1. Linear Valve Physics: The Force Balance Equation

For globe and gate valves, the actuator must generate sufficient Thrust to overcome four primary opposing forces. The static force balance equation at the seat (Closed position) is:

$$ F_{total} = F_{unbalance} + F_{packing} + F_{seat} + F_{extra} $$

• Unbalance Force ($F_{unbalance}$): The force exerted by the process fluid pressure acting on the valve plug area.
  For an unbalanced single-seated valve: $F_{unb} = Area_{seat} \times \Delta P_{shutoff}$.
  Flow Direction: In Flow-to-Open (FTO), fluid pressure assists opening and opposes closing. In Flow-to-Close (FTC), fluid pressure assists closing (suction effect) but opposes opening. Sizing is always done for the worst-case direction (opposing).
• Packing Friction ($F_{packing}$): Friction from the stem seal.
  PTFE (Teflon): Low friction (~50-100 lbs/inch stem dia).
  Graphite: High friction (~300-500 lbs/inch stem dia). Used for high-temperature service (>400°F).
  Fluid Factor: Slurries or viscous fluids can increase this friction by 50-100% due to stem coating.
• Seat Load ($F_{seat}$): The contact force required to deform the gasket/seat ring to achieve the specified leakage class (FCI 70-2).
  Class IV (Metal): Standard for control. Req ~50 lbs/linear inch of seat circumference.
  Class VI (Soft): Bubble-tight. Req ~30 lbs/inch but limited by temp.

2. Rotary Valve Physics: Torque Dynamics

Quarter-turn valves (Ball, Butterfly, Plug) require Torque rather than thrust. The physics are more complex due to the geometry.

$$ T_{total} = T_{bearing} + T_{packing} + T_{seat} + T_{hydro} $$

• Bearing Torque ($T_{bearing}$): Friction in the shaft bearings caused by the pressure drop pushing the ball/disc against the downstream bearing.
  $T_{bearing} = F_{pressure\_load} \times R_{shaft} \times \mu_{bearing}$
  Where $F_{pressure\_load} \approx \Delta P \times Area_{projected}$.
• Seat Torque ($T_{seat}$): Friction between the ball/disc and the seat ring. This is highest at "Breakout" (closed position) and decreases once moving ("Run Torque").
  Floating Ball: High seat torque as line pressure pushes the entire ball into the downstream seat.
  Trunnion Ball: Lower seat torque as bearings take the pressure load.
• Hydrodynamic Torque ($T_{hydro}$): As fluid flows over a butterfly disc, it creates an airfoil lift effect that tries to close the valve. This dynamic torque peaks around 60-70 degrees open. Actuators must be sized to handle both the static breakout torque AND this dynamic running torque.

3. Actuator Mechanics: Bench Set vs. Supply

Bench Set: The range of pressure required to stroke the actuator spring with no valve forces applied (on the bench). For a 6-30 psi bench set:
- At 6 psi, the spring just begins to compress.
- At 30 psi, the spring is fully compressed.

For an Air-to-Open (Fail Closed) valve, the closing force is provided entirely by the spring.
Seating Force = Spring Preload = Min Bench Set × Diaphragm Area.
If you need more closing force, you need a higher minimum bench set (e.g., 10-30 instead of 6-30), which requires a stronger spring.

For an Air-to-Close (Fail Open) valve, the closing force is provided by Air Pressure fighting the Spring.
Seating Force = (Supply Pressure × Area) - (Max Bench Set × Area).
Ideally, Supply Pressure should be at least 5-10 psi higher than the Max Bench Set to ensure positive seating.

4. Fluid Service Factors

Standard calculations assume clean water/air. Real-world fluids behave differently.

• Clean Liquid/Gas (1.0): Baseline friction.
• Dry Gas/Steam (1.2): Lack of lubrication increases friction in metal bearings and graphite packing.
• Slurry/Paste (1.5 - 2.0): Particulates get embedded in soft seats and packing, drastically increasing torque and wear. High safety factors are mandatory.

5. Safety Margins & Sizing Criteria

Safety Factor (SF):
- Control Valves: Typically 1.3 (30% margin). This ensures smooth throttling without stick-slip.
- On/Off Valves: Typically 1.5 to 2.0. Since they sit static for long periods, "stiction" (static friction) build-up is significant.
- Emergency Shutdown (ESD): Often 2.0 to 3.0 to guarantee movement under fire/accident conditions.