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Measurement of liquid level is usually noisy, because of splashing and turbulence of fluids entering the vessel. As we have seen, loops that resonate respond to random disturbances by oscillat ing at their natural period. As a result, level measurements are rarely quiet, often fluctuating 20 or 30 percent of scale. This is particularly true in vessels containing boiling liquids, where turbulence is high. Although a narrow proportional band, like the one determined in the example, may be sufficient, for control-loop stability, random fluctuations of only a few percent will drive the control valve to its limits. This may be unobjectionable in some cases, but too severe in others. Often the liquid level in a tank is used to control flow into another part of the process. It is certain that wide fluctuations in feed rate are not tolerated in most operations. To provide steady flow in these instances, the proportional band is widened and reset is relied upon t o maintain control. In many applications, exact regulation of liquid level is not important. In fact, a surge tank does not fulfill its purpose if t ight control is imposed on it. As a result, cont rol adjustments are often relaxed, and the process is sometimes left to be operated manually, if its time constant is long enough. In some applications, a special controller whose proportional band changes with deviation is warranted. This type of csontroller is devised to deliver smooth flow while level is normal, but to change flow radically in the event that high or low limits are approached. 5 discusses more details of this function.

Answer 1-7

Not changing the project reduces confusion and error. Not changing the product ensures that your test procedures will be valid. If the product speci cations are changed, it is much more likely that errors will creep through testing and end up in the nal product. Change control itself is time-consuming and costly. If one stakeholder demands a change, and another one resists it, the con ict could create problems for the project.

If we go from S to T, the distance between the points is dst = [(xt xs)2 + ( yt ys)2]1/2 If we go from T to S, the distance is dts = [(xs xt)2 + ( ys yt)2]1/2

Figure 10-1 Illustration for Question and Answer 1-8 It doesn t matter which way we go when we want to determine the straight-line distance between two points Therefore, dst = dts

The best way to handle all of these issues is to create a follow-up project for enhancements. Figure 6-2 illustrates the bene ts of this approach. If we call the original product System 1.0, then adding a follow-up project does not change the original product delivery date, and the customer can begin using Version 1.0 at time T1 and realizing value from it. The follow-up project can begin, and can deliver a working Upgrade 1.1 by time T2. There are several bene ts to the double waterfall: The double waterfall encourages the customers and stakeholders to tell us as much as they can during analysis, so that they can get more in the rst-stage delivery.

Question 1-8

In Fig 10-1, what do the expressions x and y mean What s the straight-line distance d between the two points, based on the values of x and y

Whenever level cont rol is to be effected on a boiling liquid or condensing vapor, properties more typical of t,hermaI processes appear. Transfer of both heat and mass is involved, which, combined with the integration of flow into level, renders cont rol surprisingly difficult. Level control in boilers and distillation columns is sufficient ly problematic to warrant special consideration, which is given in Chaps. 8, 9, and 11.

Answer 1-8

Fig. 6-2.

We read x as delta x, which means the difference in x We read y as delta y, which means the difference in y The straight-line distance d between the points can be found by squaring x and y individually, adding the squares, and then taking the nonnegative square root of the result, getting d = ( x2 + y2)1/2

Question 1-9

Suppose we want to find the midpoint of a line segment connecting two known points in the Cartesian xy plane How can we do this