Nettoveranderingsstelling

The Net Change Theorem is an interpretation of the Fundamental Theorem of Calculus. It states that when a rate function is integrated over an interval, it gives the net change in the original quantity.

This applies to real systems like reservoir management. Here, the net rate of volume change includes inflow from a river and outflow through spillways.

The inflow remains constant, while the outflow increases steadily over a 6-hour period.

The reservoir's initial volume is 260 million cubic meters, and its maximum capacity is 300 million cubic meters.

Exceeding this capacity increases internal pressure and creates a serious risk of flooding.

Applying the Net Change Theorem and integrating the net rate over 6 hours, the total change in volume is calculated.

This change is added to the initial volume to find the total volume of water at the end of the period.

The calculation shows that the final volume exceeds the reservoir’s safe capacity.

This shows how the Net Change Theorem aids in flood risk prediction and improves discharge planning and safety.