BACK to KOSTIC Homepage * © M. Kostic

Engineering Problem Solving with a Typical Example: Filling-up and Overflow in a Tank
Back to Some Suggestions for Problem Solving

This is a typical, general type problem, for which no specific prerequisites are necessary. An intelligent man may solve it without using calculus, see the last two methods. This is a simple problem solved as an example to show how several different methods (using MathCAD) may be used in general to solve engineering problems:

The following methods were used to solve the above simple Example:
… if the equation(s) may be solved "explicitly," … by separation of variables, than the solution is straightforward (in our example, using the MathCAD built-in integral solvers):

… direct numerical integration;
… direct symbolic integration;
… symbolic evaluation of indefinite integral and using upper and lower limits;

… if the equation(s) can NOT be solved "explicitly," then we have to use other method(s), i.e. to review the work done, and readjust/modify our approach and work..., usually by
trial-and-error, or numerical iteration, etc. (in our example, using the MathCAD built-in functions):

… the Runge-Kutta numerical method for solving any ordinary differential equation(s);
… "common-sense" finite difference approximation (very elegant in this case);
… approximation of variable exit-flow with its average value (we have to be very cautious with this approach).

For more advanced use of MathCAD, including programming, see the following:
The famous Blasius Flow Over the Flat Plate: Solved using MathCAD and the "Shooting Method" (html file)

Professor M. Kostic's Web Site: www.kostic.niu.edu *Usage Policy & © Copyright by M. Kostic