Qj ' outflow, ft3/min
A = vessel cross-sectional area, ft2 (vertical, cylindrical vessel assumed) H = liquid level, feet
= level transmitter output signal K^ = 12 psi/Afir for pneumatics
AHt = level transmitter input span, feet of process fluid K& G^s) = controller transfer function Qc = controller output signal ft3/min , dQ„/dBc = valve gain, or flow control loop gain,-:— (see discussions in Sections 3.9 and 4.7) PS1
For a cascade level-flow system: where ddc K„f
K^ = flow measurement gain of linear flow meter 12 '
|Qp\m = maximum flow of flow-meter span, ft3/min
The analysis employed here is further simplified in that the effects of variable valve-pressure drop are omitted, as are transmitter dynamics.
Equations (16.1) through (16.4) may be combined into the signal flow diagram of Figure 16.2, from which we may write by inspection:
For this case K^ G^is) becomes simply Kch. Then equation (16.5) becomes:
and equation (16.6) becomes:
QAs) dQ0 A
If the input span of the valve positioner is the same as the transmitter output span (as, for example, 3-15 psig), and if the valve has an installed linear flow characteristic with a wide-open capacity approximately equal to four times flowsheet flow, QpS, then:
This last equation is very useful for finding the desired holdup, A AHT, provided a value of rH is specified. Usually we choose Kj, = 2 and bias the
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