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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