Two-Phase Pressure Drop (Lockhart–Martinelli Approx.) Calculator

Calculator inputs

Enter pipe, fluid, and flow values. The result appears above this form after submission.

Mass flux, G (kg/m²·s)

Vapor quality, x (0 to 1)

Pipe length, L (m)

Hydraulic diameter, D (m)

Pipe roughness, ε (m)

Elevation change, Δz (m)

Liquid density, ρ_L (kg/m³)

Gas density, ρ_G (kg/m³)

Minor loss coefficient, K

Liquid viscosity, μ_L (Pa·s)

Gas viscosity, μ_G (Pa·s)

Plotly graph

The chart sweeps vapor quality from 0.01 to 0.99 using your current pipe and fluid properties.

Example data table

Example baseline: G = 350 kg/m²·s, L = 12 m, D = 0.020 m, ε = 0.000045 m, ρ_L = 950 kg/m³, ρ_G = 5.2 kg/m³, μ_L = 0.00028 Pa·s, μ_G = 0.000013 Pa·s, Δz = 0 m, K = 2.5.

Quality x	Frictional drop (kPa)	Total drop (kPa)	φL²	Martinelli X
0.10	29.74600	32.83577	31.59777	0.70031
0.30	78.53107	87.47803	132.66575	0.19155
0.50	119.51558	134.31973	373.03328	0.08528
0.70	152.07950	172.74084	1,186.01586	0.03869
0.90	168.69998	195.21850	12,367.48182	0.00984

Formula used

Single-phase basis for each phase:
ΔP_L = f_L(L/D)·(ρ_Lv_L²/2)
ΔP_G = f_G(L/D)·(ρ_Gv_G²/2)

Superficial phase velocities from mass flux:
v_L = G(1 − x) / ρ_L
v_G = Gx / ρ_G

Reynolds numbers:
Re_L = G(1 − x)D / μ_L
Re_G = GxD / μ_G

Darcy friction factor:
Laminar flow uses f = 64 / Re.
Turbulent flow uses the Churchill explicit correlation with pipe roughness.

Lockhart–Martinelli parameter and multipliers:
X = √(ΔP_L / ΔP_G)
φ_L² = 1 + C/X + 1/X²
φ_G² = 1 + CX + X²

Chisholm constant, C:
20 for turbulent–turbulent, 12 for laminar liquid–turbulent gas, 10 for turbulent liquid–laminar gas, and 5 for laminar–laminar.

Two-phase frictional pressure drop:
ΔP_friction = φ_L²·ΔP_L

Additional engineering terms used here:
ΔP_static = ρ_mixgΔz
ΔP_minor = K·G² / (2ρ_mix)
ΔP_total = ΔP_friction + ΔP_static + ΔP_minor

Void fraction and mixture density are approximated here with a simple homogeneous expression. That makes the added static and minor-loss terms convenient for screening calculations.

How to use this calculator

Enter total mass flux, vapor quality, and pipe length.
Enter hydraulic diameter and pipe roughness.
Enter liquid and gas densities and viscosities.
Add elevation change if the pipe rises or falls.
Enter the total minor loss coefficient for fittings and valves.
Click Calculate pressure drop.
Review total, frictional, static, and minor-loss contributions.
Use the chart to study quality sensitivity.
Download the current result set as CSV or PDF.

8 FAQs

1) What does this calculator estimate?

It estimates two-phase pipe pressure drop using a Lockhart–Martinelli frictional model, then adds optional static and minor-loss terms. The result is useful for quick screening, comparison studies, and preliminary sizing work.

2) What is the Lockhart–Martinelli parameter?

It is a dimensionless ratio built from the liquid-only and gas-only pressure-drop bases. In this calculator, X = √(ΔP_L/ΔP_G). It helps convert single-phase pressure drops into a two-phase friction estimate.

3) When is this approximation most useful?

It is most useful for fast engineering estimates in pipe flow where a classical separated-flow pressure-drop model is acceptable. It works well for sensitivity studies, early design checks, and order-of-magnitude comparisons.

4) Why can total drop differ from frictional drop?

The frictional term comes from the Lockhart–Martinelli approximation. Total pressure drop here also includes elevation effects and fitting losses. In horizontal systems with small K, total and frictional values may be very close.

5) Which inputs usually affect the result the most?

Mass flux, vapor quality, diameter, phase densities, and viscosities usually dominate the answer. Diameter is especially powerful because it changes Reynolds number, velocity, friction factor, and the basic single-phase pressure-drop levels.

6) Can I use x = 0 or x = 1?

Yes. The file handles those edge cases as liquid-only or gas-only flow. For actual two-phase Lockhart–Martinelli calculations, use a quality strictly between 0 and 1.

7) How is the flow regime selected?

Each phase Reynolds number is checked separately. A Reynolds number below 2300 is treated as laminar, and a higher value is treated as turbulent. That regime pairing selects the Chisholm constant C.

8) Is this valid for every vertical boiling or condensation case?

No. Real two-phase systems can involve acceleration, strong slip, heating, phase change, and regime transitions. For detailed design, compare this screening result with a more specialized correlation or a validated test dataset.

Engineering notes

This page is intended for preliminary engineering use.
The Lockhart–Martinelli part models frictional pressure drop, not full thermal-hydraulic behavior.
Use careful property data at actual operating temperature and pressure.
For strongly heated, condensing, or high-pressure systems, compare against a more specialized model.