Pressure Drop Calculations in Heat Exchangers

Pressure drop is a critical design parameter that affects pump/fan sizing, operating costs, and system performance. This guide covers calculation methods for various heat exchanger configurations.

Components of Pressure Drop

Total pressure drop consists of:

Frictional losses - Due to wall friction

Acceleration losses - Due to velocity changes

Gravitational losses - Due to elevation changes

Minor losses - Due to fittings, bends, etc.

Single-Phase Tube-Side

Darcy-Weisbach Equation

ΔP = f × (L/D) × (ρV²/2)

Friction Factor Correlations

Laminar flow (Re < 2300):
f = 64/Re

Turbulent flow (Blasius):
f = 0.316 × Re^(-0.25) for Re < 10^5

Turbulent flow (Colebrook-White):
1/√f = -2log(ε/3.7D + 2.51/Re√f)

Typical Design Values

Liquids: 10-50 kPa per pass

Gases: 1-5 kPa per pass

Two-Phase Pressure Drop

Homogeneous Model

Treats mixture as single fluid with average properties:
ΔP_tp = f_tp × (L/D) × (G²/2ρ_m)

Separated Flow Model (Lockhart-Martinelli)

ΔP_tp = ΔP_l × φ_l²

Where φ_l is the two-phase multiplier based on Martinelli parameter X.

Friedel Correlation

More accurate for refrigerants:
φ_lo² = E + 3.24FH / (Fr^0.045 × We^0.035)

Air-Side Pressure Drop

Plain Fins

ΔP = f × (A_o/A_c) × (ρV_max²/2)

Wavy/Louvered Fins

Use appropriate friction factor correlations from literature.

Typical Design Values

Evaporator coils: 50-150 Pa

Condenser coils: 30-100 Pa

Heating coils: 50-200 Pa

Shell-Side Pressure Drop

Bell-Delaware Method

Accounts for:

Cross-flow pressure drop

Window pressure drop

Baffle leakage effects

ΔP_s = ΔP_c × R_b × R_l + ΔP_w × N_b

Kern Method (Simplified)

ΔP_s = f × G_s² × D_s × (N_b + 1) / (2ρ × D_e × φ_s)

Minor Losses

K-Factor Method

ΔP = K × (ρV²/2)

Typical K values:

90° elbow: 0.3-0.9

Tee (branch): 1.0-1.5

Sudden expansion: (1 - A₁/A₂)²

Sudden contraction: 0.5(1 - A₂/A₁)

Equivalent Length Method

Convert fittings to equivalent pipe length:
L_eq = K × D / f

Design Considerations

Allowable Pressure Drops

ApplicationTube-sideShell/Air-side

Water systems35-70 kPa20-50 kPa
Refrigerant20-50 kPa30-100 Pa
Process fluids10-100 kPaVaries

Trade-offs

Lower ΔP = larger equipment, lower operating cost

Higher ΔP = smaller equipment, higher operating cost

Optimize for total cost of ownership

Conclusion

Accurate pressure drop calculations ensure proper system design and efficient operation. Consider all components and use appropriate correlations for the specific application.