EQUATRAN Tutorial 1: Basic Equation Entry and Solving
In this first tutorial we will show how to enter a simple equation into EQUATRAN and obtain a solution. We will use the Antoine equation which relates the vapour pressure of a pure substance to temperature. The equation is:
log10 P = A - B / (T + C)
A, B and C are constants. The vapour pressure P can be calculated for a given temperature T, or the reverse calculation can find T for a given P.
This particular equation is trivial and can easily be rearranged to give either ‘P =’ or ‘T =’ on the left hand side. However in EQUATRAN there is no need to rearrange the equation. This becomes a great advantage when more complex equations or large numbers of equations are to be solved and a direct solution is difficult or impossible.
After installing EQUATRAN, start by running EQUATRAN either from the Windows Start menu or from the desktop icon. This window will open:
A new problem can be started by clicking File / New / Source Text on the menu. This opens a Source Text window. File / Save As can be used to give the new problem file a name with the file extension ‘.eqs’.
Now enter the equation, the values of constants A, B and C, and the value of T for which P is to be found.
Some points to note:
- The equals sign (=) is used in its true mathematical sense, i.e. to indicate equality between the left and right sides of an equation. It is not an assignment as in computer programming languages where the variable on the left side is given the value calculated on the right. The expression on the left can therefore be complex, more than just a single variable.
- Many mathematical functions are available, for example the LOG10 function used here.
- Comments can be added to the source text by preceding a line with //. These lines are ignored by the solver.
To solve the equation, click the Run () button.
The equation is solved and the output is displayed as below. We can see the calculated value of P is 126.4.
Finally we can reverse the direction of the calculation without any need to rearrange the equation. Replace the last line of code to specify P instead of T and run again. This time the value of T is calculated.
Next: Tutorial 2 - Simultaneous Equations