When we are first introduced to equations, the equation format we are taught is closed equation format
, that is y = f(x).
|y = mx + c||equation of a straight line|
|Q = UALmtd||design equation of heat exchanger|
To write an equation in open equation format
, the closed format equation is rearranged with all the terms on one side. The equation is then evaluated to find the residual. For example;
|Closed Equation Format||Open Equation Format|
|y = mx + c||R = y - mx - c|
|Q = UALmtd||R = Q - UALmtd|
So why would we want to work with open equations?
- For linear equations, any term in the equation, (not just the left-hand term), can be found without the need rearrange the equation or solve it via iteration
- If the model is over-specified the use of open equations provides a method to reconcile the data
- Inter-related equations can be linked by simple connection equations, rather than by eliminating variables and equations