Hydraulic Pump Flow & Power Calculator — Displacement, Flow Rate (GPM/LPM) & Input Power (HP/kW)
Calculate hydraulic pump flow rate, input horsepower, and electric motor sizing. Includes volumetric and mechanical efficiency for gear, vane, and piston pumps.
Quick Answer
For a 45 cc/rev gear pump at 1800 RPM, 210 bar: Flow = 45 × 1800 / 1000 = 81 L/min (theoretical), Actual Flow ≈ 72.9 L/min (90% volumetric efficiency). Input Power = (72.9 × 210) / (600 × 0.85) ≈ 30 kW ≈ 40 HP. Use a 50 HP electric motor (next standard size, 25% margin).
Pump Sizing Fundamentals
The pump is the heart of a hydraulic system — undersize it and the machine is slow. Oversize it and you waste energy, generate heat, and pay too much.
1. Flow Rate
Q_theoretical = V_d × N / 1000 (L/min), where V_d=displacement (cc/rev), N=RPM. Actual flow: Q_actual = Q_theo × η_vol. Volumetric efficiency: gear pumps 85-92%, vane 90-95%, piston 92-97%. Internal leakage (slippage) increases with pressure and wear.
2. Input Power
P_input = (Q_actual × p) / (600 × η_overall) kW, where p=bar, η_overall = η_vol × η_mech. Mechanical efficiency: gear 85-90%, vane 88-93%, piston 90-95%. Overall efficiency: gear ~76%, vane ~85%, piston ~90%. Piston pumps are 15-20% more efficient than gear — less heat into the oil, smaller cooler.
3. Motor Sizing
Electric motor: round up P_input to next standard HP/kW size, add 10-25% margin. Diesel engine: derate 15% for continuous duty (diesel rated at intermittent). Direct drive (bell housing): check shaft torque. Belt drive: check pulley sizing and belt tension.
Common Mistakes
- Forgetting that flow drops as pressure increases — Internal leakage (slippage) increases with pressure. A pump delivering 100 L/min at 50 bar may deliver only 88 L/min at 250 bar. Size for flow at maximum operating pressure, not at low pressure. The flow loss is 0.5-2% per 10 bar for gear pumps, less for piston.
- Using pump displacement as system flow — A 45 cc pump at 1800 RPM is 81 L/min only if efficiency is 100%. Real flow with 90% volumetric efficiency is 73 L/min. Ignoring efficiency overestimates actuator speed by 11% — and your machine won’t meet cycle time.
- Running fixed-displacement pump with throttle control — Throttling excess flow across a relief valve at full pressure wastes power and heats oil fast. Power = p × Q_bypass / 600 kW. At 210 bar, bypassing 30 L/min wastes 10.5 kW (14 HP) — that’s a space heater in your hydraulic tank. Use variable-displacement or load-sensing instead.
- Not checking inlet (suction) conditions — Pump inlet velocity >1.2 m/s causes cavitation. Minimum inlet pressure: −0.2 bar(g) for gear/vane, −0.3 bar(g) for piston (pressurized inlet recommended above 1800 RPM). Cavitation sounds like gravel in the pump and destroys it in hours. Size inlet line one size larger than pressure line.
- Ignoring case drain flow when sizing tank — Piston pump case drain flow is 1-3% of total flow — hot, unfiltered oil returning directly to tank. For a 200 L/min system: 2-6 L/min to case drain. Account for this in tank return line sizing and cooling load.
Frequently Asked Questions
What pump type should I choose?
Gear (external): <210 bar, fixed displacement, low cost, low efficiency — general industrial, log splitters. Vane: <210 bar, fixed or variable, medium cost — machine tools, moderate duty. Axial piston: 210-450 bar, variable displacement, high cost, high efficiency — mobile equipment, presses, high power. Radial piston: 350-700 bar, highest cost, for extreme pressure. The pump type drives system efficiency and cost.
How do I convert between displacement units?
cc/rev to in³/rev: divide by 16.387. in³/rev to cc/rev: multiply by 16.387. Common displacements: 1 in³/rev ≈ 16.4 cc/rev. Flow: GPM = (cc/rev × RPM) / (3785 × η_vol). L/min = (in³/rev × RPM × 0.0164) × η_vol. Quick check: 45 cc/rev at 1800 RPM ≈ 21 GPM (theoretical at 100% eff).
What is load-sensing and why does it save energy?
Load-sensing (LS) pump adjusts displacement to maintain constant pressure drop (usually 15-25 bar) across the directional valve. The pump delivers exactly the flow demanded, at pressure just above the highest load. Unused flow = zero. Energy savings: 30-70% vs fixed pump with open-center valve. Payback on LS pump upgrade: typically <1 year for >15 kW systems.
How do I calculate the hydraulic reservoir (tank) size?
Rule of thumb: 2-3× pump flow per minute. 80 L/min system → 160-240 L tank. For mobile: 0.5-1× (space constrained, use oil cooler). For industrial: 3-5× (more thermal mass, less cooler dependence). Tank size is driven by: (1) Thermal capacity (cooling), (2) De-aeration (bubble rise time), (3) Contaminant settling. The 3× rule is for cooling.
How does pump speed affect life?
Pumps rated for specific RPM range. Below minimum: poor lubrication, metal contact. Above maximum: cavitation, rapid wear. Typical ranges — Gear: 500-3000 RPM. Vane: 600-1800 RPM (some to 2500). Piston: 500-3000 RPM (small), 600-1800 RPM (large). Running at max RPM continuously reduces life 2-3× vs 75% of max. Use 4-pole motors (1450/1750 RPM) for longest life.
What is the difference between open and closed loop hydraulic circuits?
Open loop: pump draws from tank, returns to tank — simple, most common, needs large tank for cooling. Closed loop (hydrostatic): pump to motor back to pump — compact, high efficiency, for vehicle propulsion and rotary drives. Closed loop needs charge pump (10-15% of main flow) to make up leakage. Closed loop is efficient but more expensive.
How do I calculate heat load and cooling requirements?
Heat load = input power − output power = P_input × (1 − η_overall). Example: 50 HP (37.3 kW) input at 80% overall efficiency = 7.5 kW heat. Tank cooling: ~0.5 kW per 100L of oil per 30°C temperature rise. For 7.5 kW heat load with 200L tank, you need an oil cooler (~5 kW additional cooling). Heat is the #1 cause of hydraulic system failure — don’t undersize cooling.
How do I select the right electric motor for a hydraulic power unit?
Standard: TEFC (Totally Enclosed Fan Cooled), NEMA Premium efficiency. Sizing: next standard HP above P_input. For 27.5 kW, use 30 kW (40 HP) motor — 50 HP is next standard with margin. Check starting method: DOL (Direct On Line) for <15 HP, soft start or VFD for >20 HP to limit inrush current. Bolt-on pump/motor bell housing with flexible coupling — check shaft alignment <0.05mm TIR.