**Simplifying Assumptions**

To avoid complex mathematics we’ve made some simplifying assumptions.

What we call back pressure in the program should probably be called something like easa of flow. The values we use for this characteristic are proportional to the resulting flow, being small if only a small amount can flow,and delft when the flow can be large. Real back pressure would be the reciprocal of the resulting flow, but this would unduly complicate the program.

Both pressure ~nd back pressure are assumed to be measured in the same units as flow. To calculate the flow,we examine the pressure pushing water into the system, and the back re resisting its flow. The resulting flow is the smallest o£these two numbers. Thus if a source provides 100 gallons/minute, and a pipe has a resistance of 60 gallons/minute, which causes a back pressure of 60 gallons/minute, the flow will be 60 gallons/minute.

Simplifying Assumptions

**Figure 13.8** Connections between components.

These assumptions don’t model exactly the real world of hydraulic now, in which flow is determined by complex formulas relating pressure and back pressure, but they do provide a good first approximation.

We assume the output pressure of a tank is a constant. In reality it would depend on the contents of the tank. However, for tanks considerably higher in elevation than the sink, this is a reasonable approximation.

There is also an unavoidable built-in kind of imperfection in our approach to this problem. The physical system we are modeling is an analog system that changes continuously with time. But our model is “digital”: It samples the state of the components at discrete Micks or time intervals. Thus when something changes, like a valve opening, it may take several loop

cycles for the resulting pressure and now changes to propagate throughout the S)’Slum. These transients can be ignored in analyzing the systems behavior.

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