fluid-power

name	fluid-power
description	Hydraulic and pneumatic systems — cylinder force/speed, pump displacement, actuator sizing, pressure relief valves, flow control, circuit design, accumulators, efficiency.
metadata	{"priority":6,"promptSignals":{"phrases":["hydraulic","pneumatic","hydraulic cylinder","hydraulic pump","fluid power","actuator","accumulator","pressure relief"],"minScore":4}}

Fluid Power (Hydraulics & Pneumatics) — Complete Skill

Hydraulic Cylinder

Force

Extend force: F_ext = p × A_bore = p × π×D_bore²/4 Retract force: F_ret = p × A_rod = p × π×(D_bore²-D_rod²)/4 Net force with back-pressure: F_net = p_supply×A_bore - p_back×A_rod

Speed

Extend velocity: v_ext = Q/A_bore [m/s or in/s] Retract velocity: v_ret = Q/A_rod (faster — smaller area) Flow required: Q = A × v

Power

P = F × v = p × Q [W, if p in Pa and Q in m³/s] Or: P = p × Q/1714 [hp, p in psi, Q in gpm]

Hydraulic Pump

Displacement and Flow

Displacement: V_d [cc/rev or in³/rev] Flow: Q = V_d × n × η_vol [L/min or gpm] η_vol = volumetric efficiency (typically 0.90-0.98) n = pump speed [rpm]

Common pumps: Gear pump: simple, noisy, lower efficiency (η_overall ≈ 0.75-0.82) Vane pump: medium, balanced, η ≈ 0.80-0.88 Piston (axial/radial): high pressure capable, η ≈ 0.88-0.94, variable displacement

Torque to Drive Pump

T = V_d × Δp/(2π × η_mech) [N·m] Power: P = T × ω = Q × p/η_overall

System Pressure

p_system = F_load/A_cylinder + p_losses p_losses = pipe friction + valve drops (typically 0.3-2 MPa total) Set relief valve: p_relief = p_system × 1.1-1.2

Accumulators

Bladder accumulator (common): Precharge pressure: p₁ = p_min × 0.9 (nitrogen gas) Usable volume: ΔV = V₀ × (p₁/p_max)^(1/γ) × (1 - (p_max/p_min)^(1/γ)) γ = 1.4 (adiabatic), γ = 1.0 (isothermal, slow discharge)

Applications: energy storage, dampening pulsations, emergency actuation

Flow Control Valves

Pressure compensated flow control: Q = C_v × √ΔP (constant regardless of load variation) Meter-in: flow control on actuator inlet (extends slower, cylinder can be pulled by external load) Meter-out: flow control on actuator outlet (safer — prevents runaway under external pull) Bypass (bleed-off): wastes less energy than meter-in/meter-out for light loads

Relief Valve

Cracking pressure: p_c = set point pressure Override pressure: p_full = p_c × (1 + 0.1-0.15) (fully open, 10-15% above cracking) Heat generation when relieving: P_heat = Q_relief × Δp_relief (all converted to heat)

Pneumatic Systems

Lower pressures (4-10 bar), compressible fluid — more complex transient analysis F = p × A × η_seal (seal friction reduces effective force, η ≈ 0.85-0.95) Flow: Q = C_v × p₁/16.04 × √((T₁)/(T_ref)) × Y × ... (more complex than hydraulic)

SCFM (standard cubic feet per minute): at 14.7 psi, 68°F Actual flow at p: Q_actual = Q_SCFM × (14.7/(p+14.7)) × ((T+460)/528)

Efficiency and Heat

Overall system efficiency: η_total = P_output/P_motor = η_pump × η_line × η_valve × η_cyl Typical η_total: 0.50-0.75 (much lower than electric motors at 0.90-0.97) Heat generation = P_motor × (1-η_total) Oil cooler required if: ΔT > 30°C above ambient (typical max: 60°C oil temp)

Pipe Sizing (Hydraulic)

Suction lines: V ≤ 1.0-2.0 m/s (prevent cavitation) Pressure lines: V ≤ 4-6 m/s (standard) or up to 8 m/s (high pressure systems) Return lines: V ≤ 2-4 m/s Q = A × V → D = √(4Q/(π×V))

Output

Provide: cylinder force [kN], speed [mm/s], pump displacement [cc/rev], pressure [MPa], flow [L/min], motor power [kW], heat load [kW].