Vol. Advanced Theory
Chapter More Principles of Industrial Instrumentation (Animated)

Understanding the Calculus Concepts of Differentiation and Integration

The following animation shows the calculus concepts of differentiation and integration (with respect to time) applied to the filling and draining of a water tank.


The animation shows two graphs relating to the water storage tank: one showing the volume of stored water in the tank (\(V\)) and the other showing volumetric flow rate in and out of the tank (\(Q\)). We know from calculus that volumetric flow rate is the time-derivative of volume:

\[Q = {dV \over dt}\]

We also know that change in volume is the time-integral of volumetric flow rate:

\[\Delta V = \int_{t_0}^{t_1} Q \> dt\]

Thus, the example of a water storage tank filling and draining serves to neatly illustrate both concepts in relation to each other.