27.15Review of fundamental principles

Shown here is a partial listing of principles applied in the subject matter of this chapter, given for the purpose of expanding the reader’s view of this chapter’s concepts and of their general interrelationships with concepts elsewhere in the book. Your abilities as a problem-solver and as a life-long learner will be greatly enhanced by mastering the applications of these principles to a wide variety of topics, the more varied the better.

•Definition of pressure: P = FA (pressure is the amount of force applied over a specified area by a fluid. Relevant to fluid-powered valve actuators: the amount of force developed by an actuator is proportional to the fluid pressure applied to it and the area of its piston or diaphragm.

•Pascal’s principle: changes in fluid pressure are transmitted evenly throughout an enclosed fluid volume. Relevant to fluid-powered valve actuators.

•Fluid seals: accomplished by maintaining tight contact between solid surfaces. Relevant to control valve plug and seat design, where even seating force is critical to maintaining tight shut-o . Also relevant to valve packing design.

•Conservation of energy: energy cannot be created or destroyed, only converted between di erent forms. Relevant to fluid velocities and pressures inside of a control valve.

of Energy Conservation, stating that the sum of all forms of energy in a moving fluid stream (height, kinetic, and pressure) must remain the same. Relevant to calculations of pressure drop and pressure recovery across control valve trim.

•Conservation of mass: mass is an intrinsic property of matter, and as such cannot be created or destroyed. Relevant to the Continuity Principle for moving fluids, where the mass flow rate of a fluid entering a control valve must equal the mass flow rate exiting the valve.

•Linear equations: any function represented by a straight line on a graph may be represented symbolically by the slope-intercept formula y = mx + b. Relevant to control valve positioners and split-ranging.

•Zero shift: any shift in the o set of an instrument is fundamentally additive, being represented by the “intercept” (b) variable of the slope-intercept linear formula y = mx + b. Relevant to control valve calibration: adjusting the “zero” of a valve positioner always adds to or subtracts from the valve stem position.

•Span shift: any shift in the gain of an instrument is fundamentally multiplicative, being represented by the “slope” (m) variable of the slope-intercept linear formula y = mx + b. Relevant to control valve calibration: adjusting the “span” of a valve positioner always multiplies or divides the stem stroke (compared to signal span).

•Deadband and hysteresis: the di erence in response with the independent variable increasing versus decreasing. Usually caused by friction in a mechanism. Relevant to control valve response: a control valve will not go to the same position with its command signal at

some value increasing as it does at that same value decreasing, due to friction in the trim and packing.

•Inverse mathematical functions: an inverse function, when applied to the result of its counterpart function, “un-does” the operation and leaves you with the original quantity. Relevant to control valve characterization, where the inherently nonlinear response of a control valve installed in a process with variable pressure drop is made to behave more linearly by skewing the shape of the valve trim in an inverse manner.

•Negative feedback: when the output of a system is degeneratively fed back to the input of that same system, the result is decreased (overall) gain and greater stability. Relevant to control valve positioners as well as self-actuated regulators.

•Self-balancing pneumatic mechanisms: all self-balancing pneumatic instruments work on the principle of negative feedback maintaining a nearly constant ba e-nozzle gap. Forcebalance mechanisms maintain this constant gap by balancing force against force with negligible motion, like a tug-of-war. Motion-balance mechanisms maintain this constant gap by balancing one motion with another motion, like two dancers moving in unison.

References

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Riveland, Marc, Fundamentals of Valve Sizing for Liquids, Technical Monograph 30, Fisher Controls International Inc., Marshalltown, IA, 1985.

Schafbuch, Paul, Fundamentals of Flow Characterization, Technical Monograph 29, Fisher Controls International Inc., Marshalltown, IA, 1985.

Warnett, Chris, Using Valve Actuators as Predictive Maintenance Tools for MOVs, Rotork Controls, Inc., Rochester, NY, 2000.

“Valve Sizing Technical Bulletin”, document MS-06-84-E, revision 3, Swagelok Company, MI, 2002.