Engineering Problem Solving with a Typical Example (Prof. M. Kostic)

Engineering Problem Solving with a Typical Example: Filling-up and Overflow in a Tank
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:

Click this to view the Example as a Web Power-Point presentation (better for viewing, but sorry, no animations like in my presentation), or

Click this to view the Example in its original form, in Acrobat PDF format, wich is better for printing.

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)