concept flow rate graph in category python
This is an excerpt from Manning's book Math for Programmers: 3D graphics, machine learning, and simulations with Python MEAP V11.
Suppose we’re breaking the 10-hour period into 1-hour intervals, even though we know this won’t give us very accurate results. The only 10 points on the flow rate graph we care about are the beginning times of each interval: 0 hours, 1 hour, 2 hours, 3 hours, and so on, up to 9 hours. Figure 8.20 shows these points marked on a graph.
Figure 8.23: The volume as a sum of the area of 30 rectangles (left) or 100 rectangles (right) under the flow rate graph (figure 8.20)
From these pictures, you can see that as our intervals get smaller and our computed result approaches the actual change in volume, the rectangles come closer and closer to filling the space under the flow rate graph. The insight here is that the area under the flow rate graph on a given time interval is (approximately) equal to the volume added to the tank on the same interval.