now in Figure 4 we’ll begin looking at a “level” control application ... in this first example, we’ll simply take a full tank of water and allow it to drain by opening a valve at the bottom ...

as shown in the graph on the left, the tank begins draining rather rapidly at first ... but then the rate of drain becomes slower as the test proceeds ... so instead of getting a straight line (a constant rate) for our draining process, we get a curve with a characteristic shape ... now at first glance, a beginner might think that the shape of this “gravity draining” curve is exactly like the shape of a capacitor discharge curve ... or like a curve produced by a cooling application ... but the draining curve is not exactly the same shape ... notice the difference as shown in the detailed graph on the right ... the draining curve is not as “rounded” in appearance as the cooling curve ... the reason is that the effect of gravity plays a part in the shape of this curve ... specifically, the amount of water draining when the tank is full is much greater than the amount draining when the tank is nearly empty ... notice the stream of water (1) which results when the level is higher at point (H) ... this stream is much larger than the stream of water (2) when the tank level is lower at point (L) ... anyone who wants to do some research on this effect should start by looking up Torricelli’s Theorem in any decent physics textbook ... for our purposes today, we can simply agree on what basic common sense and life’s experiences tell us is true ... specifically, a tank which is nearly full will drain much faster than a tank which is almost empty ...