Suppose you want to calculate the required horsepower for a motor which could raise a
2000 lbf elevator to the top of a 10 story building (assuming 12 feet
per story) in 1 minute, you could enter the equation:
Expression: 2000 lbf * (10 * 12 feet) / 1 minute
Result Unit: horsepower

Indicating that you want to multiply 2000 pounds force by 10 times 12
feet, divide that by 1 minute, and then express the final result in
horsepower. Calchemy would respond:
= 7.27273 horsepower

If, on the other hand, you had made a mistake in the original equation
and left out the "/ 1 minute":
Expression: 2000 lbf * (10 * 12 feet)
Result Unit: horsepower

Calchemy would have responded with a Dimensional Mismatch dialog
containing:
TIME^-1

Indicating that the left hand side of the equation was missing a factor
of 1/TIME -- the equation was not dimensionally correct, and therefore,
could not be evaluated.
Calchemy can also be used as a simple dimensionless calculator by
eliminating the result unit from the equation. For example, you could
enter the equation:
Expression: 2+3*5
Result Unit:

Calchemy would respond with the algebraically correct answer:
= 17

You could also enter the original equation in the following less
explicit form:
Expression: 2000 lb; 10 stories; 12 feet/story; 1 minute
Result Unit: horsepower

Indicating that you want to *combine* 2000 pounds, 10 stories, 12
feet/story, and 1 minute in such a way that the equation is
dimensionally correct, and then express the final result in horsepower.
Calchemy would again respond:
= 7.27273 horsepower

This example illustrates the following features:
### Solving By Dimensional Analysis

The ";" operator tells Calchemy to use dimensional analysis to determine
whether its operands should be in the numerator or the denominator of
the equation. In this example, Calchemy placed the first three operands
in the numerator and the last operand in the denominator. This allows
you to be less involved with the actual mechanics of the equations.
The "lb" unit is an overloaded unit, meaning that it has more than one
common definition. It is primarily defined as "lbm" (pounds mass) and
secondarily defined as "lbf" (pounds force). Calchemy automatically uses
the appropriate definition, again based on dimensional analysis. In
this example, Calchemy used "lbf". This allows you to naturally use
units with multiple common definitions.
### Free Units

The "stories" and "story" units are called free units. Free units are
units which are not actually understood by Calchemy, except in that they
are new and unique dimensions which must "cancel out" in the end. This
allows you to enter equations in a more natural format.
### Pluralized Units

The "stories" and "story" units also illustrate that Calchemy understands
basic pluralization rules for units. This, again, allows you to enter
equations in a more natural format.

Calchemy Software Inc.

Fort Collins, CO

Last Updated 6/21/2009

© Copyright 1996-2009 Calchemy Software Inc.