Samir Khan: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=613
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 05 Mar 2021 19:26:26 GMTFri, 05 Mar 2021 19:26:26 GMTNew applications published by Samir Khanhttps://www.maplesoft.com/images/Application_center_hp.jpgSamir Khan: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=613
Transmission Line Simulation via Numerical Inversion of Laplace Transforms
https://www.maplesoft.com/applications/view.aspx?SID=154674&ref=Feed
This application numerically inverts the Laplace transforms that describe the voltage and current in a transmission line.
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The Laplace transforms are based on the Telegrapherâ€™s Equations, a pair of coupled partial differential equations.
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The results describe the transient variation of current and voltage at any point on the transmission line.<img src="https://www.maplesoft.com/view.aspx?si=154674/Transmission_Line.png" alt="Transmission Line Simulation via Numerical Inversion of Laplace Transforms" style="max-width: 25%;" align="left"/>This application numerically inverts the Laplace transforms that describe the voltage and current in a transmission line.
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The Laplace transforms are based on the Telegrapherâ€™s Equations, a pair of coupled partial differential equations.
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The results describe the transient variation of current and voltage at any point on the transmission line.https://www.maplesoft.com/applications/view.aspx?SID=154674&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanLoad Flow Analysis of a Five-Bus Power System
https://www.maplesoft.com/applications/view.aspx?SID=154675&ref=Feed
This application analyzes a five-bus power system, and calculates the voltages and real and reactive powers at each bus.
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Two approaches to numerically solving the nonlinear load flow equations are demonstrated
<UL>
<LI>The symbolic real and reactive load flow equations are generated, and solved with fsolve (a powerful numerical equation solver).
<LI>The system Jacobian is constructed, and solved with Newton-Raphson iteration.
</UL><img src="https://www.maplesoft.com/view.aspx?si=154675/Five_Bus_Power_System.png" alt="Load Flow Analysis of a Five-Bus Power System" style="max-width: 25%;" align="left"/>This application analyzes a five-bus power system, and calculates the voltages and real and reactive powers at each bus.
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Two approaches to numerically solving the nonlinear load flow equations are demonstrated
<UL>
<LI>The symbolic real and reactive load flow equations are generated, and solved with fsolve (a powerful numerical equation solver).
<LI>The system Jacobian is constructed, and solved with Newton-Raphson iteration.
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154675&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanCable Ampacity using the Nehers-McGrath Method
https://www.maplesoft.com/applications/view.aspx?SID=154677&ref=Feed
Heat is generated when current flows through a cable. The ampacity of a cable is the amount of current a cable can carry without exceeding its temperature rating. Accurately estimating ampacity is critical to minimizing the total lifetime cost of a cable installation.
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This application implements the Nehers-McGrath equations and cross-checks the results against those tabulated in the National Electrical Code (2017); the good agreement means that this worksheet can be the basis of more complex cable ampacity calculations.<img src="https://www.maplesoft.com/view.aspx?si=154677/Cable_Amapacity.png" alt="Cable Ampacity using the Nehers-McGrath Method" style="max-width: 25%;" align="left"/>Heat is generated when current flows through a cable. The ampacity of a cable is the amount of current a cable can carry without exceeding its temperature rating. Accurately estimating ampacity is critical to minimizing the total lifetime cost of a cable installation.
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This application implements the Nehers-McGrath equations and cross-checks the results against those tabulated in the National Electrical Code (2017); the good agreement means that this worksheet can be the basis of more complex cable ampacity calculations.https://www.maplesoft.com/applications/view.aspx?SID=154677&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanPer Unit Analysis of a Three-Phase Power Distribution System
https://www.maplesoft.com/applications/view.aspx?SID=154679&ref=Feed
This application analyzes the power flows in a three-phase system on a per unit basis.
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Power system parameters (such as voltage, current and impedance) are often normalized to a base power and voltage before an analysis. This simplifies the analysis of the power flow in the system; for example, for a transformer, you can ignore turns ratios of transformers.<img src="https://www.maplesoft.com/view.aspx?si=154679/Per_Unit_Analysis_of_a_Power_Distribution_System.png" alt="Per Unit Analysis of a Three-Phase Power Distribution System" style="max-width: 25%;" align="left"/>This application analyzes the power flows in a three-phase system on a per unit basis.
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Power system parameters (such as voltage, current and impedance) are often normalized to a base power and voltage before an analysis. This simplifies the analysis of the power flow in the system; for example, for a transformer, you can ignore turns ratios of transformers.https://www.maplesoft.com/applications/view.aspx?SID=154679&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanUnbalanced Three-Phase Wye-Connected Load
https://www.maplesoft.com/applications/view.aspx?SID=154681&ref=Feed
An unbalanced 3-phase Wye-connected load is connected to a balanced 3-phase four-wire source. The load impedances and line voltage are known.
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This application calculates the currents in the system, and the total power drawn by the load.<img src="https://www.maplesoft.com/view.aspx?si=154681/Three Phase Wye Connected Load2.png" alt="Unbalanced Three-Phase Wye-Connected Load" style="max-width: 25%;" align="left"/>An unbalanced 3-phase Wye-connected load is connected to a balanced 3-phase four-wire source. The load impedances and line voltage are known.
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This application calculates the currents in the system, and the total power drawn by the load.https://www.maplesoft.com/applications/view.aspx?SID=154681&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanCross-Section of Metallic Steel Tape for Earthing of 110/30 kV Substation: Interactive Application
https://www.maplesoft.com/applications/view.aspx?SID=154682&ref=Feed
This interactive tool helps electrical power systems engineer calculate the cross-sectional area of metallic tape needed to adequately earth a substation.
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The equations and parameters are correct to EN 50522:2010 (Earthing of Power Installations Exceeding 1 kV A.C.)<img src="https://www.maplesoft.com/view.aspx?si=154682/Substation_Earthing_Interactive_Application.png" alt="Cross-Section of Metallic Steel Tape for Earthing of 110/30 kV Substation: Interactive Application" style="max-width: 25%;" align="left"/>This interactive tool helps electrical power systems engineer calculate the cross-sectional area of metallic tape needed to adequately earth a substation.
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The equations and parameters are correct to EN 50522:2010 (Earthing of Power Installations Exceeding 1 kV A.C.)https://www.maplesoft.com/applications/view.aspx?SID=154682&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanCross-Section of Metallic Tape for Substation Earthing
https://www.maplesoft.com/applications/view.aspx?SID=154683&ref=Feed
This application calculates the cross-section of steel tape to earth a conductor for a 110/30 kV substation, correct to IEC 60287-3-1.<img src="https://www.maplesoft.com/view.aspx?si=154683/cross_section.png" alt="Cross-Section of Metallic Tape for Substation Earthing" style="max-width: 25%;" align="left"/>This application calculates the cross-section of steel tape to earth a conductor for a 110/30 kV substation, correct to IEC 60287-3-1.https://www.maplesoft.com/applications/view.aspx?SID=154683&ref=FeedWed, 17 Feb 2021 05:00:00 ZSamir KhanSamir KhanZero Padding a Signal to More Accurately Estimate Amplitudes from a DFT
https://www.maplesoft.com/applications/view.aspx?SID=154653&ref=Feed
You can use a discrete Fourier transform (DFT) to identify the amplitude of a sinusoidal signal. Given a signal with N samples and a sample rate of Fs, the frequency spacing of its DFT is Fs/N. An amplitude at a frequency that falls in a DFT bin can be accurately estimated.
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But what if a signal frequency falls between DFT bins? Its energy will be shared between the adjacent bins, and its amplitude will not be accurately identified.
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One possible solution to better amplitude estimation is zero padding the time domain signal. If you zero-pad the signal, the value of N increases, and the frequency spacing of the DFT decreases. For example, if you double the time-domain signal with zero-padding, the frequency spacing decreases by a factor of two.
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This is not a magical way of increasing the sampling rate, or injecting more data. Zero-padding in the time domain is simply equivalent to sinc interpolation of the DFT.
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In this application, we will
<UL>
<LI>generate a sinusoidal signal with three frequencies at three amplitudes (one frequency will fall in a DFT bin, but two won't)
<LI>use a DFT to estimate the signal amplitudes
<LI>zero-pad the original signal
<LI>use a DFT of the zero-padded signal to again estimate the amplitudes
</UL>
You will see that zero-padding the signal results in better amplitude estimation.<img src="https://www.maplesoft.com/view.aspx?si=154653/thumb.png" alt="Zero Padding a Signal to More Accurately Estimate Amplitudes from a DFT" style="max-width: 25%;" align="left"/>You can use a discrete Fourier transform (DFT) to identify the amplitude of a sinusoidal signal. Given a signal with N samples and a sample rate of Fs, the frequency spacing of its DFT is Fs/N. An amplitude at a frequency that falls in a DFT bin can be accurately estimated.
<BR><BR>
But what if a signal frequency falls between DFT bins? Its energy will be shared between the adjacent bins, and its amplitude will not be accurately identified.
<BR><BR>
One possible solution to better amplitude estimation is zero padding the time domain signal. If you zero-pad the signal, the value of N increases, and the frequency spacing of the DFT decreases. For example, if you double the time-domain signal with zero-padding, the frequency spacing decreases by a factor of two.
<BR><BR>
This is not a magical way of increasing the sampling rate, or injecting more data. Zero-padding in the time domain is simply equivalent to sinc interpolation of the DFT.
<BR><BR>
In this application, we will
<UL>
<LI>generate a sinusoidal signal with three frequencies at three amplitudes (one frequency will fall in a DFT bin, but two won't)
<LI>use a DFT to estimate the signal amplitudes
<LI>zero-pad the original signal
<LI>use a DFT of the zero-padded signal to again estimate the amplitudes
</UL>
You will see that zero-padding the signal results in better amplitude estimation.https://www.maplesoft.com/applications/view.aspx?SID=154653&ref=FeedMon, 17 Aug 2020 04:00:00 ZSamir KhanSamir KhanThe Speed of Sound on Mars
https://www.maplesoft.com/applications/view.aspx?SID=154652&ref=Feed
This application computes the speed of sound on Mars with the <A HREF="/support/help/Maple/view.aspx?path=ThermophysicalData/Property">ThermophysicalData:-Property</A> command. The application takes into account the atmospheric composition of Mars, and a recently recorded temperature at Elysium Planitia (the landing site of the Mars Insight).<img src="https://www.maplesoft.com/view.aspx?si=154652/THUMB.png" alt="The Speed of Sound on Mars" style="max-width: 25%;" align="left"/>This application computes the speed of sound on Mars with the <A HREF="/support/help/Maple/view.aspx?path=ThermophysicalData/Property">ThermophysicalData:-Property</A> command. The application takes into account the atmospheric composition of Mars, and a recently recorded temperature at Elysium Planitia (the landing site of the Mars Insight).https://www.maplesoft.com/applications/view.aspx?SID=154652&ref=FeedThu, 30 Jul 2020 04:00:00 ZSamir KhanSamir KhanTrajectory of a Bullet Using an Air Resistance Correlation
https://www.maplesoft.com/applications/view.aspx?SID=154651&ref=Feed
This application models the trajectory of a bullet fired from a gun. Specifically, the application numerically solves the differential equations that describe the motion of the bullet (assuming three degrees of freedom), together with a correlation for air resistance. The predictions are compared to manufacturer-supplied velocity-range data for a specific type of bullet; the model closely matches the manufacturer's data.<img src="https://www.maplesoft.com/view.aspx?si=154651/thumb2.png" alt="Trajectory of a Bullet Using an Air Resistance Correlation" style="max-width: 25%;" align="left"/>This application models the trajectory of a bullet fired from a gun. Specifically, the application numerically solves the differential equations that describe the motion of the bullet (assuming three degrees of freedom), together with a correlation for air resistance. The predictions are compared to manufacturer-supplied velocity-range data for a specific type of bullet; the model closely matches the manufacturer's data.https://www.maplesoft.com/applications/view.aspx?SID=154651&ref=FeedThu, 02 Jul 2020 04:00:00 ZSamir KhanSamir KhanVapor-Liquid Equilibrium of Benzene and Toluene
https://www.maplesoft.com/applications/view.aspx?SID=154649&ref=Feed
This application calculate the vapor-liquid equilibrium of a benzene-toluene mixture. Specifically, the application calculates the:
<UL>
<LI>temperature, given the composition of the liquid phase and pressure
<LI>dew point and composition of the liquid phase given composition of the vapor phase and pressure
</UL>
The application employs the empirical Antoine equation to calculate the vapor pressures of benzene and toluene. The parameters are sourced from the NIST Chemistry Webbook.
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The techniques used here can be applied to many other mixtures - you just need to find the right data for the Antoine equation.<img src="https://www.maplesoft.com/view.aspx?si=154649/thumb.png" alt="Vapor-Liquid Equilibrium of Benzene and Toluene" style="max-width: 25%;" align="left"/>This application calculate the vapor-liquid equilibrium of a benzene-toluene mixture. Specifically, the application calculates the:
<UL>
<LI>temperature, given the composition of the liquid phase and pressure
<LI>dew point and composition of the liquid phase given composition of the vapor phase and pressure
</UL>
The application employs the empirical Antoine equation to calculate the vapor pressures of benzene and toluene. The parameters are sourced from the NIST Chemistry Webbook.
<BR><BR>
The techniques used here can be applied to many other mixtures - you just need to find the right data for the Antoine equation.https://www.maplesoft.com/applications/view.aspx?SID=154649&ref=FeedTue, 30 Jun 2020 04:00:00 ZSamir KhanSamir KhanHeat Transfer Coefficient and Critical Heat Flux for Nucleate Pool Boiling
https://www.maplesoft.com/applications/view.aspx?SID=154650&ref=Feed
This application computes the:
<UL><LI>heat transfer coefficient for nucleate pool boiling using the correlation published by Foster and Zuber (1955)
<LI>and actual and critical heat fluxes.
</UL>
If the actual heat flux is greater than the critical heat flux, a vapor film separates the liquid from rewetting the surface of the container. This decreases the efficiency of heat transfer.<img src="https://www.maplesoft.com/view.aspx?si=154650/thumb.png" alt="Heat Transfer Coefficient and Critical Heat Flux for Nucleate Pool Boiling" style="max-width: 25%;" align="left"/>This application computes the:
<UL><LI>heat transfer coefficient for nucleate pool boiling using the correlation published by Foster and Zuber (1955)
<LI>and actual and critical heat fluxes.
</UL>
If the actual heat flux is greater than the critical heat flux, a vapor film separates the liquid from rewetting the surface of the container. This decreases the efficiency of heat transfer.https://www.maplesoft.com/applications/view.aspx?SID=154650&ref=FeedTue, 30 Jun 2020 04:00:00 ZSamir KhanSamir KhanMinimum Road Radius for Highway Superelevation
https://www.maplesoft.com/applications/view.aspx?SID=154647&ref=Feed
When a vehicle travels around a curve, a centripetal force is needed to keep the vehicle on the road. If the road is completely horizontal, this force is entirely provided by side friction (i.e. the friction of the tires on the road).
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However, road curves are usually banked - the outer edge is higher than the inner edge. This uses the weight of the vehicle to help keep the vehicle on the road, and is called superelevation.
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In this application, we derive an equation that describes the relationship between velocity, side friction, road radius and superelevation for a point-mass vehicle traveling around a bend. This relationship is then rearranged to give an explicit equation for the road radius.
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This equation is then used to calculate the road radius required to maintain the trajectory of a vehicle as it travels around a bend. For a specific set of parameters, the calculated road radius matches the minimum road radius given in the AASHTO Green Book.<img src="https://www.maplesoft.com/view.aspx?si=154647/superelevation.png" alt="Minimum Road Radius for Highway Superelevation" style="max-width: 25%;" align="left"/>When a vehicle travels around a curve, a centripetal force is needed to keep the vehicle on the road. If the road is completely horizontal, this force is entirely provided by side friction (i.e. the friction of the tires on the road).
<BR><BR>
However, road curves are usually banked - the outer edge is higher than the inner edge. This uses the weight of the vehicle to help keep the vehicle on the road, and is called superelevation.
<BR><BR>
In this application, we derive an equation that describes the relationship between velocity, side friction, road radius and superelevation for a point-mass vehicle traveling around a bend. This relationship is then rearranged to give an explicit equation for the road radius.
<BR><BR>
This equation is then used to calculate the road radius required to maintain the trajectory of a vehicle as it travels around a bend. For a specific set of parameters, the calculated road radius matches the minimum road radius given in the AASHTO Green Book.https://www.maplesoft.com/applications/view.aspx?SID=154647&ref=FeedWed, 03 Jun 2020 04:00:00 ZSamir KhanSamir KhanHighway Pavement Design using the CALTRANS method
https://www.maplesoft.com/applications/view.aspx?SID=154646&ref=Feed
A highway pavement is several layers of materials above the natural soil. This application helps you design a flexible pavement using the approach outlined in the Highway Design Manual (6th edition) published by the California Department of Transportation (CALTRANS). Specifically, this application will determine the thickness of the subbase, base and asphalt concrete layers.<img src="https://www.maplesoft.com/view.aspx?si=154646/caltrans_highway_pavement.png" alt="Highway Pavement Design using the CALTRANS method" style="max-width: 25%;" align="left"/>A highway pavement is several layers of materials above the natural soil. This application helps you design a flexible pavement using the approach outlined in the Highway Design Manual (6th edition) published by the California Department of Transportation (CALTRANS). Specifically, this application will determine the thickness of the subbase, base and asphalt concrete layers.https://www.maplesoft.com/applications/view.aspx?SID=154646&ref=FeedFri, 29 May 2020 04:00:00 ZSamir KhanSamir KhanVenting of Gas From a Hole in a Pipe
https://www.maplesoft.com/applications/view.aspx?SID=154644&ref=Feed
This application calculates the rate at which gas flows out of a hole (or throat) in a pressurized pipe. Additionally, the Mach number, gas temperature and velocity, and speed of sound at the throat are computed.
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The same analysis can be applied to a pressurized tank venting gas through a hole, as long as the internal conditions are constant.
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The hole is small compared to the pipe diameter (so that the gas vents at a greater rate than the bulk flow of gas through the pipe), and the process is at steady-state and isentropic.
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The polytropic coefficient and molecular weight of the gas are computed with the <A HREF="/support/help/maple/view.aspx?path=ThermophysicalData">ThermophysicalData package</A>.<img src="https://www.maplesoft.com/view.aspx?si=154644/Venting_of_Gas_from_a_Hole_in_a_Pipe.png" alt="Venting of Gas From a Hole in a Pipe" style="max-width: 25%;" align="left"/>This application calculates the rate at which gas flows out of a hole (or throat) in a pressurized pipe. Additionally, the Mach number, gas temperature and velocity, and speed of sound at the throat are computed.
<BR><BR>
The same analysis can be applied to a pressurized tank venting gas through a hole, as long as the internal conditions are constant.
<BR><BR>
The hole is small compared to the pipe diameter (so that the gas vents at a greater rate than the bulk flow of gas through the pipe), and the process is at steady-state and isentropic.
<BR><BR>
The polytropic coefficient and molecular weight of the gas are computed with the <A HREF="/support/help/maple/view.aspx?path=ThermophysicalData">ThermophysicalData package</A>.https://www.maplesoft.com/applications/view.aspx?SID=154644&ref=FeedMon, 25 May 2020 04:00:00 ZSamir KhanSamir KhanSpatially Varied Open-Channel Flow with Increasing Discharge
https://www.maplesoft.com/applications/view.aspx?SID=154645&ref=Feed
Consider a long rectangular concrete channel that ends in an abrupt freefall, with an inflow of water along its length.
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This application will calculate the profile of the water surface from the freefall to a specified distance upstream by numerically solving the governing differential equation.
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For a subcritical flow, downstream conditions determine the water surface profile. The water depth reaches the critical height (i.e. the minimum energy height) at a short distance before the freefall - this is the boundary condition on the solution of the governing differential equation.<img src="https://www.maplesoft.com/view.aspx?si=154645/Spatially_Varied_Open-Channel_Flow_with_Increasing_Discharge.png" alt="Spatially Varied Open-Channel Flow with Increasing Discharge" style="max-width: 25%;" align="left"/>Consider a long rectangular concrete channel that ends in an abrupt freefall, with an inflow of water along its length.
<BR><BR>
This application will calculate the profile of the water surface from the freefall to a specified distance upstream by numerically solving the governing differential equation.
<BR><BR>
For a subcritical flow, downstream conditions determine the water surface profile. The water depth reaches the critical height (i.e. the minimum energy height) at a short distance before the freefall - this is the boundary condition on the solution of the governing differential equation.https://www.maplesoft.com/applications/view.aspx?SID=154645&ref=FeedMon, 25 May 2020 04:00:00 ZSamir KhanSamir KhanGradually Varied Flow in a Trapezoidal Channel
https://www.maplesoft.com/applications/view.aspx?SID=154642&ref=Feed
Water flows along a gently sloped trapezoidal channel; this is known as gradually varied flow.
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As the flow progresses along the channel, the water depth eventually reaches a uniform depth that no longer changes with distance along the channel; this is known as the normal depth.
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This application derives a fully analytical differential equation for gradually varied flow in a trapezoidal channel. The differential equation is solved numerically, and the resulting water surface profile is plotted.<img src="https://www.maplesoft.com/view.aspx?si=154642/Trapezoidal_Channel.png" alt="Gradually Varied Flow in a Trapezoidal Channel" style="max-width: 25%;" align="left"/>Water flows along a gently sloped trapezoidal channel; this is known as gradually varied flow.
<BR><BR>
As the flow progresses along the channel, the water depth eventually reaches a uniform depth that no longer changes with distance along the channel; this is known as the normal depth.
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This application derives a fully analytical differential equation for gradually varied flow in a trapezoidal channel. The differential equation is solved numerically, and the resulting water surface profile is plotted.https://www.maplesoft.com/applications/view.aspx?SID=154642&ref=FeedThu, 21 May 2020 04:00:00 ZSamir KhanSamir KhanSpeed of Sound in Various Fluids
https://www.maplesoft.com/applications/view.aspx?SID=154641&ref=Feed
This application computes and tabulates the speed of sound in various fluids at standard temperature and pressure, as provided by the ThermophysicalData package (which uses the open-source CoolProp project for fluid properties).
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The list of fluids include water, ethanol, air, ammonia and several others. However, you can use any of the fluids in the ThermophysicalData package (this help page contains a list of available fluids).
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This application also demonstrates the use of the DocumentTools package for tabulating and formatting results.<img src="https://www.maplesoft.com/view.aspx?si=154641/thumb.png" alt="Speed of Sound in Various Fluids" style="max-width: 25%;" align="left"/>This application computes and tabulates the speed of sound in various fluids at standard temperature and pressure, as provided by the ThermophysicalData package (which uses the open-source CoolProp project for fluid properties).
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The list of fluids include water, ethanol, air, ammonia and several others. However, you can use any of the fluids in the ThermophysicalData package (this help page contains a list of available fluids).
<BR><BR>
This application also demonstrates the use of the DocumentTools package for tabulating and formatting results.https://www.maplesoft.com/applications/view.aspx?SID=154641&ref=FeedFri, 08 May 2020 04:00:00 ZSamir KhanSamir KhanShifting the Pitch of Audio in the Frequency Domain
https://www.maplesoft.com/applications/view.aspx?SID=154638&ref=Feed
This application will shift the pitch of an audio file by scaling its frequency spectrum.
<BR><BR>
Our simple approach will multiply each signal frequency by the same amount. For a piano or violin note, the harmonics will still be an integer multiple of the pitch with the same balance between amplitudes (baring some digital aliasing effects). This preserves the timbre of the sound.
<BR><BR>
If your original audio is a piano note at F4 (a pitch of 349.2 Hz), you can convert it to an A4 note by scaling the frequencies by 4 semitones (a pitch of 349.2 Hz 4/12 = 440.0 Hz).<img src="https://www.maplesoft.com/view.aspx?si=154638/Pitch_Shift.png" alt="Shifting the Pitch of Audio in the Frequency Domain" style="max-width: 25%;" align="left"/>This application will shift the pitch of an audio file by scaling its frequency spectrum.
<BR><BR>
Our simple approach will multiply each signal frequency by the same amount. For a piano or violin note, the harmonics will still be an integer multiple of the pitch with the same balance between amplitudes (baring some digital aliasing effects). This preserves the timbre of the sound.
<BR><BR>
If your original audio is a piano note at F4 (a pitch of 349.2 Hz), you can convert it to an A4 note by scaling the frequencies by 4 semitones (a pitch of 349.2 Hz 4/12 = 440.0 Hz).https://www.maplesoft.com/applications/view.aspx?SID=154638&ref=FeedMon, 04 May 2020 04:00:00 ZSamir KhanSamir KhanPressure Drop of Gas and Liquid Flowing in a Pipe
https://www.maplesoft.com/applications/view.aspx?SID=154636&ref=Feed
This application calculates the two-phase pressure gradient for gas and liquid flowing in a pipe. The Lockhart-Martinelli separated flow approach is used.<img src="https://www.maplesoft.com/view.aspx?si=154636/pipe.png" alt="Pressure Drop of Gas and Liquid Flowing in a Pipe" style="max-width: 25%;" align="left"/>This application calculates the two-phase pressure gradient for gas and liquid flowing in a pipe. The Lockhart-Martinelli separated flow approach is used.https://www.maplesoft.com/applications/view.aspx?SID=154636&ref=FeedMon, 20 Apr 2020 04:00:00 ZSamir KhanSamir Khan