Mechanical Face-Seal Calculator
Engineering screening tool—verify inputs and results independently. Use at your own risk.
Estimate closing pressure, liquid leakage, viscous friction, sliding speed, and heat generation for a parallel mechanical face seal.
Seal operating inputs
Positive net closing pressure used to normalize viscous friction.
How to use
- Use the single Liquid-film face seal mode for concentric, nominally parallel annular faces with a Newtonian liquid film.
- Enter the non-negative sealing pressure difference Δp=p₁−p₂ and spring pressure pᶠ in MPa.
- Enter balance ratio k and pressure-gradient factor k₁. Use k₁=0.5 only for a parallel-film pressure distribution.
- Enter rᵢ and rₒ in metres, with rₒ>rᵢ; enter non-negative speed n in rpm, positive film thickness h in µm, and positive dynamic viscosity η in Pa·s.
- Select Calculate; results also update while editing. Correct red validation messages and review amber range warnings.
- Read pᴳ as net closing pressure, Q as outward leakage, v as mean sliding speed, µ as an apparent viscous friction coefficient, and N as heat generated in the film.
- Select Reset example to restore the documented 2 MPa, 7000 rpm worked case.
- Do not use the model when faces are contacting, distorted, grooved, cavitating, thermally wedged, transient, gas-lubricated, or outside the constant-viscosity laminar full-film assumptions. Do not use screening results alone for seal qualification or safety decisions.
Worked example
1. Enter Δp=2 MPa, k=0.9, k₁=0.5, pᶠ=0.4 MPa, rᵢ=0.014 m, rₒ=0.0165 m, n=7000 rpm, h=1 µm, and η=0.001 Pa·s. 2. Calculate. Expected pᴳ=1.20000 MPa, Q=0.0229965 L/h, v=11.1788 m/s, µ=0.00931569, and N=29.9352 W. 3. The low predicted leakage and power apply only if a stable 1 µm liquid film and the specified viscosity are physically sustained.
Theory and method
The calculation combines a closing-pressure balance, a parallel-gap laminar leakage estimate, and Couette shear over an annular face. Positive Δp=p₁−p₂ denotes pressure falling from the sealed medium toward the downstream side; n is a non-negative speed magnitude. Leakage Q is positive in the same high-to-low direction. The model uses SI units internally.
Equations used
Net surface pressure is pᴳ=Δp(k−k₁)+pᶠ, where k=Aᴴ/A is the balance ratio, Aᴴ is the effective hydrostatic closing area, A is the annular seal-face area, k₁ is the dimensionless mean film-pressure factor, and pᶠ is spring load per seal-face area. For the documented parallel liquid film, k₁=0.5. Geometry is rₘ=(rₒ+rᵢ)/2, Lₘ=2πrₘ, Δr=rₒ−rᵢ, and A=π(rₒ²−rᵢ²).
Parallel-film leakage is Q=h³ΔpLₘ/(12ηΔr) in m³/s, converted to L/h by multiplying by 3.6×10⁶. Angular speed is ω=2πn/60 and mean sliding speed is v=ωrₘ. Viscous friction force is Fᶠ=ηvA/h; closing force is F=pᴳA; apparent friction coefficient is µ=Fᶠ/F; and heat generation is N=Fᶠv. Calculations retain floating-point precision with no intermediate or output rounding; displayed values use six significant digits.
Definitions, assumptions, and limits
Δp and pᶠ are entered in MPa; rᵢ and rₒ in m; n in rpm; h in µm; η in Pa·s. Typical guidance is 0.65<k<0.90, parallel-film k₁=0.5, and 0.1<pᶠ<0.5 MPa. The model assumes rigid aligned faces, uniform h, Newtonian constant η, steady laminar isoviscous flow, and full-film viscous shear. It excludes grooves, waviness, thermoelastic deformation, cavitation, vaporization, mixed contact, startup, pressure/temperature-dependent viscosity, and secondary-seal behavior.
References and next steps
Method reference: A. van Beek, Advanced Engineering Design, Mechanical seals calculation C10.1/e11_1. For detailed design, verify material, thermal, deformation, stability, wear, emissions, and applicable seal standards with supplier data and independent analysis.
Continue in TriboSolver to refine film behavior or independently compare a lubricated-contact model. Related tool: Dynamic O-Ring Piston and Rod Seal Calculator.