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on Using Units and Dimensions in Maple\251 Maplesoft, a division of Waterloo Maple Inc., 2005

Maple provides the most comprehensive package in the software industry for managing units and dimensions. Problems in science and engineering can now be fully managed with appropriate dimensions in any modern unit system (and even some historical systems!), including MKS, FPS, CGS, Atomic and more. Over 500 standard units are recognized by Maple's Units package. This document explains how to do simple and complex conversions between units and how to use units in your calculations. It also gives tips and examples on how to effectively use the different notation styles, how to change the default measurement system, and how to customize defaults inside an existing measurement system.

For simple conversions between units, a convenient Unit Converter Assistant is available under the Tools>Assistants menu. No knowledge of the Units package is required. All the available dimensions and units are selected from a list, so you know instantly what is available with no worries over choosing the proper spelling or abbreviation. The corresponding Maple convert command is generated so you can use it inside your worksheet or procedure.The Maple convert command can also be used directly for unit conversions.

restart; interface( warnlevel=0 ): interface( displayprecision=4 ):

Conversions of an expression that does not involve units, from one unit to another, can be done at any time without loading the Units package.convert( 1.0, units, ft, m);

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Use a symbolic variable to see the conversion formula from calories to Joules:convert(x, units, cal, J);

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Tip: The units conversion for temperature converts intervals (e.g. if the temperature changes by 5 degrees Celsius, that the same as a change of 9 degree Fahrenheit). To convert absolute temperatures from one scale to another, use the temperature option to convert().convert(5, units, degC, degF);

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convert(0, temperature, degC, degF);

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Conversions of expressions using the "Unit()" notation are available once the Units[Standard] package has been loaded.with(Units[Standard]):distance := 5.0*Unit(m);

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elapsedtime := 10*Unit(s);

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Calculate the speed in miles/hour:convert(distance/elapsedtime, 'units' , 'mi/h');

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The Natural option tells Maple that the unit variables will be expressed as ordinary variables without special notation. with(Units[Natural]):4.3*m + 32*cm;

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This convenient notation is very readable, and is suitable for many situations, including interactive calculations where you have a limited number of user-defined variable names.Tip: You should take care not to create a new user variable called km, or miles, etc. The Units package knows that a NiMqKCUja2dHIiIiJSJtR0YlKiQlInNHIiIjISIi is a NewtonmyForce := 5*g * 3 * m/s^2;

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Maple is smart enough to understand when units conflict -- for example, adding a length (ft) to a mass (kg) does not make sense, and Maple returns an error if the user tries to do so.3.2*ft + 1.0*kg;

Error, (in Units:-Standard:-+) the units `ft` and `kg` have incompatible dimensions

The Natural units notation is suitable for situations in which you are confident you will not create naming conflicts or expressions that appear ambiguous. Because the Unit package supports so many different types of units, many names are "taken" when the Natural notation is used. This list will contain many unit names which you may not even be aware are units (e.g. f, year, barn, Pa). Using these names as variables could inadvertently create problems with your unit calculations. An alternate notation is available which always makes it clear which quantities represent variables and which denote units.

restart; interface(warnlevel=0): interface(displayprecision=4):

with(Units[Standard]):m := 3.0*Unit(kg) + 2.2*Unit(lb);

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After defining the variable m, it is still possible to do calculations with meters. However, the m must be enclosed in forward quotes so Maple does not evaluate it before sending it to the Unit function.distance := 1.0*Unit('m') + 3.1*Unit('m');

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Tip: If you want to protect against accidental corruption of unit names, it is good practise to always enclose unit names in forward quotes, no matter which notation you are using.

restart; interface(warnlevel=0): interface(displayprecision=4): with(Units[Natural]): with (ScientificConstants):

First, define the dollar value of the gold, cost per troy ounce (assume $268), and the density.val := 10^9 * USD; costPerOz := 268.00 * USD/oz[troy]; density := 19.3 * g/cm^3;

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The resulting mass and volume are:mass := val/costPerOz; volume := mass/density;

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What is the length of one side of a cube having this volume?length_side := root[3](volume);

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Maple automatically converts the answer to a default unit system and unit. SI is the default unit system used by the Units package.

restart; interface(warnlevel=0): interface(displayprecision=4): with(Units): with(Units[Natural]):

myDist := 4*ft + 3.5*inches;

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You can easily express the above in standard US (FPS - Foot Pound Second) system using the convert commandconvert( myDist, system, FPS);

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The default unit system can be changed using the Units[UseSystem] command.Units[UseSystem](FPS);myDist := 4*ft + 3.5*inches;

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Inside each measurement system, each dimension has a specified default unit. For example, all length calculations done inside the SI system will return answers in meters. It is possible to change the default unit for a particular dimension, which will be respected even after combining and simplifying units, while leaving the rest of the measurement system unchanged.

restart; interface(warnlevel=0): interface(displayprecision=4): with(Units): with(Units[Standard]):

Add a new system, and override only the length dimension:AddSystem( NewSI, GetSystem(SI), mm ); Use the new system in calculations. Note that length calculations are now in millimeters, but area and volume are unchanged.UseSystem( NewSI);Unit(3*cm),Unit(5*cm^2),Unit(11*ft^3);

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Override length, area and volume:AddSystem( NewSI, GetSystem(SI), mm, mm^2, mm^3 ); UseSystem( NewSI);Unit(3*cm),Unit(5*cm^2),Unit(11*ft^3);

NiUsJC1JJVVuaXRHNiI2IzcjSSNtbUdGJiIjSSwkLUYlNiM3IyokRikiIiMiJCsmLCQtRiU2IzcjKiRGKSIiJCMiLGtTbU4qUSIkRCI=

Legal Notice: The copyright for this application is owned by Maplesoft. The application is intended to demonstrate the use of Maple to solve a particular problem. It has been made available for product evaluation purposes only and may not be used in any other context without the express permission of Maplesoft. 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