Dr. Griffin's Distribution Page

7/1/07 - Its been a while since I spent any time sprucing up this site. I am in the process of going through the
files and fixing the ones that don't work or have mistakes as a result of changes in Mathcad versions.
Let me know what needs to be fixed.

7/25/07 - I've been adding problems to the dynamics section

You can access various problem topics by clicking on the following targets :

FILES DEVELOPED BY CURRENT AND 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

**CHEMISTRY**
**(some are annotated better than others)**
File	Description of File
Strong acid strong base titration version 1 - solve block	Numerical solution of a strong acid strong base titration with associated plots
Strong Acid-Strong base titration version 2	This file details the 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 .
chemistry problem	Total dissolved carbon in a solution in contact with solid calcite
PDF version of file above	PDF file of file above
Chemistry Problem	pH of rain water from an acid atmosphere
Chemistry Problem	partial pressure of CO₂ in solution
Chemistry	A discussion of alkalinity in natural waters
Sodium bicarbonate addition for pH control and buffering	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.
Master Variable Diagram for H2S Species	Species concentrations as function of pH
Ammonia Speciation	Problem deals with computing the ammonia/ammonium distribution in water
H2S concentration in a section of Sewer	Calculations to determine the speciation of H₂ S in section of sewer. Comments on the practical use of such calculations
Solvent Spill	Calculations relating to evaparation of solvents after a spill
Fog	calculations dealing with pollutants in fog vapor
Alkalinity Equations	Numerical and analytical calculations for computing alkalinity
Development of alkalinity equations	Development of concepts and equations used to quantify alkalinity in natural waters
pH of weak acid solution - 2 weak acids	Numerical solution of the salts of 2 weak acids in water
Chemistry	Alkalinity of a sodium bicarbonate-sodium carbonate solution - solve block used
Examination of alkalinity variation in solution	Carbon at varying pH-alkalinity levels
System with constant carbon concentration	Find the partial pressure of an acidified system where the aqueous C concentration remains constant
NaOH added to CO₂ /water system	NaOH is added to a CO₂ /water system to produce NaHCO₃
Sodium hypochlorite added to water	The effect on pH of the addition of the salt of a weak acid to water
Magnesium precipitation	Effect of buffer on requirements for precipitation. Based on problem from Snoeyink and Jenkins text
How much Freon in the bottle ?	A neat applied problem using a little chemistry and a little thermodynamics. From the Environmental Organic Chemistry text by Schwarzenbach et al.
Spill of TCE and PER	Another neat problem from Environmental Organic Chemistry by Schwartzenbach, et.al , posted 5/1/03, 4:40 p.m.
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
A chemistry problem for engineers	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.
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
CO₂ transfer across lake surface	A problem from Stumm and Morgan's Text, posted 4/14/03, 12 noon
Computing the precipitation potential	Shows how to determine if CaCO₃ precipitation will occur and how much , posted 4/29/03, 3:30 pm
Scotch and Soda - the Hard Way	A neat Gibbs Free energy problem showing the location of the equilibrium point graphically. Posted 5/12/03 , 8:35 am
Monochloramine Kinetics	A kinetics problem dealing with chlorine residuals. Posted 5/14/03, 10:24 am
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

CHEMISTRY
(some are annotated better than others)

File

Description of File

Strong acid strong base titration
version 1 - solve block

Numerical solution of a strong acid strong base titration with associated plots

Strong Acid-Strong base titration version 2

This file details the 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 .

chemistry problem

Total dissolved carbon in a solution in contact with solid calcite

PDF version of file above

PDF file of file above

Chemistry Problem

pH of rain water from an acid atmosphere

Chemistry Problem

partial pressure of CO₂ in solution

Chemistry

A discussion of alkalinity in natural waters

Sodium bicarbonate addition for pH control and buffering

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.

Master Variable Diagram for H2S Species

Species concentrations as function of pH

Ammonia Speciation

Problem deals with computing the ammonia/ammonium distribution in water

H2S concentration in a section of Sewer

Calculations to determine the speciation of H₂ S in section of sewer. Comments on the practical use of such calculations

Solvent Spill

Calculations relating to evaparation of solvents after a spill

Fog

calculations dealing with pollutants in fog vapor

Alkalinity Equations

Numerical and analytical calculations for computing alkalinity

Development of alkalinity equations

Development of concepts and equations used to quantify alkalinity in natural waters

pH of weak acid solution - 2 weak acids

Numerical solution of the salts of 2 weak acids in water

Chemistry

Alkalinity of a sodium bicarbonate-sodium carbonate solution - solve block used

Examination of alkalinity variation in solution

Carbon at varying pH-alkalinity levels

System with constant carbon concentration

Find the partial pressure of an acidified system where the aqueous C concentration remains constant

NaOH added to CO₂ /water system

NaOH is added to a CO₂ /water system to produce NaHCO₃

Sodium hypochlorite added to water

The effect on pH of the addition of the salt of a weak acid to water

Magnesium precipitation

Effect of buffer on requirements for precipitation. Based on problem from Snoeyink and Jenkins text

How much Freon in the bottle ?

A neat applied problem using a little chemistry and a little thermodynamics. From the Environmental Organic Chemistry text by Schwarzenbach et al.

Spill of TCE and PER

Another neat problem from Environmental Organic Chemistry by Schwartzenbach, et.al , posted 5/1/03, 4:40 p.m.

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

A chemistry problem for engineers

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.

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

CO₂ transfer across lake surface

A problem from Stumm and Morgan's Text, posted 4/14/03, 12 noon

Computing the precipitation potential

Shows how to determine if CaCO₃ precipitation will occur and how much , posted 4/29/03, 3:30 pm

Scotch and Soda - the Hard Way

A neat Gibbs Free energy problem showing the location of the equilibrium point graphically. Posted 5/12/03 , 8:35 am

Monochloramine Kinetics

A kinetics problem dealing with chlorine residuals.
Posted 5/14/03, 10:24 am

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

**AIR POLLUTION**
Air Pollution Problem	Air flow at non-standard temperature and pressure. Notice that this problem is basically a fluids and gas law application
Air Pollution Emissions	Particulate emission calculations
Air Pollution - Puff Model	A simple steady-state air pollution model - uses a Mathcad surface plot for illustration
Air Pollution	Flue gas flow calculations
Coal combustion analysis	Stoichiometric analysis of coal combustion
Unit conversion for concentration unit in air pollution	converting ppm to micrograms per cubic meter- a discussion and some examples posted 11 am, 6/20/00
PDF version of previous file	PDF version of unit conversion file with discussion and explanation, posted 11 am, 6/20/00

AIR POLLUTION

Air Pollution Problem

Air flow at non-standard temperature and pressure. Notice that this problem is basically a fluids and gas law application

Air Pollution Emissions

Particulate emission calculations

Air Pollution - Puff Model

A simple steady-state air pollution model - uses a Mathcad surface plot for illustration

Air Pollution

Flue gas flow calculations

Coal combustion analysis

Stoichiometric analysis of coal combustion

Unit conversion for concentration unit in air pollution

converting ppm to micrograms per cubic meter- a discussion and some examples posted 11 am, 6/20/00

PDF version of previous file

PDF version of unit conversion file with discussion and explanation, posted 11 am, 6/20/00

**PROBABILITY AND STATISTICS**
probability problem	A probability problem which computes the odds of winning a lottery
An interesting probability problem	A cool probability problem from the best seller "Innumeracy" by John A. Paulos
Statistics-Chemistry Problem	A statistics problems using pH data. Uses many of Mathcad's statistical functions
Linear Regression	A simple but insightful problem using linear regression
Linear and non linear parameter estimation	parameter estimation in an environmental problem
Statistics using pH and DO lab data	Shows what can be done with even simple data sets - A PDF file
Kruskal_Wallis.pdf	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
Mann_Whitney.pdf	Based on file from Mathcad ebook. Nonparametric version of the t test. A PDF file. Posted 6/21/00 7:40 am
Monte Carlo Methods using a normal distribution	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
The Central limit Theorem and the Lognormal Distribution	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.
Haan - binomial_distribution_ example.mcd	A hydrologic example of the use of the binomial distribution, posted 3/5/01, 5:10 pm
BIVARIATE_NORMAL_DISTRIBUTION.mcd	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

PROBABILITY AND STATISTICS

probability problem

A probability problem which computes the odds of winning a lottery

An interesting probability problem

A cool probability problem from the best seller "Innumeracy" by John A. Paulos

Statistics-Chemistry Problem

A statistics problems using pH data. Uses many of Mathcad's statistical functions

Linear Regression

A simple but insightful problem using linear regression

Linear and non linear parameter estimation

parameter estimation in an environmental problem

Statistics using pH and DO lab data

Shows what can be done with even simple data sets - A PDF file

Kruskal_Wallis.pdf

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

Mann_Whitney.pdf

Based on file from Mathcad ebook. Nonparametric version of the t test. A PDF file. Posted 6/21/00 7:40 am

Monte Carlo Methods using a normal distribution

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

The Central limit Theorem and the Lognormal Distribution

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.

Haan - binomial_distribution_ example.mcd

A hydrologic example of the use of the binomial distribution, posted 3/5/01, 5:10 pm

BIVARIATE_NORMAL_DISTRIBUTION.mcd

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

**CIVIL ENGINEERING**
Specific Energy plot and calculations for pipe	From V. T. Chow's book, a simple specific energy problem with some bells and whistles added
BOD problem	Problem uses real data collected from a malt plant in Moorhead Minn.
Uniform open channel flow	A simple problem computing normal depth in a channel
Clear water transfer capacity of aerator ANSI/ASCE 2-91	Shows both linear and nonlinear regression procedures
PDF version of the file above	Here it is - let me know if you want assistance interpreting it. The second part of the document is the ASCE standard procedure.
Normal depth in a triangular channel	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
Hydrogeology - groundwater plume	2 dimensional solution - long time frame. Uses a surface plot to present results
Model of an Ant colony	Mathematical Model of an ant colony using data from *an American Scientist* article**
Fluids Problem Illustrating a Cross Connection	Must reading for municipal engineers
PDF file for the problem above	Same file as above but in PDF format
A PDF file for the Ant colony problem	PDF File
Prob_3-24_sluice_gate-stilling_basin.mcd	A neat little problem from Henderson's classic open channels text. Enlightening computations regarding the conditions for hydraulic jump formation.
An optimization problem - Sewer pipe	Based on a problem from the text by Ozzenbrugen
PDF version of sewer optimization problem above	PDF FILE
Acrobat version of reservoir computations file	PDF File
hydrology/land use problem

CIVIL ENGINEERING

Specific Energy plot and calculations for pipe

From V. T. Chow's book, a simple specific energy problem with some bells and whistles added

BOD problem

Problem uses real data collected from a malt plant in Moorhead Minn.

Uniform open channel flow

A simple problem computing normal depth in a channel

Clear water transfer capacity of aerator ANSI/ASCE 2-91

Shows both linear and nonlinear regression procedures

PDF version of the file above

Here it is - let me know if you want assistance
interpreting it. The second part of the document is the ASCE standard procedure.

Normal depth in a triangular channel

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

Hydrogeology - groundwater plume

2 dimensional solution - long time frame. Uses a surface plot to present results

Model of an Ant colony

Mathematical Model of an ant colony using data from
an American Scientist article

Fluids Problem Illustrating a Cross Connection

Must reading for municipal engineers

PDF file for the problem above

Same file as above but in PDF format

A PDF file for the Ant colony problem

PDF File

Prob_3-24_sluice_gate-stilling_basin.mcd

A neat little problem from Henderson's classic open channels text. Enlightening computations regarding the conditions for hydraulic jump formation.

An optimization problem - Sewer pipe

Based on a problem from the text by Ozzenbrugen

PDF version of sewer optimization problem above

PDF FILE

Acrobat version of reservoir computations file

PDF File

hydrology/land use problem

2001		4450
2002		16449
2003		13260
2004		16117
2005		21273
2006		24908

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