Engineering & Science
Petukhov Smooth-Pipe Darcy Friction Factor & Turbulent Nusselt Formula
Cut turbulent heat-exchanger tube error from ±25% (Dittus-Boelter) down to ±5% using Boris Petukhov’s (1970) momentum-heat analogy Nu_D and explicit Darcy friction factor f = (0.790 * LN(Re) - 1.64)^(-2).
Why modern heat-transfer textbooks replace Dittus-Boelter with Petukhov’s friction-coupled analogy!
Classic Dittus-Boelter (0.023 * Re^0.8 * Pr^n) can err by up to 25% across liquid cooling loops! Boris S. Petukhov (Advances in Heat Transfer, 1970) coupled turbulent eddy diffusivity directly to smooth-tube Darcy friction factor f = (0.790 * LN(Re_D) - 1.64)^(-2) over fully turbulent flow 10^4 <= Re_D <= 5 × 10^6 and 0.5 <= Pr <= 2000: Nu_D = ((f / 8) * Re_D * Pr) / (1.07 + 12.7 * SQRT(f / 8) * (Pr^(2/3) - 1)), achieving ~5% accuracy across gases, water, and thermal oils!
Check cooling water at 40 °C (Pr = 4.34) inside a smooth condenser tube at Re_D = 50,000: Petukhov explicit Darcy friction factor f = 0.02096 yields Nu_D = 264.47, rising to Nu_D = 471.49 when pump flow doubles to Re_D = 100,000!
| Tube Reynolds Number Re_D (Water Pr = 4.34) | Petukhov Darcy Friction f | Petukhov Nusselt Nu_D | Regime Check |
|---|---|---|---|
| Re_D = 50,000 (Standard Exchanger Tube) | 0.02096 | 264.47 | Fully Turbulent (Re >= 10,000) |
| Re_D = 100,000 (High-Velocity Pass) | 0.01799 | 471.49 | +78.3% Convective Conductance |
| Re_D < 10,000 or Pr < 0.5 | Out of Range | "Outside Petukhov Turbulent Range" | Validity Guard |
Petukhov Fully Turbulent Smooth-Tube Nusselt Number Nu_D
Evaluates ((f / 8) * Re * Pr) / (1.07 + 12.7 * SQRT(f / 8) * (Pr^(2/3) - 1)) with f = (0.79 * LN(Re) - 1.64)^(-2) for Re_D >= 10,000 (B2) and Pr >= 0.5 (B3).
=IF(OR(B2 < 10000, B3 < 0.5), "Outside Petukhov Turbulent Range", ROUND((((((0.79 * LN(B2) - 1.64) ^ (-2)) / 8) * B2 * B3) / (1.07 + 12.7 * SQRT(((0.79 * LN(B2) - 1.64) ^ (-2)) / 8) * ((B3 ^ (2 / 3)) - 1))), 2))Petukhov Explicit Smooth-Pipe Darcy Friction Factor f
Computes (0.790 * LN(Re_D) - 1.64)^(-2) without iterative Colebrook-White solving.
=IF(B2 < 10000, "Outside Petukhov Turbulent Range", ROUND((0.79 * LN(B2) - 1.64) ^ (-2), 5))Try the example
Use the original values or change them to test your understanding.