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TABLE 3.2
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The Significance of Pressure as a Measurement of Specific Volume and Enthalpy of Steam and Water at 100 psia
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System Superheated vapor at 1000 F.
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Spec. vol. change, % Pressure change, %
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Enthalpy change,% Pressure change, %
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Compressed liquid at 100 F. .
volume are inversely proportional, with enthalpy playing a relatively minor role. When a vapor is in equilibrium with its liquid, however, a change in enthalpy of the system will produce a pronounced pressure change, while voIume variations will have less effect. Liquids, moreover, are virtually incompressible, with the result that neither pressure nor enthaIpy have much influence over system volume. The thermodynamic properties of gas, vapor, and liquid systems have been brought out expressly to estabhsh that the properties of system pressure are decidedly a function of state. It is extremely important to attach the correct significance to the pressure measurement, if acceptable performance of a control loop is to be gained. Table 3.2 gives an example of each of the three st,ates listed above, where water is the substance under pressure. It indicates the conditions under which pressure is a suitable measurement of the material content (specific volume) and energy content (ent halpy) of the system. The table points out that pressure is an adequate measurement of the material content of a system which contains only gas. Enthalpy of a gas, on the other hand, is more a function of temperature than of pressure. Consequently gas pressure should be controlled by manipulating the material content of the system, i.e., inflow or outflow. But, in a system where vapor and liquid are in equilibrium, pressure could be controlled by adjusting the flow of either material or heat. Finally, pressure is a poor measure of either heat or mass content of a liquid, so another approach must be taken in stipulating its control.
Gas Pressure
The perfect gas law states that pV = MRT where p 1 dl R T = system pressure = volume = mole content = gas constant = absolute temperature
Analysis of Some Common Loops
The rate of change of pressure in a constant-volume system is related to the change in material content of the system: z=
dM RT dt V
If R and 7 are both constant, the rate of change of mass content of the system is the difference between mass inflow and outflow:
E (fi - fo> -iE=v where F = nominal mass flow fi = fractional inflow f0 = fractional outflow Integration of the last equation places pressure in terms of flow: P = & / (fi - fo) dt (3.3)
For dimensional conformity, p would be in units of atmospheres, V in cubic feet, and F in standard cfm, that is, cfm at 1.0 atm. Thus the time constant V/F is expressed in minutes. Just as level control was used to close a liquid material balance around a tank, pressure control is used to close a gas material balance. The gaspressure process is ordinarily self-regulating, excaept at zero flow, because pressure always influences inflow and outflow. The process is fundamentally single-capacity, although the pressure transmitter and valve can add very small secondary lags. If there is no transmitter, as with a self-contained regulator, one secondary lag is eliminated. Pressure of a gas is easy to control, even when the volume of the system is small, e.g., only piping. In fact, the narrow-band proportional action of self-contained regulators is sufficient for most applications. They are, for the most part, as sensitive as their simple construction will allow, indicating that loop gain is not a problem. Pressure acting on the diaphragm compresses the spring, moving the plug within the valve. Each position of the seat corresponds to a given pressure on the diaphragm. Initial compression of the spring sets the pressure at which the valve begins to open. Because pressure will vary with flow, as in Fig. 3.4, a regulator is said to exhibit Ldroop. Regulators differ, but a typical proportional band would be 5 percent. Near zero flow, extra pressure is needed for shutoff; at the other extreme, the valve is wide open and acts as a fixed resistance.
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