Gear Pump Calculator
Upgrade positive displacement calculations. Compute gear pump displacement (cc/rev, in³/rev), flow rates (GPM, LPM), hydraulic input power, shaft torque, volumetric slippage losses, and efficiency curves.
Gear Pump Sizing & Performance Calculator
How to Size a Gear Pump
Sizing a positive displacement gear pump requires matching target flow rates to operating speed RPM while ensuring driver torque tolerances are not exceeded.
- 1Identify Flow Demand: Estimate the required flow rate in GPM or LPM under full load.
- 2Select Speed: Determine drive motor RPM (typically 1200 or 1800 RPM).
- 3Calculate CC Sizing: Compute required displacement in cc/rev or in³/rev.
- 4Determine Torque & Power: Select standard electric motor drivers to handle pressure spikes.
Gear Pump Displacement
Displacement describes the theoretical fluid volume swept per revolution of the gear pump meshes. Standard ratings are in cc/rev or cubic inches per revolution (in³/rev). Volumetric displacement directly dictates flow output capacities:
Selecting pump displacements from catalogs accounts for internal leakage slippage at maximum pressures.
Gear Pump Flow Rate
Unlike centrifugal pumps, positive displacement gear pumps deliver output flows directly proportional to operating speed RPM, minus high-pressure fluid slippage:
Using 231 as the conversion constant for in³/rev to GPM, or 3785.4 for cc/rev to GPM, facilitates direct performance verification.
Gear Pump CC Calculator
Sizing in cubic centimeters (cc/rev) identifies the exact metric capacity of external or internal gear pumps. The CC rating dictates required casing clearances, adapter flanges, and motor coupling torque needs.
Gear Pump GPM Calculator
GPM capacities describe the actual volumetric output delivered under load. Tracking GPM versus RPM speeds verifies volumetric wear or internal slippage losses.
Gear Pump Power
Input torque and brake horsepower BHP are dictated by system pressure. Gear pumps require high torque during initial starts because fluids must be pushed out against full pressure heads:
Sizing must include motor safety margins to prevent stalling during maximum system load spikes.
Gear Pump Efficiency
Evaluating volumetric, mechanical, and overall efficiencies locates leakage pathways within side plates and gear tolerances:
Overall efficiency values represent the product of volumetric slippage and mechanical friction losses.
Engineering Formulas
Review the primary mathematical models used in our calculations:
- Theoretical GPM Flow: Q_theor = (Disp_cc × RPM) / 3785.4
- Volumetric slippage: Q_slip = Q_theor × (1 − Eff_vol)
- Shaft Input Torque (Nm): Torque = (9550 × Power_kW) / RPM
- Input Torque (lb-ft): Torque_in_lb = (Disp_in3 × Pressure_psi) / (2π × Eff_mech)
Worked Examples
Review these step-by-step sizing scenarios for hydraulic gear pumps.
Example 1: Hydraulic Power Unit
Sizing a gear pump to deliver 15 GPM at 3,000 PSI system pressure. The drive speed is 1,800 RPM. Volumetric efficiency is 90% and mechanical efficiency is 85%.
2. Convert to metric = 2.14 × 16.387 = 35.1 cc/rev.
3. Hydraulic power output = (15 × 3000) / 1714 = 26.3 HP.
4. Shaft BHP = 26.3 ÷ (0.90 × 0.85 Overall Efficiency) = 34.4 HP. Select: 40 HP standard motor.
Example 2: Industrial Hydraulic Press
A 45 cc/rev gear pump runs at 1,500 RPM under 210 bar (3045 PSI) load pressure. Volumetric efficiency is 88%.
2. Actual flow GPM = 17.8 × 0.88 = 15.7 GPM.
3. Hydraulic Power HP = (15.7 × 3045) / 1714 = 27.9 HP.
Example 3: Mobile Hydraulic Equipment
Sizing a gear pump for a tractor loader requiring 12 GPM flow at 2,500 PSI, driven directly from a power take-off (PTO) shaft spinning at 1,000 RPM.
2. Select: 3.3 in³/rev (54 cc/rev) external gear pump.
Example 4: Injection Molding Machine
Testing volumetric efficiency: theoretical flow is calculated at 24.5 GPM, but actual measured flow at 2,000 PSI is 20.8 GPM.
2. Volumetric slip loss = 24.5 − 20.8 = 3.7 GPM.
Example 5: Gear Pump Selection
A lubrication loop requires a small gear pump delivering 3 GPM at 150 PSI, driven by a 1,725 RPM motor.
2. HP required = (3 × 150) / (1714 × 0.75 overall) = 0.35 HP. Select: 0.5 HP motor.
Reference Tables
Use these reference tables for lookup estimates during gear pump design calculations.
1. Typical Gear Pump Sizes (Displacements vs. Maximum Pressures)
| Group Size | Displacement Range (cc/rev) | Displacement (in³/rev) | Max Pressure Rating |
|---|---|---|---|
| Group 1 | 1.0 − 8.0 cc | 0.06 − 0.49 in³ | 3,600 PSI (250 bar) |
| Group 2 | 4.0 − 28.0 cc | 0.24 − 1.70 in³ | 4,000 PSI (280 bar) |
| Group 3 | 22.0 − 90.0 cc | 1.34 − 5.49 in³ | 3,600 PSI (250 bar) |
| Group 4 | 80.0 − 200.0 cc | 4.88 − 12.20 in³ | 3,000 PSI (210 bar) |
2. Standard Pump Displacement Table (Metric & Imperial)
| cc/rev rating | in³/rev rating | Flow GPM at 1800 RPM (90% Vol) | Flow LPM at 1800 RPM (90% Vol) |
|---|---|---|---|
| 4.0 cc | 0.24 in³ | 1.7 GPM | 6.5 LPM |
| 10.0 cc | 0.61 in³ | 4.3 GPM | 16.2 LPM |
| 25.0 cc | 1.53 in³ | 10.7 GPM | 40.5 LPM |
| 50.0 cc | 3.05 in³ | 21.4 GPM | 81.0 LPM |
3. Torque Reference Table (at 1000 PSI, 100% Mech Eff)
| Pump CC Sizing | Displacement in³ | Torque (lb-in) | Torque (Nm) |
|---|---|---|---|
| 10 cc/rev | 0.61 in³/rev | 97 lb-in | 11.0 Nm |
| 25 cc/rev | 1.53 in³/rev | 243 lb-in | 27.5 Nm |
| 50 cc/rev | 3.05 in³/rev | 485 lb-in | 54.8 Nm |
4. Typical Gear Pump Efficiencies
| Pressure Range | Volumetric Efficiency | Mechanical Efficiency | Overall Efficiency |
|---|---|---|---|
| Shallow / Low (under 500 PSI) | 92% − 96% | 88% − 92% | 80% − 88% |
| Medium (500 − 2000 PSI) | 88% − 92% | 85% − 88% | 75% − 81% |
| High (2000 − 4000 PSI) | 82% − 88% | 80% − 85% | 65% − 75% |
5. Hydraulic Oil Densities & Viscosities (at 40°C)
| Fluid Category | ISO Grade | Density (kg/m³) | Viscosity (cSt) |
|---|---|---|---|
| Hydraulic Fluid 32 | ISO VG 32 | 870 kg/m³ | 32 cSt |
| Hydraulic Fluid 46 | ISO VG 46 | 875 kg/m³ | 46 cSt |
| Hydraulic Fluid 68 | ISO VG 68 | 880 kg/m³ | 68 cSt |
Quick Hydraulic Unit Converters
cc/rev to in³/rev Converter
GPM to LPM Converter
Nm to lb-ft Converter
PSI to Bar Converter
Applications
Gear pumps support many hydraulic systems:
- Hydraulic Power Units: Fixed displacement supply systems.
- Construction Machinery: Heavy loader arm operations.
- Agricultural Equipment: Tractor steering and attachment hydraulic loops.
- Lubrication Loops: Low-pressure continuous oil feeds.
Frequently Asked Questions
Displacement equals Flow Rate divided by the product of motor RPM speed and volumetric efficiency. Convert GPM to cubic inches or cc/rev for sizing catalog lookups.
Flow GPM equals: (Displacement cc/rev × RPM × Volumetric Efficiency) / 3785.4.
Flow is proportional to speed: Q = Displacement × RPM × Volumetric Efficiency.
Sizing matches required GPM flow and system operating pressures at target RPM motor speeds, ensuring driver torque limits are not exceeded.
Hydraulic Power HP equals GPM multiplied by pressure PSI, divided by 1714.
Use the formula: Torque (N·m) = (9550 × Power kW) / RPM or Torque (lb-in) = (Displacement in³ × Pressure PSI) / (2π × Mech Efficiency).
