Hydraulic Formulas and Calculations: Power, Flow, Force and Speed Explained

Hydraulic Formulas and Calculations Power, Flow, Force and Speed Explained

Table of Contents

What is This Page?

This page collects the hydraulic formulas engineers use every day. Each equation is shown with units that match industry practice, followed by small examples you can adapt to your system.

Key Formulas

  • Pressure–Force–Area (imperial): p(psi) = F(lbf) / A(in²); F = p × A; A = F / p
  • Hydraulic power: hp = p(psi) × Q(gpm) / 1714; kW = Q(l/min) × p(bar) / 600
  • Pump flow: Q(gpm) = n(rpm) × D(in³/rev) / 231; Q(l/min) = D(cm³/rev) × n(rpm) / 1000
  • Motor torque: T(in‑lb) = p(psi) × D(in³/rev) / 6.28; T(Nm) = D(cm³/rev) × p(bar) / (20π)
  • Cylinder area: A = πd²/4; Rod side area = Apiston − Arod
  • Cylinder force: F = p × A
  • Cylinder speed: v(ft/min) = 19.25 × Q(gpm) / A(in²); or v = Q/A in consistent units
  • Line velocity guideline: v(ft/s) = Q(gpm) × 0.3208 / A(in²)
  • Heat equivalence: 1 hp = 2545 BTU/hr ≈ 746 W

Worked Examples

  1. Hydraulic power at 150 bar and 20 L/minPh(kW) = Q × p / 600 = 20 × 150 / 600 = 5 kW (≈ 6.7 hp)
  2. Cylinder thrust with 50 mm bore at 140 barArea = π × (0.05 m)² / 4 = 0.001963 m²Force = 14 MPa × 0.001963 m² ≈ 27.5 kN
  3. Motor torque, D = 25 cm³/rev, p = 140 barT = D × p / (20π) = 25 × 140 / 62.832 ≈ 55.7 Nm
  4. Hose velocity check, Q = 30 L/min (≈ 7.93 gpm), 1/2 in IDA = π × (0.5 in)² / 4 = 0.196 in²v = 7.93 × 0.3208 / 0.196 ≈ 13.0 ft/s

How to Size an HPU (Five Steps)

  1. Define duty: cycle time, peak pressure, ambient temperature.
  2. Compute actuator area and force from required load; set design pressure with 10–20% margin.
  3. Derive flow from target speed and area; convert to pump displacement with expected rpm.
  4. Estimate hydraulic power from p and Q; apply overall efficiency to select drive motor.
  5. Check line velocity and heat load; size reservoir and cooling accordingly.

Frequently Asked Questions

What is the hydraulic horsepower formula?

hp = p(psi) × Q(gpm) / 1714. For metric systems, kW = Q(l/min) × p(bar) / 600.

How do I calculate cylinder speed?

Divide flow by piston area in consistent units. In imperial, v(ft/min) = 19.25 × Q(gpm) / A(in²).

How do I find motor torque from pressure and displacement?

Use T(in‑lb) = p(psi) × D(in³/rev) / 6.28 or T(Nm) = D(cm³/rev) × p(bar) / (20π).

What are typical hose velocity limits?

Pressure lines are commonly kept near 10–20 ft/s; suction lines are much lower. Always verify against your component specs.

How do I estimate heat load from a pressure drop?

Power lost (hp) ≈ Δp(psi) × Q(gpm) / 1714, then convert to BTU/hr or watts.

Share the Post:

Hydrath Power

Hydrath Power is your professional hydraulic power pack partner in China, ready to answer your questions about hydraulic power packs and components like manifold blocks and hydraulic cartridge valves. If you need any support or guidance, please feel free to contact Hydrath Power directly.

Related Posts

Looking for Reliable Hydraulic Solutions?

Let Our Engineering Experts Support You – Anytime.
Get A Free Quote
Scroll to Top

Contact Us