Units & Tolerances
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Introduction
You can compute with units and dimensions. Maple will track units throughout a calculation, resolve compound units to a simpler form, and help you ensure your calculations are dimensionally consistent.
Here, note how units of force over area are correctly resolved to the SI unit of stress.
withUnitsSimple:
stress≔5.4N4.5inch2
stress≔1860.003720Pa
The ThermophysicalData and ScientificConstants packages associate units with fluid properties and physical constants.
ThermophysicalData:-Propertydensity,water,pressure=1atm, temperature=293K
998.2379971kgm3
evalfScientificConstants:-Constant'c',units
2.99792458×108ms
Defining Units
You can define units using one of several methods.
Ctrl+Shift+U followed by the unit
area1≔5.5m2:
Unit function
area2≔4.5⋅Unitcm2:
Units Palette
Here's how you define a variable with a unit using Ctrl+Shift+U.
What you should see
Try it here
Type x:=3.5
Press Ctrl+Shift+U
Type m
Press the right arrow key
Type a colon and then press Enter
Changing the Units of a Result
You can also change the units of a result using the options under Convert Output Units in the Context Panel.
Simply click on a result with a unit, and navigate to the Context Panel - you can select one of several suggested unit conversions or specify your own. Number formating can also be modified.
Tolerances
Variables can also have associated tolerances, which are carried through calculations.
For example, consider a water manometer reading a height of 0.08 m with a measurement error of ±0.002 m. The possible range of pressures is thus
restart:withTolerances:
h≔0.08 ±0.002m:
g≔9.81m s−2:
ρ__water≔ThermophysicalData:-Propertydensity,water, pressure=100kPa,temperature=25degC
ρ__water≔997.0470390kgm3
ΔP≔ρ__water⋅g⋅h
ΔP≔782.±19.6Pa
Applications
Heat Flows across a Refrigeration Cycle
Ideal Brayton Cycle
Steel Beam with Torsion
Antenna Array
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