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A
problem illustrating the value of a
bivariate normal distribution in making predictions, even when data
sets are only minimally correlated ,
posted 7:35 am, 8/30/02 |
| Type
III extreme value distribution |
Comparing
a Type III EV distribution to a reference distribution created directly
from data, posted 6/27/03, 2:40 pm |
| The
Gamma Distribution |
This file steps through
an example
problem using the Gamma Distribution. I try to show how the 1
parameter, (s), version in Mathcad is related to the normal 2 parameter
version,(l, k) cited in most texts. Posted 8/2/03, 8:35 am |
| Binomial
Distribution Problem - Benjamin and Cornell |
A nice hydrology
application
problem from a very good text - Benjamin and Cornell, posted 8/4/03, 9:35 am |
| Bayes
Theorem - C.T. Haan |
A nice
little problem
from Haan's text illustrating the use of Bayes theorem. I
extended it a bit and tried to add explanation, posted 9/15/03, 5:10 pm |
| Basic
Probability
Concepts - Kottegoda and Rosso |
Basic
probability
concepts (union, intersection, conditional probability, independence)
applied to dam failure . I added a little to the basic
problem
from Kottegoda and Rosso. Don't let the minor notation change
between 2-14 and 2-19 confuse you. Posted 9/28/03, 9:35 am. |
The Normal Distribution and Mathcad |
Just a
refresher on
the normal distribution and Mathcad functions used in connection with
it, posted 10/24/03, 11:45 am |
TYPE III extreme value distribution |
Fitting an
empirical
distribution of low flows to a type III extreme value distribution,
posted 10/30/03 8:10 a.m. |
| Data file
for Type
III extreme value distribution problem above |
This is the
data for
the problem above, posted 11/1/03, 7:25 am |
Pearson Type III distribution |
I have
never seen
this done for either a Pearson Type III or an LP III
distribution. Most texts use the frequency factor approach
where
magic K values are selected from mysterious tables. This
needs to
be done in hydrology classes. Posted 11/13/03, 4:10 pm. |
LP III distribution using data from Bulletin 17 B |
Here I fit
the data
used in Example 1 in Bulletin 17B using the actual distribution, not
frequency factors. I get the same answer. This
procedure is
not illustrated in any hydrology reference I have. Posted
11/14/03, 12:05 pm |
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Here it is -
let me know if you want assistance interpreting it. The second part of the document is the ASCE standard procedure. |
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A discussion of 2 methods for dealing with Manning's equation when looking for flow depth, posted for Water resources II class, 8/16/00, 10 am |
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an American Scientist article |
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| A neat little problem from Henderson's classic open channels text. Enlightening computations regarding the conditions for hydraulic jump formation. | |
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An extension
of a simple chlorination
problem from the text by Davis and Cornwell, 3rd edition. We included
the ion product of water as one of the equations to be solved.
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as above but we neglected the ion product of
water in order to examine the effect of leaving it out
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"Metcalf and Eddy" based on type I clarification principles |
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An algorithm
for contolling flow in a pumped system using a
valve. Originally posted by Andrés Felipe Ortega Montoya,
Chemical Engineer - Universidad Pontificia Bolivariana -
Medellín, Colombia.
E - Mail:
aortega@janua.upb.edu.co.
I just added
some comments and dressed it up a little,
posted 7/3/2000
PDF version of problem 9-1 from
Wastewater Engineering, collection and pumping of wastewater.
posted 7/16/00
In this file
(a pdf file) we read in 2 external data sets.
One was logged using an American Sigma 950 data logger attached to a 4"
McCrometer water meter with transmitter. The other was logged using an
American Sigma ultrasonic level sensor attached to a second 950 unit.
We then carry out the necessary calculations to compute flow volumes.
This data comes from an Interstate rest area on I-55 at the
Louisiana/Mississippi border. Real world stuff....posted 12/24/00, 2:15
pm
Headloss in a
horizontal pipe, f not known a priori
Solution uses
a solve block. Problem illustrates the fact
that pressure gages can have same reading in flow through an inclined
pipe. Could not happen if pipe was horizontal. posted 11/19/00, noon
Fluid
mechanics for
real people
Based on an
on-going
research project. The insensitivity of the flow rate to the
length of the discharge line was unexpected.
Numerical
methods used to get the equation for the pump characteristic, the rest
is fluids. posted 7:45 am 9/7/03
link
How can you have pipe
flow when the pressure at two different points is the same ?
Posted 8/22/09, 3:30 pm
Analysis of reservoir gate
This is a file I found on my
hard
disk. It was apparently oringinally done by either Mathsoft
or
perhaps the Schaum's outline people. In any case it was a
bare
bones solution. I have added alot of description and text in
the
hopes of making the problem understandable to undergraduates in a
fluids class, posted 3/30/04, 11 am
Flowrate when pressure
drop is zero
Analysis of
Tainter Gate
Analysis
of Hydrostatic force on a Tainter gate. I have included
several
drawings showing how each component can be visualized, posted 1/15/07,
8 am
Depth of water needed to open
gate
This problem comes out of
Hydraulic
Engineering Systems by Hwang and Houghtalen. Its pretty
straight
forward. I just beat it to death. The drawings were
done
with Visio. I set it up so system parameters could be easily
changed. Posted 1/12/05, 9:45 am
Statistics in Fluid mechanics
This problem appears in Frank
Whites
Fluids text. It can be solved by linearization but I chose to
do
it using nonlinear regression, posted 4/4/04, 9:25 am
Pipeline diameter required for
flow
A standard pipeline solution
using a solve
block. I have tried to make the template somewhat general in
nature. The equations in the solve block are put into "ratio
form" for improved convergence. Posted 4/10/04, 8:15 am. Note
that the minor losses aren't in this problem.
Time
Required to Fill a
Water Tank
This problem is from Gearhart,
Gross and
Hochstein, 2nd edition. I like it because it combines basic
fluids and the solution of a differential equation. However,
for
the second part of the problem I got about 6.4 hours whereas the text
got 18.2 hours. If you see an error in my solution let me
know.
Posted 6/11/04 7:25 am.
Tainter Gate
Problem
A simple hydrostatics problem
involving a
tainter gate. I added drawings to try to better illustrate
the
components of the vertical
hydrostatic force, posted 1/21/05, 8:10 am
Flow between
Reservoirs
This is a
problem from
Hwang's hydraulics text. I do it assuming complete turbulence
and
then numerically, making no such assumption. It appears that
the
complete turbulence assumption should be made cautiously. Posted
2/20/05, 4 pm
The
complete
turbulence assumption
I have become fascinated with
how
difficult it can be to make the "complete turbulence assumption" and
get away with it. If the Reynolds number is low, substantial
differences in computed flows can occur. Posted 3-1-05,
9 am.
Flow to
shower head
This shows
the kind of
problems that can be solved in an undergraduate fluids class using
Mathcad. The student can think at a more abstract level if
Mathcad does the busy work, posted 5/9/05, 6 pm
Illustrates
computation
of the pressure-force on the underside of a cylindrical dome, posted
6/19/05, 9:35 am
Static and
dynamic
pressures across pump
This
problem illustrates the interplay of static and dynamic pressure
changes across a pump. Posted 6/20/05, 10:40 am
Pipeline between
Reservoirs - Iterative Solution
Just
another simple pipeflow problem with explanation. The problem
says to ignore velocity at the outfall so I explore the validity of
that assumption...easy to do with Mathcad posted 1/27/06 8:45 am
Are Minor Losses always
minor
This problem
takes a look at "minor losses". It ain't always the
case.....posted 2/12/06, 7:30 am
Buoyancy
- Water line of a tethered buoy
This problem
looks at how high the tide must rise to float away a buoy with a brass
anchor. posted 1/17/06, 3:30 pm
Pipe
Friction Loss Experiment
The
results of a fluids lab experiment examining head loss in laminar and
turbulent flow, uses an Excell spreadsheet inside a Mathcad
file. posted 1/18/09, 2:30 pm
An Ion Exchange problem Computation of the capacity of an Ion exchange resin and other relationships. Uses the spline algorithm in Mathcad
A worksheet for BOD analysis Worksheet computes reaction rate constants as well as BOD 5 for three different, seeded dilutions. Compares fitted BOD equation to observations for each dilution.
Laplace_transforms_RHS=0_data_set_1.mcd Solution
of two coupled second order ODE using Laplace transforms.
Uses a
solve block for a symbolic solution - I had not seen this
before.
Also uses keywords for symbolic manipulation.
Ammonia Assimilation
- A
pretty straight
forward problem showing how to
compute quantities in ammonia assimilation in biological waste
treatment, posted 1/19/2009, 3:45 pm
Unfortunately many of the most powerful Mathcad capabilities are not well documented, or the documentation is not in one place. The files below attempt to provide some better explanation of Mathcad statements and algorithms. Some attempt to demonstrate how the more powerful features (programming, solve blocks, root solvers) in Mathcad can be combined. Email regarding mistakes, incorrect interpretations or ambiguities is welcomed. dmg@coes.latech.edu
Local assignments - A good start for those who want to learn to program - This file comes from the Mathcad Treasury. I doctored it a little to, hopefully, make it easier to understand. posted 11/15/00, 2:16 pm
An_interesting_statement.mcd A close examination of a Mathcad statement that isn't well documented in the existing manuals
iterating_a_solve_block.mcd I got this file off the Mathcad Web site. The file itself is essentially unchanged. I tried to add to and rewrite the explanation. Iterating a solve block is a very powerful tool that is not explained very well in most places. Posted 10/28/00 noon
calling_solve_block_from_program.mcd - The original of this file came from the Mathsoft web site but, in my judgement, it is not documented or explained very well. I have added considerable explanation and tried to make the procedure easier to follow for the non-expert. Posted 10/30/00 11:45 am
finding and extracting soln values meeting a condition - The original of this file also came from the Mathcad Web site. It involves finding a set of solutions with a solve block and then uses a program function to extract those values meeting a specified condition. I just dressed it up a little and added some explanation, posted 11/4/00, 11:20 am
Examples of 'while' loops - I have taken some simple examples of applications of while loops and added some explanation. I also note where the operation of the program seems confusing. posted 11/5/00, 11:05 am
breaking out of a loop - A simple, annotated, example showing several ways to break out of a loop, posted 11/5/00, 11:10 am
Using the root function repeatedly and storing the output - Here we use the root function to solve a single equation many times. The results are stored in a matrix. posted 11/5/00, 11:20 am
Examination of the Conditional statement - An example from the manual with a little bit more explanation - posted 11/11/00 11:40 am
A program for extracting vector element locations - A minor change in an existing Mathcad quicksheet allows one to extract all locations (rather than values) of the maximum valued element in a vector. Posted 11/14/00
A file showing the definition and use of Boolean type functions - File originally from Mathcad Web site. I dressed it up a little and added some explanation. File also uses uniform random number generator, rnd(x). Added 11/22/00, 7:30 am
Elementary row operations -
This file originally came from the Mathcad web site.
I have tried to disect it a little and add additional explanation for
the non-expert. posted 12/27/00,
7:25 am
symbolic solution using keywords - Here we solve a separable differential equation using Mathcad keywords, posted 2/1/01, 11:40 am
multiple_SB_for_simultaneous_equations.MCD
-
This is an interesting file demonstrating the repeated use of a solve
block coupled with a small piece of Mathcad code. The file solves two
simple equations repeatedly. Posted 6/4/02, 7:30 am
Plotting
3-D Space Curves - I developed this file
because I had
a very hard time figuring out how to rationally a plot a space curve
using cartesian, spherical or cylindrical data. The
documentation
in Mathcad is not very good. See if this is
understandable,
if not email me and tell me. Posted 8/5/05, 9 am.
NUMERICAL
METHODS
click on underlined portion to bring
up file
Secant Procedure An illustration of the mechanics of the secant procedure for finding roots of equations
numerical_methods/False_position_algorithm2.mcd A study of the number of iterations required for the family of functions: xn - 1
Newton Raphson Algorithm Here used to solve the Colebrook White equation. The C-W equation is used in fluid mechanics to determine the friction factor for flow in pipes. A graphical description of the procedure is included.
numerical_methods/Redlich_Kwong Here I explore the convergence properties of two forms of the Redlich Kwong equation of state, posted 9/22/02, 10:45 am
falling_object_fixed_point_method.mcd
A simple problem
exploring the fixed point solution procedure and its convergence
properties, posted 9/26/02, 11 am.
Motion
with resistance, numerical integration A
simple problem
dealing with the time required for a particle to decelerate.
Corrections for units are required. Posted 7/30/05, 3 pm.
Numerical Integration Computing the area of a stream cross section. A common calculation when modeling streamflow. PDF version below. Uses several versions of Simpsons rule to compute the integral.
PDF file for numerical integration
- A PDF file version of the problem above
Finite
Difference Approximations of the First Derivative A comparison of the foward,
backward and
centered
difference approximations with the analytical
derivative
Euler's Implicit Method for solving the Advection Equation - A finite difference approximation . This file requires that the" Thomas" algorithm for solving the tridiagonal matrix generated. It is in the same directory and should work fine. File was produced using version 11. Posted 11/27/02. 2:15 pm
A
finite difference
approximation for the solution of the
steady
state advection
dispersion equation
- The
solution is for a reactor. Could be a river also.
Modified Lax Method applied to the advection equation - Can change flow velocity to show what happens when stability criteria are violated. Useful for predicting bulk motion.
modified_lax_method_applied_to_advection_equation.PDF
- PDF version of the
file above
The Basics of Euler's Method A simple problem illustrating Euler's Method for solving ordinary differential equations
Predictor corrector modification for Eulers Method This file uses subscripts instead of Mathcad programming to carry out the procedure. This requires that the procedure be cast using a single variable name subscripted for time. Solves the radiation equation.
Numerical solution of the radiation equation Use the modified Euler predictor-corrector method. This version uses Mathcad programming. As a result, differing variable names can be used. Solves the same radiation equation as the file above.
Numerical solution of a stiff ODE Uses the Euler explicit solution technique
A
PDF version of a stable and unstable
soln to a stiff ODE
Same as the
problem above PDF version
Note
- One definition of a "stiff ODE" is an ODE in
which the solution function exhibits rapid and extreme changes in the
dependent variable with small variations in the independent variable.
As a result a plot of the solution function over long time frames (time
is the independent variable) will look quite different from a plot over
short time frames.
An example showing progressive instability in Eulers Method A nice example showing progressive instability as a function of the size of the time step
A comparison of 1. analytical 2. Euler's explicit and 3. Leapfrog method Three ways to solve the same problem. An examination of the relative error for the numerical methods
Solution of a 2nd order boundary value ODE In this problem the derivative of the depndent variable is assumed, then adjusted until the right hand BC is met. Consideration of mesh size is examined. "Odesolve" also using for a comparative solution. posted 8/6/00, 5 pm
PDF solution for the problem above Same problem, in Adobe for non-Mathcad
types, posted
8/6/00, 5 pm
Second order boundary value differential equation - heat loss along a rod - A comparison of (1) the internal algorithm "odesolve" (based on 4th order R-K procedures), (2) a Mathcad programming solution in which the second order equation is reduced to a system of first order equations, these are then solved using the modified Euler predictor corrector procedure and (3) the analytical solution to the second order differential equation describing heat loss by convection and conduction along a rod, posted 8/6/00 7:45 am
A PDF version of the heat loss from a rod problem - Same problem as above, in Adobe for those who don't have Mathcad, posted 8/6/00, 7:45 am
The basic difference between the various numerical procedures used to solve ODEs is the way in which the functional relationship BETWEEN the points on the solution function is approximated. While Euler's technique is one of the simplest, using a linear approximation, the Runge Kutta procedures use more sophisticated relationships.
A comparison of 2 numerical procedures- Euler explicit and 4th order RK A comparison of these methods used to solve the radiation equation. Here we use the Mathcad function for the 4th order R-K procedure rather than code it directly.
A discussion of R-K 2nd order solution technique and an example - A mathcad file. Here I try to give some introduction and backround regarding the solution procedure. The procedure is demonstrated on a badly behaved function
The Runge Kutta Fehlberg Method - This procedure allows for efficient determination of local truncation error. A Mathcad file. E-mail me if you think my analytical solution is incorrect.
numerical_methods/gradually_varied_flow_Runge_Kutta.mcd - Mathcad programming used to implement the 4th order R-K procedure to plot a water surface profile , posted Oct 13, 2002 , 10:45 am
2
Lakes in series - This file uses both the R-K fixed algorithm
in
Mathcad as well as a Mathcad program to solve ODEs related to
contaminant concentrations in a lake.
Posted 11/12/02, 7:50 am
COURSE
MATERIALS FOR CE 314 - Environmental Engineering
Click
on the
underlined item to bring up the PDF or Mathcad
file
Assorted Problems and notes - click on the underlined portion to open the file, most are in PDF format
Nonlinear
regression
to determine BOD rate constant
Here I use nonlinear regression to obtain the reaction rate constant,
k, and the ultimate BOD, L. This seems easier than the
earlier,
manual methods, e.g. Thomas slope, etc.
Note that I also compute the
statistics for the model fit
Posted 5/9/03, 8:50 am
Problem
3-17
3rd edition Davis and Cornwell PDF file
Chlorination problem ion
product of water not included
Problem
3-17
3rd edition Davis and Cornwell. In this
version the ion product of water was included in the
solution.
PDF file
Chlorination Problem - includes ion product
of water
Problem
3-23 A
simple alkalinity calculation makes use of
the mathematical definition of
alkalinity
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PDF
file
A
simple alkalinity problem
A
problem from
Davis and Cornwell illustrating calculations
relating to alum addition
3-37
Davis and Cornwell - alum addition
Problem
3-31
Davis and Cornwell dealing
with hardness
calculations - PDF
file
hardness_calc.PDF
Design
of a rapid mix basin
- The procedure with
explanation(s) and
justification
for the choices made. posted 12/17/00 7am
A
flocculation basin design - Very similar
to the problem
above, posted 2/25/05, 6:50 am
A precipitation
problem showing the effect of a
buffer. In this particular problem the presence of a bicarbonate buffer
increases the amount of base needed to raise the pH of the solution
sufficiently to precipitate magnesium hydroxide by a factor of 16 ! PDF file
Mg_precipitation.PDF
Design
of a
primary clarifier
A
primary clarifier design problem
PDF File
-
replaces 2 earlier trickling filter files
All
purpose 2 stage trickling
filter design file based on NRC equations
IC distribution in an open system - Here I create a function which calls a solve block to find the inorganic carbon (IC) distribution in an open system for a range of partial pressures of CO 2 posted 12/2/2000, 7:20 am. The plot is commonly called a Master variable diagram. In this case the partial pressure of CO 2 is the "master variable"
PDF version of the IC distribution file immediately above - For those who don't have Mathcad, posted 12/2/00, 7:40 am
A simple solubility product problem Here I take a simple problem and beat it to death. Hopefully the annotations and explanations are useful, posted 12/2/00, 7:30 am
Simple solubility product Mg(OH)2 Just a simple solubility product problem with alot of explanation, posted 11/4/00, 3:55 pm
A second order rate Process A simple second order rate problem. Uses some of Mathcad's linear regression algorithms (slope(x,y) intercept(x,y) corr(x,y). Some explanation and examples of important rate dependent processes are given. Posted 12/8/00, 7:20 am
A generalized Type I settling algorithm - using units - Uses an iterative solve block, with units, to compute terminal settling velocity of a spherical particle using Newton's law, Reynold's number equation, and C D -N R relationship. This is done using Mathcad 2001.
Type I clarification - PDF file - Same file as above, in PDF format, posted 1/5/01, 7:25 am
Hers's the Gp data set - Here is the file
E qualization_basin_sizing_and_analysis.mcd - Based on problems from Chapter 5 of Davis and Cornwell, 3rd edition. Also a little discussion as to why the concept does not always work well in practice. Posted January 25, 2002, 10:15 am.
5-20_problem_and_additional_HW.mcd
- A simple,
complete mix activated
sludge problem showing the interrelationship of the various
equations used in design, posted 2/28/03, 7:25 am
Notes on
Type I Clarification - Some basic notes on discrete settling,
the
concept of overflow rate, and some design parameters for horizontal
flow, gravity type, grit chambers. The technology is
admittedly
dated but the theory allows a nice development of the concept of
overflow rate not possible for other types of settling.
Posted
1/27/04, 8 am
Alum dosage and sludge calculations - A basic chemical dosage problem (from Davis and Cornwell) using alum as the coagulant. Calculations for needed alkalinity as well as explanation of the process are provided. Sludge volumes produced as a function of solids content provided. Posted 2/2/05, 2:55 pm
The effect of assuming a Laminar flow regime on a particle's settling velocity This file explores the error incurred when laminar flow conditions are assumed for the settling velocity of a particle, posted 2/21/06, 10:45 am
Iron solubility in water This file illustrates the difficulties that can be encountered when using solve blocks to solve chemistry problems, posted 2/22/07 8:05 pm
Spray Irrigation This file combines an Excel spreadsheet with Mathcad to compute the volume of storage needed for a spray irrigation operation, posted 1/23/09, 4:00 pm
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Notes on
type
1 clarification-PDF file- see the Type I
settling algorithm in the section above also. Posted 1/4/01, 3:30 pm
Type
1 clarification notes
A
discussion
of the basic chemistry of alum
coagulation. A PDF
file
Alum
coagualation at the Monroe WTP
A Discussion of Chemical Equilibrium and the Ion Product of Water posted 12/4/00, 8:20am
derivation of G - velocity gradient PDF file - posted 12/4/00, 9:20 am
Using
statistics on environmental data
An example of what
simple statistics can
be used for in environmental science/enginering - a pdf file, posted
1/14/01, noon. Data set used is actual pH data collected in lab by
students, winter quarter, 2000-2001
Files to
assist students in solving ordinary
differential equations are provided in the section on numerical methods
in this web page.
click here to
go to numerical methods section
General
discussion of Streeter Phelps Equation
Here I use a simple problem as
the means for developing the Streeter Phelps Oxygen Sag Equation,
posted 7/1/07, 3:45 pm
Monte_Carlo_Analysis_Streeter_Phelps.mcd
An example of
Monte Carlo analysis applied to the Streeter
Phelps Equation, from Schnoors text posted 8/5/01, 7:05 am
From Weber and
Digiano's book. The book has an error in the
solution however. I note it in my solution. Posted 10/22/00
Temporal_aspects_of_pollutant_loading_patterns.mcd
File
illustrates use of
Heavisied step function as a switch to turn on pollutant loads. Posted
10:25 am, Jan. 1, 2005
Step input - Analytical method,
Euler's
method and Heun Method
Example
7-1 Chapra
Unsteady stae loading problem,
complete
mix system, solved 3 ways and compared, posted 12/28/04, 3:05 pm
Good use of
conditional controlled plots
posted 10:00
am 2/9/00
posted 1/23/00
10:45 am
Development of
a finite difference solution to the steady
state advection dispersion equation, posted 1/25/00, 6:20 pm. Also
listed in derivation section below. The resulting set of linear
equations is solved by matrix inversion. This is inefficient because if
you change the number of segments the matrices have to be manually
reformulated.
I think this
is a pretty neat file. Because the resulting
matrices are tridiagonal I used the "tridag" algorithm to
solve the set of linear equations. This allows the user to specify or
change the number of segments in the solution without manually
reformulating the matrices. Tridag does it automatically.
Saves
much work. I made this a PDF file because you can't implement the
tridag algorithm unless you have the numerical methods pack. Posted
1/26/00, 9am
A relatively
simple kinetics problem using data from Jerald
Schnoor's contaminant transport text.
TCE diffusion
from a lake, posted 8/19/01, 12:15 pm
Vapam, a soil
fumigant, spill in the Sacremento River,
posted 8/31/01, 11:15 am
Analytical
solutions to transport equations used. Good use
of stoichiometry too. From Fechner-Levy 2nd edition. A pdf file.
A gas transfer
problem, posted 12/19/01, 9:45 am. From
Stumm and Morgan, 3rd edition
Rate constant
determination for Fe(II) oxidation using the
method of excess. Posted 1/5/02, 10 am. From Weber and DiGiano
Laplace
Transform
solution of CMSTR ODE
I used
Laplace
Transforms to solve the mass balance ODE with constant loading and a
first order reaction term. I haven't used transforms in a
while,
pretty slick. You get somewhat of an all purpose solution,
posted
1/26/05, 8:20 am
A
General Discussion of sinusoidal inputs as part of an equation
A
general discussion of the use of sinusoidal terms to describe periodic
processes, oriented toward environmental types, posed 7/1/07, 3:15 pm
Biochemical Calculations
A
neat problem from an earlier version of the well known Metcalf and Eddy
text for waste treatment, illustrates the combined use of
stoichiometry, lab results , and kinetic equations for solving
activated sludge problems. posted 1/18/09, 1:50 pm
Chick
Watson Disinfection Model
Fits Data to the Chick
Watson Disinfection Model and Determines the coefficient of specific
lethality, posted 1/18/09, 2:20 pm
More
contaminant transport type problems can be found
in the chemistry section
Derivation
of advection equation with
reaction
A mass balance
on a cube CV in space, reaction assumed to
occur. A PDF file
derivation of oxygen
usage model, batch system, no reaeration
A simplified
DO model for a batch system - a useful place
to start - some discussion of parameters
posted 1:40 pm
2/11/00
A discussion of the S-F oxygen sag equation
-
A simple
problem used to develop the Streeter Phelps equation, some discussion
of the reaeration coefficient and the solution's sensitivity to it.
posted
2/14/00, 7:30 am
Stagnant
2 film model for phase
exchange
A derivation
of the basic model and a discussion of its
implications, PDF file
A Derivation of the mean velocity gradient, G
Development of finite
difference solution to advection dispersion equation
Although this
document contains an example problem, it is
primarily a derivation
Same file as above only in PDF format. Same file as the one above, develops a simple finite difference solution to the steady state advection, dispersion equation. posted 11/26/00, 8 am
Lake - Instantaneous spill - The derivation of the analytical solution for an instantaneous spill into a lake
WATER
RESOURCES I and II
Water
Resources II is a computer oriented class taught at
La. Tech. We make use of existing software packages from Haestad
Methods and the Army Corps of Engineers (HEC-RAS, HEC-HMS) coupled with
Mathcad to examine pipe networks, gravity drainage systems and
hydrologic modeling. Students are taught open channel hydraulics as
they are exposed to HEC-RAS.
Even though we have the HEC programs available, I like using Mathcad for much of the hydrology and hydraulics calculations because the mathematic manipulations required are input by and are visible to the student.
Mathcad is an excellent tool for carrying out UH construction (Snyder, SCS) and subsequent convolution with excess rainfall distributions. Minimizes tedious hand calculations.
Link to USACOE Hydrologic engineering center http://www.hec.usace.army.mil/
Development of gradually varied flow equations - Includes a qualitative discussion water surface profiles.
Gradually Varying Water Surface Profiles - PDF file
2-6_unit_hydrograph_construction.mcd - Simple problem demonstrating some Mathcad techniques while developing a unit hydrograph for a gaged basin, posted 3/24/01, 8:30 am
Modeling_IDF_curves.mcd - Mathematically modeling an intensity-duration-frequency curve using lsolve to evaluate the required parameters. Taken from McCuen's hydrology text, 2nd edition, posted 6/15/01 4 pm.
Snyders_synthetic_unit_hydrograph.mcd - Using Mathcad to construct and verify the volume of a unit hydrograph, uses a linear spline to replace straight line segments with a smooth curve. I then integrate the spline to check that the volume is 1 area-inch. Adjustments to recession leg points can be made, if needed. Posted 10/11/01, 3:30 pm
detention_basin_with_weir.mcd - This file explores the use of detention basins controlled by weirs loctated at the basin surface, the trade-off between plan area of the lake and the effect on the inflow hydrograph. posted 10/30/2001, 8:45 am
example_prob_SCS_handbook.mcd - This file is a rather comprehensive example problem illustrating how to use the SCS method and convolution to develop a DRH for a 6-hour rainfall event. Posted 11/5/01, 2:20 pm
SCS_dimensionless_unit_hydrograph_convolved_with_rain.mcd - This file is similar to the one above. An SCS UH is developed, excess rainfall is computed based on the UH curve number and the DRH is computed. Finally a mass balance check is performed. posted 11/12/01, 11 am
A file from Katrina - I got this file from one of my former students Rel Gray) who works for a consulting firm here. He developed it to size drainage systems for temporary housing sites for victims of Katrina and Rita (hurricanes 2005). The firm is Hunt Guillot and Associates of Ruston, Louisiana. Posted 10/29/05 3:30 pm.
convolution_using_spline_to_pick_points_in_time .mcd -
This is a comprehensive DRO problem. An SCS UH is
developed first, then convolved with a rainfall hyetograph. An
interesting wrinkle here is that, in order to get the same time
interval for the UH readings as the rainfall hyetograph values prior to
convolution, I use the interp(cspline) function to choose interpolated
UH flows at 30 minute intervals, this is much faster than doing it
manually. The technique was actually conceived by my students (and I
thought they were asleep !) Posted 5/3/02, 2:05 pm
Rainfall_IDF_curves.mcd
- A neat little file I
downloaded.
Originally developed (I assume) by Roger Hickman at the Texas
Railroad Commission. I added some explanation to try to make
more
usuable by undergraduates, posted 6/11/03, 3:15 p.m.
A
discussion of Infiltration - This is a basic discussion of
infiltration theory and a simple problem involving the Horton model for
estimating excess precipitation. In the file I embed an Excel
spreadsheet and read data from it. I like using Excel
spreadsheets because data columns can be labeled.
Looks
better than a vector or matrix. Posted 1/15/05, 9:30 am
Times of
Concentration - This is a problem from Gupta's Hydrology
Text. I added a few additional equations for computing the
time
of concentration, summarized the results in an Excel spreadsheet
embedded in the file as a component, and then computed the peak flow
using the largest and smallest values. I used a solve block
for
the methods requiring an iterative solution for tc and the rainfall
intensity, i. Students are usually surprised at the size of
the
peak flow rate. Posted 2/7/04, 5 pm
The Phi Index
- This
example comes from Bedient, 3rd edition. It works well using
conditional statements to compute the incremental volumes of runoff for
various phi values, posted 7/27/04, 7:50 am. This is a pdf
file.
Muskingum Channel Routing
- This problem is based on one in Bedient and
Huber.
In the problem the routing coefficient K is determined from data, then
the the outflow hyrograph is plotted using several values of the
weighting variable x and compared to the actual outflow
hydrograph. Posted 9/29/04, 2:45 pm
Ebook/Prob4-2_Uniform_Flow.PDF - Same file PDF format
Direct_Manning_equation_solver.mcd
- Direct
solution of Manning's equation for pipes partially
full, posted 3/19/01, 9:30 am.
I used global
definitions here so the user can change inputs and see the results
without having to page back and forth.
circular_pipe_partially_full.mcd
- This file also illustrates a couple of ways of obtaining
the
required pipe diameter for specified flow properties
One procedure employs a graphical approach, the other a solve block,
posted 6/13/04, 2:30 pm
Haested_text_chap_1_prob4.PDF
- PDF version of the file above
Chow_3-7_specific_energy.PDF
-
PDF version
prob_2-15_channel_transition.mcd - An examination of specific energy and channel transitions.
prob_2-15_channel_transition.PDF -
PDF
vsersion
Prob 1-2 Henderson surge in stream.mcd - This is a cross between an open channel flow problem and a dynamics problem. It involves motion relative to 2 different coordinate systems (observers)
Prob_1-2_Henderson_surge_in_stream.PDF -
PDF version
specific_energy_diagram_and_discussion.mcd - The classic specific energy diagram, plots for specific flow values, and some discussion as to what it all means.
specific_energy_diagram.PDF
- PDF version
Prob_5-6_canal_discharge.PDF - Same file in pdf format
pipe_network_example.mcd -
A problem from Hydraulics of Pipeline Systems
by Larock et al. Illustrates what can be done using Mathcad. Posted
10-7-00, 8:30 am
Larock_pg_66-7_pipe_network_vector_solution.mcd - This is EXACTLY the same problem as the one above only I have used vector notation where possible to reduce the amount of typing. Posted 10/26/00, 4:20 pm
Pipe_Network_Analysis_12-6-1-b_Mays.mcd - A
simple network problem from the Water Resources text by Mays posted
5/13/01, 5:45 pm
Problem
4.5.7 Mays - An overspecified problem -
This an example
of an overspecified problem. Even so, equations can be
written
and the solution values provided obtained. Its a good example
of
why one should never blindly accept results from a computer, even using
Mathcad. posted 3/28/05, 7:45 am.
developing_a_pump_characteristic_Gould_12JMC.mcd Another pump characteristic problem, similar to the one above...with the same cautions. Posted 5/12/02, 6:10 pm
8-130_3_reservoir_problem.mcd - A standard 3 reservoir problem along with some discussion regarding the details of solving such problems using computer software. Posted 10-9-00, 11:15 am.
A simple detention basin
simulation - Here is a
simple detention
basin simulation algorithm. Basin simulation is based on the principle
of conservation of mass. Most textbooks provide only graphical
procedures and, in my judgement, the connection between conservation of
mass and the actual procedure gets lost in the details of tabulation.
posted 11/10/00, 3 pm.
Determining
the operating point of a Centrifugal pump
- This file illustrates how to detrmine the
operating
pointt, brake hp and efficiency of a centrifugal pump. It is
also
a nice use of an Excel component inside a Mathcad file.
Posted
3/11/06
NPSH for a
suction
lift pump
- This problem illustrates the concept of Net
Positive
Suction Head, NPSH, and how it is obtained. This quantity is
a
determining factor in how far above the liquid level a suction lift
pump can be placed, Posted 3/19/05, 7:35 am.
Mays 9-1-1 Level
Pool.mcd
- Level pool reservoir routing procedure. I splined
data
for the storage - outflow curve to produce a continuous function,
posted 5/12/05, 8 am
Convex_channel_routing_2_reaches.mcd
- Uses
the Convex procedure to route a hydrograph through 2 reaches, posted
7/2/01, 5:30 pm
Modified
Att-Kin channel routing - Some explanation of and
an example
problem (Example 10-4 McCuen) showing the use of the Modified Att Kin
routing procedure. Posted 10/10/04, 5:30 pm
SCS_UH_with_convolution_using_D_as_the_time_increment.mcd - First we construct an SCS unit hydrograph. Then we convolve it with an excess rainfall hyetograph to obtain the DRH, posted 11/2/01, 3:50 pm
5-19_Wildcat_Creek.mcd - Assessing the fit of hydrologic data to a normal distribution. Because I have Mathcad statistical functions I did not need to use normal probability paper. I compared the data directly to a cumulative normal distribution using the mean and standard deviation of the data. Posted 3/18/02 10:10 am
7-29_rational_method_pre_and_post_development.mcd - A pretty straightforward problem using
the Rational
Method to illustrate the increase in maximum flow rate as a result of
basin development. Posted 4/7/02, 4:45 pm
Parallel pumps - A
relatively simple parallel pump problem from Gupta's text. I
use
splines to develop the curves from data given in the problem. Posted
5/12/04, 7:45 am.
Clark (time-area)
UH procedure Procedure for
developing a UH using
the "time-area" a.k.a "Clark procedure", posted 9/13/04, 11:45 am
Storage-Indication
routing Procedure - A Mathcad / Excel
file illustrating
the storage-indication reservoir routing procedure. I have
commented the Excel columns, telling where the values came from.,
Posted 10/22/04, 5:15 pm
Computer
output from Haestad Software
The files
below are in PDF format. They give an idea as to
what can be obtained from the academic version of the "Flowmaster"
software from Haestad. Reference: Computer Applications in
Hydraulic Engineering , 3rd Edition, Haestad Methods, CD
included.
I found this to be quite cost effective for students, compared to the
professional versions.
Haestad_rating_curve_problem_1-5.PDF Flowmaster output
Haestad_Detailed_Report_prob_1-5.PDF Flowmaster output. I used the "notes" window to write in the problem statement. It's at the bottom of the page.
Chow_9-8_water_surface_profile.mcd - Here I used Visio, a low end CAD package, to do the initial drawing. I used Mathcad to do some preliminary calculations. Then I used the current version of the Army corps of engineers open channel flow code, hec-ras version 2.2, to compute the water surface profiles. I then cut and pasted the graphical hec ras output into the Mathcad file. Note that I used the wrong channel width in the problem and had to revise the initial conditions (unrealistically). All of these packages are windows based, quite easy to use, and make it very easy to be quite productive and produce highly useful results. Imagine how much work this problem would be to do by hand !
Chow_9-8_water_surface_profile.PDF - PDF version of the file
A
HEC-RAS - MATHCAD-VISIO file - This file was
created by
cutting out parts of HEC-RAS output and editing them using Visio
primarily but also Mathcad. The final document was created in
Mathcad. HEC-RAS output can be "dismantled" in Visio and
edited
at a very fundamental level. Somewhat labor intensive but
produces useful prentation documents as well as useful
teaching
documents., posted 11/1/04 10:40 am
Mathcad/HEC-HMS Problems
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A simple little problem requiring the chain rule. Posted 3/26/00, 10:20 am prob. 11-16 B&J |
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prob 11-16 B&J |
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Prob. 11-21 B&J. I first published my version of this problem back in the early 90s' as part of an ASEE article. I've been working on it since, trying to develop an understandable study sheet to illustrate the usefulness of Mathcad for doing dynamics. Posted 2/27/00, 6:50 am |
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Turns out its not as easy to hit a target as it looks, posted 3/6/00, 2:45 pm |
| PDF version of the previous file, posted 7:50 am, 5/8/00 | |
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Prob 11-85 B&J. An example of what can be gleaned from a simple little dynamics problem with MathCad |
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Problem demonstrates the versatility of a well chosen acceleration term, posted 6:45 am 3/16 |
Basic x - v - t problem uses data and splines |
Basic problem
illustrating relationship between acceleration, velocity and
position. Uses data and numerical techniques,
posted
5/24/05, 8 am |
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2 versions given, involves integrating the ODE for acceleration, posted 3/15/00 4:30 pm |
| Car Crash with Data | Determining the speed of a car from crash test data. I like problems with data, posted 7/7/07 4:05 pm |
| Space Shuttle Re-entry | Kinematics applied to space shuttle re-entry posted 8/12/08, 7:50 am |
| Angular Momentum of a System of Particles | |
| Inextensible cord problem | Posted 9/4/08 4:15 pm |
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3-196 M&K, simple but interesting, at least to me, posted 3/29/00, 8:50 am, A truck drives along a barge initially at rest in the water. Which way does the barge move and what's the name of the guy driving the truck ? |
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conservation of momentum used to find the initial speed of a car - posted 4/13/00 2:20 pm, 14-19 B&J 6th edition |
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14-19 B&J 6th edition posted 6:45 am 5/9/00 |
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linear momentum 3-196 M&K,posted 3/29/00 3:50 pm |
| Linear Momentum with collision | A neat little problem illustrating conservation of linear momentum with energy loss, posted 7/28/07, 4:10 pm |
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Compute the work done firing a bullet - problem uses data and spline functions for numerical integration - A good example of integrating numerical mathematics into dynamics. |
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Requires some judgement in dealing with nonlinear materials, solution to MEMT 312 extra credit problem, posted 4/4/00, 1 pm |
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Combines ideal gas and definition of work, posted 11/26/00, 11:30 am |
| Blocks released from rest | I just thought this was pretty neat problem, posted 10/16/05, 8 am |
| Truck with Load on a Slope | Nice, straightforward problem. I also show the effect of the slope on required stopping distance, 12/20/05, 3:20 pm |
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problem shows the convenience of working directly with vectors in Mathcad, posted 7:10 am 3/16/00 |
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good use of i-j-k vector notation, posted 4/13/00, 2:20 pm |
| 14-12%20car%20accident.mcd | A really neat application of linear momentum to accident reconstruction, posted 11/8/05, 5:45 pm |
| Newton's Second Law | |
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| Meaning of zero gravity | posted 7/25/07, 8:45 am, a simple problem exploring the weightlessness |
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posted 7:14 am 3/1/2000, prob 12-19 B&J, 6th Ed. system 1 |
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12-19 B&J |
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Newton's 2nd Law applied to ship motion to determine velocity |
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A discussion of the crates acceleration from different frames of reference, posted ? pm on 3/15/00, 3-11 M&K |
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| A discussion of friction forces and frames of reference, posted 3/21/00, 6:30 am | |
| Numerical Solution - Range of a Golf Ball | A numerical solution based on Newton's 2nd Law applied to a golf ball, posted 9/4/05, 11:40 am |
| Edmund Fitzgerald | A simple dynamics problem and the story of the Edmund Fitzgerald, no real connection but interesting all the same. Posted 11:15 am, 11/20/05 |
| Car on circular track | Explores the forces on a vehicle traveling in a circle. There is no centrifugal force, as such. Posted 7/1/07, 9:50 am |
| Tension in Wrecking Ball Cable | Explores those factors affecting tension in wrecking ball cable, basic 2nd law problem in n-t axis. Posted 7-6-07, 9:40 am |
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Shows the value of the cross product and i,j,k notation for determining linear velocities in rotating systems, posted 4/15/00, 7:25 am, problem 15-10 |
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A simple illustration of how to use vector algebra to solve a 3-D motion problem where visualization is difficult. A PDF file, posted 4/15/00, 11:20 am |
| angular velocity and acceleration of rotating disk | A simple problem illustrating direction of the angular velocity and acceleration vector, posted July 4, 2007, 9:35 am |
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posted 4/24/00, 9:35 am, Visio drawings used |
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The classwork problem for April 19. Posted 3:45 pm 4/19/00, pdf format , 15-32 B&J |
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The classwork problem for April 19. Posted 3:45 pm 4/19/00, Mathcad version 7, 15-32 B&J |
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posted 5/3/00, 7:45 am, lots of pictures |
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posted 4/23/00 7:25 am, numerous drawings using Visio, saved as version 7 Mathcad |
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posted 5/1/00, 4:10 pm, A discussion concerning how to locate a velocity center and what to do with it when you find it ! |
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| Web_site_dynamics/Sample_problem_vehicle_motion.mcd |
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| Web_site_dynamics/4-13_M_and_K_angular_momentum_of_spheres.mcd | angular momentum of system relative to inertial coordinate system, uses vector algebra, posted 4/18/00, 2 pm |
| Web_site_dynamics/16-1_board_in_back_of_pickup.mcd |
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| Web_site_dynamics/16-55_B&J_rolling_sprocket_wheel.mcd |
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| Web_site_dynamics/16-55_B&J_rolling_sprocket.PDF |
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| Web_site_dynamics/16-3_rod_in_slots.mcd |
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| Web_site_dynamics/16-3_rod_in_slots.PDF |
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| Web_site_dynamics/17-3_rotating_element.mcd |
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| Web_site_dynamics/17-3_rotating_element.PDF |
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| Web_site_dynamics/P17-1_rotor_rotation.mcd |
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| Web_site_dynamics/P17-1_rotor_rotation.PDF |
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| Web_site_dynamics/17-12_and_13_brake_pedal_assembly.mcd |
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| Web_site_dynamics/17-12_and_13_brake_pedal.PDF |
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| Web_site_dynamics/16-13_P-K_rotating_element.mcd | Determining the velocity and acceleration of a point on a rotating element. Vector algebra used, posted 11:30 am 8/14/00 |
| Notes on the Cross Product | In this file I try to illustrate the usefulness of the cross product as a tool for determining the linear velocity of a point on a rotating system, posted 7/6/07, 11:05 am |
| 3-D Rotation - angular and linear velocities | A rotating cyliner. I use the vector product to compute the linear velocity of a point on the cylinder. Much explanation and many schematics. The cross product is a valuble tool for these types of problems because they are not easily visualized and one is forced to rely on the vector algebra. posted 6/4/06, 10:15 am |
| 2-D Rigid Body Rotation | 2-D rigid body rotation , makes use of relative motion and vector algebra, not easily visualized, posted 7/11/07, 3:10 pm |
| Torque produced by an operating motor | How does a motor on springs react when it is operating and producing power ? Posted 8/19/07, 3:50 pm |
| Work-energy for a 2-D rigid system | Work energy applied to solve for the velocity of a wheel attached to a spring, posted 8/16/09, 12:17 pm |
| Rigid Body rotation | A beam being lifted by two cables, posted 8/16/09, 4:00 pm |
| Conservation of angular momentum of an SUV in a rollover, posted 8/16/09, 4:10 pm | |