Two-Phase Pressure Drop (Lockhart-Martinelli)

Estimate two-phase frictional ΔP from the single-phase liquid and gas drops using the Martinelli parameter and Chisholm two-phase multiplier.

InputX² = (ΔP_L)/(ΔP_G) , φ_L² = 1 + C/X + 1/X² , ΔP_TP = φ_L²·ΔP_L

Liquid-alone ΔP (kPa)or enter psi — converts to kPaGas-alone ΔP (kPa)or enter psi — converts to kPaChisholm C

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The engineering

The Lockhart-Martinelli method treats a two-phase gas-liquid pressure drop as the single-phase liquid drop scaled up by a two-phase multiplier φ². You compute the pressure gradient as if the liquid flowed alone and as if the gas flowed alone, form the Martinelli parameter X from their ratio, then apply the Chisholm correlation for φ². It is the workhorse first-pass estimate for horizontal two-phase lines where the phases are separated or intermittent.

Pick C from the flow regime of each phase: 20 for turbulent-turbulent (the common case in process lines), down to 5 for laminar-laminar. The gotcha is consistency — both single-phase drops must be evaluated for the actual mass flow of that phase through the full pipe, not a partitioned area. If X ≫ 1 the liquid dominates and φ_L² approaches 1; if X ≪ 1 the gas dominates.

Where this math comes from

R. W. Lockhart and R. C. Martinelli published their separated-flow correlation in 1949 at UC Berkeley, working from air-liquid data in small horizontal pipes. Their insight was to normalize the two-phase drop against the drop each phase would produce running alone, collapsing messy data onto a single parameter X that still bears Martinelli's name.

Duncan Chisholm gave the multiplier its convenient algebraic form φ² = 1 + C/X + 1/X² in 1967, tabulating C by the laminar/turbulent state of each phase. G. F. Hewitt and P. B. Whalley later folded the method into the standard multiphase-flow references used across the process and nuclear industries, where it remains a standard hand-check.

1949R. W. Lockhart & R. C. MartinelliPublish the separated-flow correlation and the Martinelli parameter X.
1967Duncan ChisholmCasts the two-phase multiplier as φ² = 1 + C/X + 1/X² with regime-based C.
1987P. B. WhalleyCodifies the method in 'Boiling, Condensation, and Gas-Liquid Flow' as a standard estimate.

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