Maple Document: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=1337
en-us2018 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 24 Mar 2018 07:50:24 GMTSat, 24 Mar 2018 07:50:24 GMTNew applications in the Maple Document categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgMaple Document: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=1337
Solving ODEs using Maple: An Introduction
https://www.maplesoft.com/applications/view.aspx?SID=154422&ref=Feed
In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.<img src="https://www.maplesoft.com/view.aspx?si=154422/ode.PNG" alt="Solving ODEs using Maple: An Introduction" style="max-width: 25%;" align="left"/>In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.https://www.maplesoft.com/applications/view.aspx?SID=154422&ref=FeedFri, 23 Mar 2018 04:00:00 ZDr. Francis PoulinDr. Francis PoulinNewton’s Method
https://www.maplesoft.com/applications/view.aspx?SID=154421&ref=Feed
Newton's Method is a method of successive iteration that helps us to find the roots of an algebraic function f(x).
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Given an initial guess, x0, we can compute an x1, then an x2 and so on. This worksheet shows different ways to apply Newton’s Method in Maple.<img src="https://www.maplesoft.com/view.aspx?si=154421/newtons_method.PNG" alt="Newton’s Method" style="max-width: 25%;" align="left"/>Newton's Method is a method of successive iteration that helps us to find the roots of an algebraic function f(x).
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Given an initial guess, x0, we can compute an x1, then an x2 and so on. This worksheet shows different ways to apply Newton’s Method in Maple.https://www.maplesoft.com/applications/view.aspx?SID=154421&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonRiemann Sums
https://www.maplesoft.com/applications/view.aspx?SID=154423&ref=Feed
This worksheet demonstrates the use of the Riemann Sums command in the <A HREF="/support/help/maple/view.aspx?path=Student/Calculus1">Student Calculus 1 package</A>.<img src="https://www.maplesoft.com/view.aspx?si=154423/riemann_sums.PNG" alt="Riemann Sums" style="max-width: 25%;" align="left"/>This worksheet demonstrates the use of the Riemann Sums command in the <A HREF="/support/help/maple/view.aspx?path=Student/Calculus1">Student Calculus 1 package</A>.https://www.maplesoft.com/applications/view.aspx?SID=154423&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonBurgers' Vortex
https://www.maplesoft.com/applications/view.aspx?SID=154424&ref=Feed
The Burgers vortex is a well known solution of the Navier Stokes equations that combines vorticity and shear. It allows for the study of a realistic flow in analytical form, thereby offering intuition for more complex flows. However, the cylindrical coordinate system makes certain calculations cumbersome to carry out by hand. This worksheet allows the user to explore aspects of the flow without having to carry out the calculations.<img src="https://www.maplesoft.com/view.aspx?si=154424/burgersvortex.PNG" alt="Burgers' Vortex" style="max-width: 25%;" align="left"/>The Burgers vortex is a well known solution of the Navier Stokes equations that combines vorticity and shear. It allows for the study of a realistic flow in analytical form, thereby offering intuition for more complex flows. However, the cylindrical coordinate system makes certain calculations cumbersome to carry out by hand. This worksheet allows the user to explore aspects of the flow without having to carry out the calculations.https://www.maplesoft.com/applications/view.aspx?SID=154424&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonSlow Manifold Analysis
https://www.maplesoft.com/applications/view.aspx?SID=154425&ref=Feed
This worksheet goes through the slow manifold analysis following Hek's discussion of the predator prey system.<img src="https://www.maplesoft.com/view.aspx?si=154425/slow_manifold_analysis.PNG" alt="Slow Manifold Analysis" style="max-width: 25%;" align="left"/>This worksheet goes through the slow manifold analysis following Hek's discussion of the predator prey system.https://www.maplesoft.com/applications/view.aspx?SID=154425&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonCarbon Monoxide Combustion
https://www.maplesoft.com/applications/view.aspx?SID=154398&ref=Feed
One mole of carbon monoxide and 0.5 moles of oxygen are ignited at 298.15 K and 1 atm. The reaction is
<BR><BR>
CO + 0.5 O<SUB>2</SUB> → CO<SUB>2</SUB>
<BR><BR>
The combustion products undergo dissociation and contain CO<SUB>2</SUB>, CO, O and O<SUB>2</SUB>.
<UL>
<LI>The equilibrium composition is found by minimizing the Gibbs Energy of the combustion products (formulated as a series of equations constructed via the method of Lagrange multipliers)
<LI>The adiabatic flame temperature is found by balancing the enthalpy of the reactants against the enthalpy of the products
</UL>
The resulting equations are solved numerically to give the adiabatic flame temperature and equilibrium composition of the mixture.<img src="https://www.maplesoft.com/view.aspx?si=154398/image.png" alt="Carbon Monoxide Combustion" style="max-width: 25%;" align="left"/>One mole of carbon monoxide and 0.5 moles of oxygen are ignited at 298.15 K and 1 atm. The reaction is
<BR><BR>
CO + 0.5 O<SUB>2</SUB> → CO<SUB>2</SUB>
<BR><BR>
The combustion products undergo dissociation and contain CO<SUB>2</SUB>, CO, O and O<SUB>2</SUB>.
<UL>
<LI>The equilibrium composition is found by minimizing the Gibbs Energy of the combustion products (formulated as a series of equations constructed via the method of Lagrange multipliers)
<LI>The adiabatic flame temperature is found by balancing the enthalpy of the reactants against the enthalpy of the products
</UL>
The resulting equations are solved numerically to give the adiabatic flame temperature and equilibrium composition of the mixture.https://www.maplesoft.com/applications/view.aspx?SID=154398&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanMaximum Deflagration Pressure of the Combustion of Hydrogen in Air at Constant Volume
https://www.maplesoft.com/applications/view.aspx?SID=154404&ref=Feed
Hydrogen is combusted in air at constant volume, with the reactants at an initial temperature of 298.15 K. The chemical reaction is
<BR><BR>
<CENTER>
H<SUB>2</SUB> + 0.5 O<SUB>2</SUB> + 1.88 N<SUB>2</SUB> → H2O + 1.88 N<SUB>2</SUB>
</CENTER>
<BR>
This application will calculate the maximum pressure generated by the combustion process.
<BR><BR>
Thermodynamic properties are calculated using the empirical correlations provided by the ThermophysicalData package. The equations arising from the combustion enthalpy balance are solved numerically with <A HREF="/support/help/maple/view.aspx?path=fsolve">fsolve</A>.<img src="https://www.maplesoft.com/view.aspx?si=154404/image.png" alt="Maximum Deflagration Pressure of the Combustion of Hydrogen in Air at Constant Volume" style="max-width: 25%;" align="left"/>Hydrogen is combusted in air at constant volume, with the reactants at an initial temperature of 298.15 K. The chemical reaction is
<BR><BR>
<CENTER>
H<SUB>2</SUB> + 0.5 O<SUB>2</SUB> + 1.88 N<SUB>2</SUB> → H2O + 1.88 N<SUB>2</SUB>
</CENTER>
<BR>
This application will calculate the maximum pressure generated by the combustion process.
<BR><BR>
Thermodynamic properties are calculated using the empirical correlations provided by the ThermophysicalData package. The equations arising from the combustion enthalpy balance are solved numerically with <A HREF="/support/help/maple/view.aspx?path=fsolve">fsolve</A>.https://www.maplesoft.com/applications/view.aspx?SID=154404&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanPerformance of a Monomethylhydrazine-Dinitrogen Tetroxide Rocket
https://www.maplesoft.com/applications/view.aspx?SID=154410&ref=Feed
Liquid monomethylhydrazine (CH<sub>6</sub>N<sub>2</sub>) and dinitrogen tetroxide (N<sub>2</sub>O<sub>4</sub>) are burned in the combustion chamber of a rocket engine. The oxidizer to fuel ratio is 2.5 (i.e. in the ratio of 1 mole of CH<SUB>6</SUB>N<SUB>2</SUB> to 1.2518 moles of N<SUB>2</SUB>O<SUB>4</SUB>).
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This application will calculate
<UL>
<LI>the adiabatic flame temperature and composition of the combustion products (i.e. in the combustion chamber)
<LI>the pressures and temperatures in the throat and exit
<LI>and the theoretical rocket performance, including the ideal specific impulse, characteristic velocity, and sonic velocity.
</UL><img src="https://www.maplesoft.com/view.aspx?si=154410/image.png" alt="Performance of a Monomethylhydrazine-Dinitrogen Tetroxide Rocket" style="max-width: 25%;" align="left"/>Liquid monomethylhydrazine (CH<sub>6</sub>N<sub>2</sub>) and dinitrogen tetroxide (N<sub>2</sub>O<sub>4</sub>) are burned in the combustion chamber of a rocket engine. The oxidizer to fuel ratio is 2.5 (i.e. in the ratio of 1 mole of CH<SUB>6</SUB>N<SUB>2</SUB> to 1.2518 moles of N<SUB>2</SUB>O<SUB>4</SUB>).
<BR><BR>
This application will calculate
<UL>
<LI>the adiabatic flame temperature and composition of the combustion products (i.e. in the combustion chamber)
<LI>the pressures and temperatures in the throat and exit
<LI>and the theoretical rocket performance, including the ideal specific impulse, characteristic velocity, and sonic velocity.
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154410&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanPropane Combustion
https://www.maplesoft.com/applications/view.aspx?SID=154413&ref=Feed
This application calculates the adiabatic flame temperature of propane (C<SUB>3</SUB>H<SUB>8</SUB>) burned with 250% theoretical air, both initially at 298.15 K.
<BR><BR>
The combustion reaction is
<BR><BR>
<CENTER>
C<SUB>3</SUB>H<SUB>8</SUB> (g) + 12.5 O<SUB>2</SUB> (g) + 47 N<SUB>2</SUB> (g) → 3 CO<SUB>2</SUB> (g) + 4 H<SUB>2</SUB>O (g) + 7.5 O<SUB>2</SUB> (g) + 47 N<SUB>2</SUB> (g)
</CENTER>
<BR>
The enthalpy of propane, oxygen, nitrogen, carbon dioxide, nitrogen and water are calculated with the empirical data in the ThermophysicalData:-Chemicals package.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Propane Combustion" style="max-width: 25%;" align="left"/>This application calculates the adiabatic flame temperature of propane (C<SUB>3</SUB>H<SUB>8</SUB>) burned with 250% theoretical air, both initially at 298.15 K.
<BR><BR>
The combustion reaction is
<BR><BR>
<CENTER>
C<SUB>3</SUB>H<SUB>8</SUB> (g) + 12.5 O<SUB>2</SUB> (g) + 47 N<SUB>2</SUB> (g) → 3 CO<SUB>2</SUB> (g) + 4 H<SUB>2</SUB>O (g) + 7.5 O<SUB>2</SUB> (g) + 47 N<SUB>2</SUB> (g)
</CENTER>
<BR>
The enthalpy of propane, oxygen, nitrogen, carbon dioxide, nitrogen and water are calculated with the empirical data in the ThermophysicalData:-Chemicals package.https://www.maplesoft.com/applications/view.aspx?SID=154413&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanSingle Stub Matching of a Transmission Line
https://www.maplesoft.com/applications/view.aspx?SID=154415&ref=Feed
A single short circuited transmission line is a distance d from the load and of length d.
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Given a characteristic impedance of Z<SUB>0</SUB> and a load with complex impedance Z<SUB>L</SUB>, this application will calculate the values of d and l.
<UL>
<LI>The real part of the impedance at the stub location must match the transmission line characteristic impedance
<LI>The imaginary part of the impedance at the stub location must equal 0
</UL>
This results in two equations that must be solved numerically using <A HREF="/support/help/maple/view.aspx?path=fsolve">Maple’s fsolve function</A>. Units are used throughout the calculation.
<BR><BR>
Reference: Iskander, Magdi F., Electromagnetic Fields and Waves, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1992.<img src="https://www.maplesoft.com/view.aspx?si=154415/image.png" alt="Single Stub Matching of a Transmission Line" style="max-width: 25%;" align="left"/>A single short circuited transmission line is a distance d from the load and of length d.
<BR><BR>
Given a characteristic impedance of Z<SUB>0</SUB> and a load with complex impedance Z<SUB>L</SUB>, this application will calculate the values of d and l.
<UL>
<LI>The real part of the impedance at the stub location must match the transmission line characteristic impedance
<LI>The imaginary part of the impedance at the stub location must equal 0
</UL>
This results in two equations that must be solved numerically using <A HREF="/support/help/maple/view.aspx?path=fsolve">Maple’s fsolve function</A>. Units are used throughout the calculation.
<BR><BR>
Reference: Iskander, Magdi F., Electromagnetic Fields and Waves, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1992.https://www.maplesoft.com/applications/view.aspx?SID=154415&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanSmoothly Shaded Temperature Map
https://www.maplesoft.com/applications/view.aspx?SID=154416&ref=Feed
This application generates a smoothly shaded temperature map using data from weather stations scattered across the US. The data contains the longitude and latitude of the weather station, and the recorded temperature.
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Maple 2018's Interpolation package is used to generate a regular grid of locations and temperatures from the irregular weather station data, employing a kriging method.<img src="https://www.maplesoft.com/view.aspx?si=154416/image.png" alt="Smoothly Shaded Temperature Map" style="max-width: 25%;" align="left"/>This application generates a smoothly shaded temperature map using data from weather stations scattered across the US. The data contains the longitude and latitude of the weather station, and the recorded temperature.
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Maple 2018's Interpolation package is used to generate a regular grid of locations and temperatures from the irregular weather station data, employing a kriging method.https://www.maplesoft.com/applications/view.aspx?SID=154416&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanTemperature in a Combustion Chamber Burning Methane
https://www.maplesoft.com/applications/view.aspx?SID=154417&ref=Feed
A gas turbine burns methane in 200% stoichiometric air.
<BR><BR>
<CENTER>
CH<SUB>4</SUB> + 4 O<SUB>2</SUB> + 15.04 N<SUB>2</SUB> ⇌ CO<SUB>2</SUB> + 2 H<SUB>2</SUB>O + 7.52 N<SUB>2</SUB> + 15.04 N<SUB>2</SUB> + 4 O<SUB>2</SUB>
</CENTER>
<BR>
The air and the fuel enter the combustion chamber at 600 K. This application will determine the adiabatic flame temperature in the chamber.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Temperature in a Combustion Chamber Burning Methane" style="max-width: 25%;" align="left"/>A gas turbine burns methane in 200% stoichiometric air.
<BR><BR>
<CENTER>
CH<SUB>4</SUB> + 4 O<SUB>2</SUB> + 15.04 N<SUB>2</SUB> ⇌ CO<SUB>2</SUB> + 2 H<SUB>2</SUB>O + 7.52 N<SUB>2</SUB> + 15.04 N<SUB>2</SUB> + 4 O<SUB>2</SUB>
</CENTER>
<BR>
The air and the fuel enter the combustion chamber at 600 K. This application will determine the adiabatic flame temperature in the chamber.https://www.maplesoft.com/applications/view.aspx?SID=154417&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanAdiabatic Flame Temperature of Butane
https://www.maplesoft.com/applications/view.aspx?SID=154396&ref=Feed
Liquid butane at standard temperature and pressure is burned with 100% theoretical air. The combustion reaction is
<BR><BR>
<CENTER>
C<SUB>4</SUB>H<SUB>10</SUB> (l) + 6.5 O<SUB>2</SUB> (g) + 24.44 N<SUB>2</SUB> (g) → 4 CO<SUB>2</SUB> (g) + 5 H<SUB>2</SUB>O (g) + 24.44 N<SUB>2</SUB> (g)
</CENTER>
<BR><BR>
This application calculates the adiabatic flame temperature of the combustion products.
<BR><BR>
The enthalpy of the reactants (which is known) is equated to the enthalpy of the products (which is a function of the unknown flame temperature). The resulting equation is solved numerically using <A HREF="/support/help/maple/view.aspx?path=fsolve">fsolve</A>.
<BR><BR>
Units are used throughout the calculation, and the ThermophysicalData:-Chemicals package is used to compute temperature-dependent values of enthalpy.
<BR><BR><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Adiabatic Flame Temperature of Butane" style="max-width: 25%;" align="left"/>Liquid butane at standard temperature and pressure is burned with 100% theoretical air. The combustion reaction is
<BR><BR>
<CENTER>
C<SUB>4</SUB>H<SUB>10</SUB> (l) + 6.5 O<SUB>2</SUB> (g) + 24.44 N<SUB>2</SUB> (g) → 4 CO<SUB>2</SUB> (g) + 5 H<SUB>2</SUB>O (g) + 24.44 N<SUB>2</SUB> (g)
</CENTER>
<BR><BR>
This application calculates the adiabatic flame temperature of the combustion products.
<BR><BR>
The enthalpy of the reactants (which is known) is equated to the enthalpy of the products (which is a function of the unknown flame temperature). The resulting equation is solved numerically using <A HREF="/support/help/maple/view.aspx?path=fsolve">fsolve</A>.
<BR><BR>
Units are used throughout the calculation, and the ThermophysicalData:-Chemicals package is used to compute temperature-dependent values of enthalpy.
<BR><BR>https://www.maplesoft.com/applications/view.aspx?SID=154396&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanCoaxial Cable Transmission Line Design
https://www.maplesoft.com/applications/view.aspx?SID=154401&ref=Feed
An electrical engineer is asked to design a coaxial transmission line with a characteristic impedance of 50 Ω and a phase velocity of at least 1.8 x 108 m s-1
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This application will calculate the outer radius of the line.<img src="https://www.maplesoft.com/view.aspx?si=154401/image.png" alt="Coaxial Cable Transmission Line Design" style="max-width: 25%;" align="left"/>An electrical engineer is asked to design a coaxial transmission line with a characteristic impedance of 50 Ω and a phase velocity of at least 1.8 x 108 m s-1
<BR><BR>
This application will calculate the outer radius of the line.https://www.maplesoft.com/applications/view.aspx?SID=154401&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanEnthalpy Change of Combustion of Methane
https://www.maplesoft.com/applications/view.aspx?SID=154405&ref=Feed
This application calculates the enthalpy change of combustion of methane at standard conditions, given the reaction
<BR>
<BR>
<CENTER>
CH<SUB>4</SUB> (g) + 2 O<SUB>2</SUB> (g) → CO<SUB>2</SUB> (g) + 2 H<SUB>2</SUB>O (g)
</CENTER>
<BR>
The enthalpy of methane, oxygen, carbon dioxide and water are computed using the empirical correlations in the ThermophysicalData:-Chemicals package.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Enthalpy Change of Combustion of Methane" style="max-width: 25%;" align="left"/>This application calculates the enthalpy change of combustion of methane at standard conditions, given the reaction
<BR>
<BR>
<CENTER>
CH<SUB>4</SUB> (g) + 2 O<SUB>2</SUB> (g) → CO<SUB>2</SUB> (g) + 2 H<SUB>2</SUB>O (g)
</CENTER>
<BR>
The enthalpy of methane, oxygen, carbon dioxide and water are computed using the empirical correlations in the ThermophysicalData:-Chemicals package.https://www.maplesoft.com/applications/view.aspx?SID=154405&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanAdiabatic Flame Temperature and Composition of the Combustion Products of Hydrogen and Oxygen
https://www.maplesoft.com/applications/view.aspx?SID=154409&ref=Feed
Consider the combustion of hydrogen and oxygen.
<BR>
<BR>
<CENTER>
H<SUB>2</SUB> (g) + 0.5 O<SUB>2</SUB> (g) ⇋ H<SUB>2</SUB>O (g)
</CENTER>
<BR>
The application calculates the adiabatic flame temperature and equilibrium composition of the combustion products.
<UL>
<LI>The equilibrium composition is calculated by minimizing the Gibbs free energy of the system
<LI>The flame temperature is found by equating the enthalpy of the feed and combustion products.
</UL>
Both relationships are solved simultaneously using <A HREF="/support/help/maple/view.aspx?path=fsolve">fsolve</A>.
<BR><BR>
Temperature-dependent thermodynamic data are calculated with the ThermophysicalData:-Chemicals package.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Adiabatic Flame Temperature and Composition of the Combustion Products of Hydrogen and Oxygen" style="max-width: 25%;" align="left"/>Consider the combustion of hydrogen and oxygen.
<BR>
<BR>
<CENTER>
H<SUB>2</SUB> (g) + 0.5 O<SUB>2</SUB> (g) ⇋ H<SUB>2</SUB>O (g)
</CENTER>
<BR>
The application calculates the adiabatic flame temperature and equilibrium composition of the combustion products.
<UL>
<LI>The equilibrium composition is calculated by minimizing the Gibbs free energy of the system
<LI>The flame temperature is found by equating the enthalpy of the feed and combustion products.
</UL>
Both relationships are solved simultaneously using <A HREF="/support/help/maple/view.aspx?path=fsolve">fsolve</A>.
<BR><BR>
Temperature-dependent thermodynamic data are calculated with the ThermophysicalData:-Chemicals package.https://www.maplesoft.com/applications/view.aspx?SID=154409&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanSpontaneity of the Reaction of Nitrogen and Oxygen to form Nitrogen Monoxide
https://www.maplesoft.com/applications/view.aspx?SID=154411&ref=Feed
Nitrogen reacts with oxygen as follows.
<BR>
<BR>
<CENTER>
N<SUB>2</SUB> (g) + O<SUB>2</SUB> (g) → 2 NO (g)
</CENTER>
<BR>
This application will calculate the temperature at which this reaction becomes spontaneous.
<BR><BR>
Using the empirical data in the ThermophysicalData:-Chemicals package, the application first defines a function that describes the Gibbs Energy of the reaction at an arbitrary temperature.
<BR><BR>
This function is then numerically solved for the temperature at which the Gibbs Energy is zero. The reaction is spontaneous at or above this temperature.<img src="https://www.maplesoft.com/view.aspx?si=154411/image.png" alt="Spontaneity of the Reaction of Nitrogen and Oxygen to form Nitrogen Monoxide" style="max-width: 25%;" align="left"/>Nitrogen reacts with oxygen as follows.
<BR>
<BR>
<CENTER>
N<SUB>2</SUB> (g) + O<SUB>2</SUB> (g) → 2 NO (g)
</CENTER>
<BR>
This application will calculate the temperature at which this reaction becomes spontaneous.
<BR><BR>
Using the empirical data in the ThermophysicalData:-Chemicals package, the application first defines a function that describes the Gibbs Energy of the reaction at an arbitrary temperature.
<BR><BR>
This function is then numerically solved for the temperature at which the Gibbs Energy is zero. The reaction is spontaneous at or above this temperature.https://www.maplesoft.com/applications/view.aspx?SID=154411&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanAdiabatic Flame Temperature of Octane as a Function of Fraction of Air
https://www.maplesoft.com/applications/view.aspx?SID=154414&ref=Feed
This application will calculate and plot the flame temperature of octane for a varying amount of air. Temperature-dependent thermodynamic properties are calculated with the ThermophysicalData:-Chemicals package.
<BR><BR>
For lean combustion (i.e. 100% or more stoichiometric air), the combustion reaction is
<BR><BR>
<CENTER>
C<SUB>8</SUB>H<SUB>18</SUB> + 12.5 Y/100 (O<SUB>2</SUB> + 3.76 N<SUB>2</SUB>) → 8 CO<SUB>2</SUB> + 9 H<SUB>2</SUB>O + (Y/100-1) O<SUB>2</SUB> + 47 Y / 100 N<SUB>2</SUB>
</CENTER>
<BR>
For rich combustion (i.e. less than 100% stoichiometric air), the combustion reaction is (assuming that the combustion products contain CO<SUB>2</SUB>, H<SUB>2</SUB>O, CO and N<SUB>2</SUB>)
<BR><BR>
<CENTER>
C<SUB>8</SUB>H<SUB>18</SUB> + 12.5 Y/100 (O<SUB>2</SUB> + 3.76 N<SUB>2</SUB>) → (25Y - 1700)/100 CO<SUB>2</SUB> + 9 H<SUB>2</SUB>O + (2500 - 25Y)/100 CO + 47 Y /100 N<SUB>2</SUB>
</CENTER><img src="https://www.maplesoft.com/view.aspx?si=154414/image.png" alt="Adiabatic Flame Temperature of Octane as a Function of Fraction of Air" style="max-width: 25%;" align="left"/>This application will calculate and plot the flame temperature of octane for a varying amount of air. Temperature-dependent thermodynamic properties are calculated with the ThermophysicalData:-Chemicals package.
<BR><BR>
For lean combustion (i.e. 100% or more stoichiometric air), the combustion reaction is
<BR><BR>
<CENTER>
C<SUB>8</SUB>H<SUB>18</SUB> + 12.5 Y/100 (O<SUB>2</SUB> + 3.76 N<SUB>2</SUB>) → 8 CO<SUB>2</SUB> + 9 H<SUB>2</SUB>O + (Y/100-1) O<SUB>2</SUB> + 47 Y / 100 N<SUB>2</SUB>
</CENTER>
<BR>
For rich combustion (i.e. less than 100% stoichiometric air), the combustion reaction is (assuming that the combustion products contain CO<SUB>2</SUB>, H<SUB>2</SUB>O, CO and N<SUB>2</SUB>)
<BR><BR>
<CENTER>
C<SUB>8</SUB>H<SUB>18</SUB> + 12.5 Y/100 (O<SUB>2</SUB> + 3.76 N<SUB>2</SUB>) → (25Y - 1700)/100 CO<SUB>2</SUB> + 9 H<SUB>2</SUB>O + (2500 - 25Y)/100 CO + 47 Y /100 N<SUB>2</SUB>
</CENTER>https://www.maplesoft.com/applications/view.aspx?SID=154414&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanTheoretical Performance of a LOX-LH2 Rocket
https://www.maplesoft.com/applications/view.aspx?SID=154419&ref=Feed
Liquid hydrogen (at 20.27 K) and liquid oxygen (at 90.17 K) are burned in the combustion chamber (with an infinite area ratio) of a rocket.
<BR><BR>
The combustion products contain H<SUB>2</SUB>, O<SUB>2</SUB>, H, O, OH, HO<SUB>2</SUB> and H<SUB>2</SUB>O<SUB>2</SUB>
<BR><BR>
This application will calculate
<UL>
<LI>the adiabatic flame temperature and composition of combustion products
<LI>the pressures and temperatures in the throat and exit
<LI>and the theoretical rocket performance, including the ideal specific impulse, characteristic velocity, sonic velocity and more
</UL>
Assumptions:
<UL>
<LI>The combustion chamber is large compared to the throat, hence the assumption of an infinite area ratio
<LI>The flow composition does not change through the nozzle expansion (i.e. reaction rate is slow compared to flowrate). This is also known as "frozen" flow
</UL><img src="https://www.maplesoft.com/view.aspx?si=154419/image.png" alt="Theoretical Performance of a LOX-LH2 Rocket" style="max-width: 25%;" align="left"/>Liquid hydrogen (at 20.27 K) and liquid oxygen (at 90.17 K) are burned in the combustion chamber (with an infinite area ratio) of a rocket.
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The combustion products contain H<SUB>2</SUB>, O<SUB>2</SUB>, H, O, OH, HO<SUB>2</SUB> and H<SUB>2</SUB>O<SUB>2</SUB>
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This application will calculate
<UL>
<LI>the adiabatic flame temperature and composition of combustion products
<LI>the pressures and temperatures in the throat and exit
<LI>and the theoretical rocket performance, including the ideal specific impulse, characteristic velocity, sonic velocity and more
</UL>
Assumptions:
<UL>
<LI>The combustion chamber is large compared to the throat, hence the assumption of an infinite area ratio
<LI>The flow composition does not change through the nozzle expansion (i.e. reaction rate is slow compared to flowrate). This is also known as "frozen" flow
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154419&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanVoronoi Diagram of Airports in the US
https://www.maplesoft.com/applications/view.aspx?SID=154420&ref=Feed
This application generates a Voronoi diagram of the airports in the US. Each polygon contains a single airport, and bounds the area closest to that airport.
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An Excel spreadsheet attached to this workbook contains the longitude and latitude of over 2000 US airports. Using this data, the Voronoi diagram is generated with the ComputationalGeometry package.<img src="https://www.maplesoft.com/view.aspx?si=154420/image.png" alt="Voronoi Diagram of Airports in the US" style="max-width: 25%;" align="left"/>This application generates a Voronoi diagram of the airports in the US. Each polygon contains a single airport, and bounds the area closest to that airport.
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An Excel spreadsheet attached to this workbook contains the longitude and latitude of over 2000 US airports. Using this data, the Voronoi diagram is generated with the ComputationalGeometry package.https://www.maplesoft.com/applications/view.aspx?SID=154420&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir Khan