DIMENSION

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The DIMENSION keyword is encountered in the ATOM and CONSTANT declarations in ASCEND syntax. It is used to declare the dimension that a particular variable or constant will be required to take.

Real values have dimensionality such as length/time for velocity. Dimensionality is to be distinguished from the units such as km/h or ft/s. ASCEND takes care of mapping between units and dimensions. Many different measurement units may exist for a variable of any given dimensionality. A value without units (this includes integer values) is taken to be dimensionless. Dimensionality is built up from the following base dimensions:

Symbol definition typical units symbol
L length metre m
M mass kilogram kg
T time second s
E electric current ampere A
Q quantity mole mol
TMP temperature kelvin K
LUM luminous intensity candela cd
P plane angle radian rad
S solid angle steradian srad
C currency US dollars USD

The ATOM and CONSTANT definitions in the library illustrate the use of dimensionality. Dimensions may be any combination of these symbols along with rounded parentheses, (), and the operators *, ^ and /. Examples include M/T or M*L^2/T^2/TMP (this latter means (M*(L^2)/(T^2))/TMP). The second operand for the to-the-power-of operator, ^, must be an integer value (e.g., -2 or 3) because fractional powers of dimensional numbers are physically undefined in ASCEND. If the dimensionality for a real value is undefined, then ASCEND gives it a wildcard dimensionality. If ASCEND can later deduce its dimensionality from its use in a model definition it will do so. For example consider the real variable a, suppose a has wildcard dimensionality, b has dimensionality of L/T. Then the statement

a + b = 3 {ft/s};

requires that a have the same dimensionality as the other two terms, namely, L/T. ASCEND will assign this dimensionality to a. The user will be warned of dimensionally inconsistent equations.

See also