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API 682 Rotating Equipment, Centrifugal Pump Mechanical Seals & Tribology PV Limits

Mechanical Shaft Seal Balance Ratio, PV & Heat Formula

Calculate Net Seal-Face Contact Pressure Pf (MPa), Mean Sliding Velocity v (m/s), Tribological PV Factor (MPa·m/s), and Seal-Chamber Flush Heat Generation (W).

Put an unbalanced mechanical seal (B > 1.0) into a 18-bar boiler feed pump and fluid closing force boils the lubrication film dry in seconds!

API 682 rotary mechanical end-face seals ride on a sub-micron liquid film between a stationary carbon/SiC ring and a rotating SiC/WC mating ring of Contact Area `A_f` (mm²) and Mean Diameter `d_m` (mm). Hydraulic **Balance Ratio `B = A_closing / A_f`** (`~0.68–0.78` on stepped-sleeve balanced seals vs `1.10–1.25` on cheap unbalanced seals!) pitted against Fluid Film Pressure-Gradient Factor `k` (`~0.50` for linear non-flashing liquid drop) plus Mechanical Spring Pressure `P_sp` (MPa) determines Net Mechanical Face Contact Pressure `P_f = (B - k) * Delta_P + P_sp` (MPa)! Multiplying `P_f` by Mean Sliding Speed `v = (PI() * (d_m / 1,000) * RPM) / 60` (m/s) yields the critical Tribological `PV = P_f * v` (MPa·m/s) and Frictional Flush Heat Load `Q_seal = f * (P_f * 10^6) * (A_f * 10^-6) * v = f * P_f * A_f * v` watts—sizing the API Plan 11 / Plan 23 seal-flush cooler!

Verify on an API 682 Balanced SiC-vs-Carbon Pump Seal—Hydraulic_Balance_Ratio `B` = 0.72 (B2), Film_Gradient_Factor `k` = 0.50 (B3), Seal_Chamber_Differential `Delta_P` = 1.80 MPa (`18` bar, B4), Spring_Pressure `P_sp` = 0.18 MPa (B5 -> Net Face Contact `P_f = 0.576` MPa in E2), Mean_Face_Diameter `d_m` = 58.0 mm (B6), Pump_Speed = 2,950 RPM (B7 -> Sliding Speed `v = 8.96` m/s in E3), Seal_Face_Area `A_f` = 1,090.0 mm² (B8), and Mixed-Film_Friction `f` = 0.07 (B9): Face `PV` equals `5.16` MPa·m/s (E4), generating `393.7` W of face heat (E5)!

API 682 Mechanical Seal KPI (B=0.72, k=0.50, dP=1.80 MPa, dm=58 mm @ 2,950 RPM)FormulaVerified Output
Net Face Contact Pressure Pf (MPa)(Balance_B - Film_k) * dP_MPa + P_spring0.576 MPa (1.350 MPa @ unbalanced B=1.15!)
Mean Face Sliding Speed v (m/s)(PI() * (Mean_Diam_mm / 1000) * RPM) / 608.96 m/s
Tribological PV Factor (MPa·m/s)Net_Contact_Pf_MPa * Sliding_Speed_m_s5.16 MPa·m/s (12.09 @ unbalanced B=1.15!)
Frictional Face Heat Load (W)Friction_f * Pf_MPa * Face_Area_mm2 * v393.7 W (922.8 W vaporizes film @ B=1.15!)

API 682 Seal Balance Ratio, Face PV & Flush Heat Generation Formula

Validate `Balance_Ratio B` in `(0.55, 1.50]` (`B <= k` would pop the seal faces open under pressure spikes!), `Film_Factor k` in `[0.3, 0.8]`, `B > k`, `Delta_P >= 0` MPa, `Spring_Pressure > 0` MPa, `Mean_Diam > 10` mm, `RPM > 0`, `Face_Area > 50` mm², and `Friction f` in `(0.01, 0.30]`!

=LET(br_s, B2, kf_g, B3, dp_m, B4, ps_m, B5, dm_m, B6, nr_m, B7, af_m, B8, fr_c, B9, IF(OR(kf_g < 0.3, kf_g > 0.8, br_s <= kf_g, br_s > 1.5, dp_m < 0, ps_m <= 0, dm_m <= 10, nr_m <= 0, af_m <= 50, fr_c <= 0.01, fr_c > 0.3), "Invalid Seal Input", LET(pf_m, (br_s - kf_g) * dp_m + ps_m, vs_m, (PI() * (dm_m / 1000) * nr_m) / 60, ROUND(fr_c * pf_m * af_m * vs_m, 1))))

Unbalanced Seal (B = 1.15) High-Pressure Film-Flashing Failure Check (Set Balance Ratio B2 = 1.15)

Install a low-pressure unbalanced seal (`B` B2 = 1.15) in the same `18`-bar stuffing box: Net Face Pressure E2 more than doubles to `1.350` MPa, `PV` E4 surges to `12.09` MPa·m/s, and Face Heat Generation E5 jumps `+134%` to `922.8` W—flashing the liquid boundary layer into dry-running thermal shock cracks!

=IF(ISTEXT(E5), E5, LET(pf_m, (B2 - B3) * B4 + B5, vs_m, (PI() * (B6 / 1000) * B7) / 60, ROUND(pf_m * vs_m, 2)))

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