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barcode reading in asp.net W = w,  W , K 5 = H%  Hcs UA UA in Software
W = w,  W , K 5 = H%  Hcs UA UA ANSI/AIM Code 128 Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Encoding USS Code 128 In None Using Barcode maker for Software Control to generate, create USS Code 128 image in Software applications. dTv 1
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Data Matrix ECC200 Creator In None Using Barcode creation for Software Control to generate, create ECC200 image in Software applications. Make UPC  13 In None Using Barcode printer for Software Control to generate, create EAN 13 image in Software applications. From Eq. (21.15), we see that the steam temperature &&depends on the steam flow rate WV and the water temperature TL. The combination of Eqs. (21.9) and (21.15) give the dynamic response of the water temperature to changes in water flow rate, inlet water temperature, and steam flow rate. These equations are represented by a portion of the block diagram of Fig. 21.4. Before completing the analysis of the control system, we must consider the effect of valvestem position on the steam flow rate. Barcode Generation In None Using Barcode encoder for Software Control to generate, create bar code image in Software applications. Code 39 Full ASCII Creator In None Using Barcode creation for Software Control to generate, create Code 3/9 image in Software applications. Analysis of Valve
Code11 Encoder In None Using Barcode generation for Software Control to generate, create Code11 image in Software applications. Code 128C Generator In Java Using Barcode printer for Java Control to generate, create ANSI/AIM Code 128 image in Java applications. The flow of steam through the valve depen& on three variables: steam supply pressure, steam pressure in the jacket, and the valvestem position, which we shall assume to be proportional to the pneumatic valuetop pressure p. For simplicity, assume the steam supply pressure to be constant. with the result that the steam flow rate is a function of only the two remaining variables; thus (2l.L) WV = f@1PY) Because of the assumption that the steam in the jacket is always saturated, we know that pv is a function of T,; thus Make GS1  13 In None Using Barcode drawer for Online Control to generate, create EAN / UCC  13 image in Online applications. Draw Code 39 Extended In Java Using Barcode drawer for Java Control to generate, create Code 39 image in Java applications. pv = gU v) Recognizing GTIN  13 In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Print USS Code 39 In None Using Barcode generation for Microsoft Excel Control to generate, create ANSI/AIM Code 39 image in Excel applications. (21.17) Generate UPCA Supplement 5 In .NET Framework Using Barcode printer for ASP.NET Control to generate, create UPCA Supplement 2 image in ASP.NET applications. UPCA Maker In Java Using Barcode encoder for Android Control to generate, create UCC  12 image in Android applications. THEORETICAL
ANALYSIS
COMPLEX
PROCESSES
This functional relation can be obtained from the saturated steam tables. Equations (21.16) and (21.17) can be combined to give WV = fb,g(~,)l =
fl(p> T ) The function ft@, T,,) is in general nonlinear, and if an analytic expression* is available, the function can be linearized as described previously:In this example, we shall assume that an analytic expression is not available. The linearized form of fi(P, T,) can be obtained by making some experimental tests on the valve. If the valvetop pressure is fixed at its steadystate (or average) value and wV is measured for several values of TV (or p,), a curve such as the one shown in Fig. 21.3~ can be obtained. If the steam temperature T, (or p,) is held constant and the flow rate is measured at several values of valvetop pressure, a curve such as that shown in Fig. 21.3.b can be obtained. These two curves can now be used to evaluate the partial derivatives in thelinear expansion of fl(p,T,) as we shall now demonstrate. Expanding w,. about the operating point ps ,T,, and retaining only the linear terms give This equation can be written in the form
Vv  Tv,) (21.20) 1 = R, *The flow of steam through a controJ valve dn &en be represented by the relationship. WY I~:&& &q ** . where ps = supply pressure of steam pv = pressure downstream of valve S & = crosssectionai area for flow of steam through valve C, = constant of the vaive (21.18) For a linear valve, A0 is propokonal to stem position and the stem position is proportional to valvetop pressure p; under these conditions, Eq. (21.18) takes the form w=c:PvFE .
(21.19) 326 PROCESS
APPLICATIONS
IP, P0) T,, = T,, FIGURE 213 Linearization of valve characteristics from experimental tests.
The coefficients K, and l/R, in Eq. (21.20) am the slopes of the curves of Fig. 21.3 at the operating point ps, TV,. This follows from the definition of a partial derivative. Notice that l/R, has been defined as the negative of the slope so that R, is a positive quantity. The experimental approach described here for obtaining a linear form for the flow characteristics of a valve is always possible in principle. However, it must be emphasized that the linear form is useful only for small deviations from the operating point. If the operating point is changed considerably, the coefficients K, and l/R,, must be reevaluated. Notice that, in writing Eq. (21.20), we have assumed the valve to have no dynamic lag between p and stem position. This assumption is valid for a system having large time constants, such as a steamjacketed kettle, as was demonstrated in Chap. 10.

