Units of Fuel Consumption - Maple Programming Help

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Units of Fuel Consumption

Description

 • Fuel consumption has the dimension volume of petroleum per length or length per volume of petroleum.  The three standard units of fuel consumption are the liter of petroleum per 100 kilometers, the mile per gallon of petroleum, and the kilometer per liter of petroleum.
 • Maple knows the units of fuel consumption listed in the following table.

 Name Symbols Context Alternate Spellings Prefixes mile_per_gallon mpg US_liquid * miles_per_gallon UK

 An asterisk ( * ) indicates the default context, an at sign (@) indicates an abbreviation, and under the prefixes column, SI indicates that the unit takes all SI prefixes, IEC indicates that the unit takes IEC prefixes, and SI+ and SI- indicate that the unit takes only positive and negative SI prefixes, respectively.  Refer to a unit in the Units package by indexing the name or symbol with the context, for example, miles_per_gallon[US_liquid] or mpg[UK]; or, if the context is indicated as the default, by using only the unit name or symbol, for example, miles_per_gallon.
 • Because liters per 100 kilometers and miles per gallon have inverse dimensions, the conversion between them includes taking a reciprocal.
 • Maple uses Unit annotations for units of fuel consumption.
 The unit of fuel consumption is defined as follows.
 A US liquid or UK mile per gallon is defined as a standard mile per US liquid or UK gallon of petroleum, respectively.

Examples

The dimensions of the three units of fuel consumption are not all the same.

 > $\mathrm{convert}\left(\frac{'L\left(\mathrm{petroleum}\right)'}{100'\mathrm{km}'},'\mathrm{dimensions}','\mathrm{base}'=\mathrm{true}\right)$
 $\frac{{{\mathrm{length}}{}\left({\mathrm{petroleum}}\right)}^{{3}}}{{\mathrm{length}}}$ (1)
 > $\mathrm{convert}\left('\mathrm{mpg}','\mathrm{dimensions}','\mathrm{base}'=\mathrm{true}\right)$
 $\frac{{\mathrm{length}}}{{{\mathrm{length}}{}\left({\mathrm{petroleum}}\right)}^{{3}}}$ (2)
 > $\mathrm{convert}\left(\frac{'\mathrm{km}'}{'L\left(\mathrm{petroleum}\right)'},'\mathrm{dimensions}','\mathrm{base}'=\mathrm{true}\right)$
 $\frac{{\mathrm{length}}}{{{\mathrm{length}}{}\left({\mathrm{petroleum}}\right)}^{{3}}}$ (3)

Because of Unit annotations, miles per gallon of petroleum cannot directly be converted to meters per gallon (the dimensions are different). The symbolic option makes convert ignore this.

 > $\mathrm{convert}\left(1,'\mathrm{units}','\mathrm{mpg}',\frac{'m'}{'\mathrm{gal}'}\right)$
 > $\mathrm{convert}\left(1,'\mathrm{units}','\mathrm{mpg}',\frac{'m'}{'\mathrm{gal}'},'\mathrm{symbolic}'=\mathrm{true}\right)$
 $\frac{{201168}}{{125}}$ (4)

Convert 4.4 L/100 km to mpg.

 > $\frac{1}{\mathrm{convert}\left(4.4,'\mathrm{units}',\frac{'L\left(\mathrm{petroleum}\right)'}{100'\mathrm{km}'},\frac{1}{'\mathrm{mpg}'}\right)}$
 ${53.45785984}$ (5)

Convert 17.2 mpg to L/100 km.

 > $\frac{1}{\mathrm{convert}\left(17.2,'\mathrm{units}','\mathrm{mpg}',\frac{1}{\frac{'L\left(\mathrm{petroleum}\right)'}{100'\mathrm{km}'}}\right)}$
 ${13.67526647}$ (6)

Convert 4.4 L/100 km to km/L.

 > $\frac{1}{\mathrm{convert}\left(4.4,'\mathrm{units}',\frac{'L\left(\mathrm{petroleum}\right)'}{100'\mathrm{km}'},\frac{1}{\frac{'\mathrm{km}'}{'L\left(\mathrm{petroleum}\right)'}}\right)}$
 ${22.72727273}$ (7)

Convert 19.3 km/L to mpg.

 > $\mathrm{convert}\left(19.3,'\mathrm{units}',\frac{'\mathrm{km}'}{'L\left(\mathrm{petroleum}\right)'},\mathrm{mpg}\right)$
 ${45.39641458}$ (8)