Units:
Inputs
Current units: SI
Inner diameter (e.g., 0.05)
Total of both phases
Water ~ 958 at 100°C
Steam ~ 0.6 at 100°C
Positive upward adds pressure drop
Enter sum of K for fittings
Typical: LL=5, LT=10, TL=12, TT=20
Key Results
Pressures in Pa and psi; gradients in Pa/m
ΔP Total: —
ΔP Friction: —
ΔP Static: —
ΔP Minor: —
Mode: —
Mini Flow Map (Heuristic)
Axes in superficial velocities (m/s). Marker shows current jg and jl.
Flow-Pattern Hint (Heuristic)
Based on superficial velocities jl, jg and Martinelli X.
Detailed Steps & Formulas
Method: Lockhart–Martinelli with Chisholm parameter C. Compute single-phase friction gradients for liquid-only and gas-only at their portion of mass flux, then apply two-phase multiplier.
Single-phase preliminaries
- Area
A = π D²/4, total mass fluxG = ṁ/A - Liquid mass flux
G_l = G(1−x), Gas mass fluxG_g = Gx - Velocities alone (superficial):
V_lo = G_l/ρ_l,V_go = G_g/ρ_g - Reynolds numbers:
Re_l = G_l D/μ_l,Re_g = G_g D/μ_g - Churchill friction factor (Darcy):
f = 8 [ (8/Re)^{12} + 1/(A+B)^{1.5} ]^{1/12},A = [2.457 ln((7/Re)^{0.9} + 0.27 ε/D)]^{16},B = (37530/Re)^{16} - Single-phase gradients:
(dp/dz)_lo = f_l (ρ_l V_lo²)/(2D),(dp/dz)_go = f_g (ρ_g V_go²)/(2D)
Two-phase multiplier
- Martinelli parameter:
X = √( (dp/dz)_lo / (dp/dz)_go ) - Chisholm form:
φlo² = 1 + C/X + 1/X² - Frictional gradient:
(dp/dz)_{tp} = φlo² (dp/dz)_lo - Frictional drop:
ΔP_f = (dp/dz)_{tp} L - Mixture density (homogeneous with α from x):
α = 1 / [1 + ((1−x)/x)(ρ_g/ρ_l)],ρ_m = α ρ_g + (1−α) ρ_l - Static head:
ΔP_s = ρ_m g Δz; Minor:ΔP_m = K_Σ (ρ_m V_m²/2),V_m = G/ρ_m - Total:
ΔP = ΔP_f + ΔP_s + ΔP_m
Example Data (click “Load” to populate)
| Load | D | L | ε | ṁ | x | ρl | μl | ρg | μg | Δz | KΣ | Mode |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.05 | 30 | 0.000045 | 0.5 | 0.10 | 958 | 0.00028 | 0.6 | 1.3e-5 | 5 | 2 | auto | |
| 0.025 | 12 | 0.000015 | 0.25 | 0.30 | 900 | 0.001 | 2 | 1.8e-5 | 0 | 1 | tt | |
| 0.1 | 50 | 0.00026 | 1.2 | 0.05 | 970 | 0.0006 | 1 | 1.5e-5 | -3 | 4 | manual |
How to Use
- Choose your preferred unit system at the top.
- Enter pipe diameter, length, roughness, flow rate, and gas quality.
- Provide liquid and gas densities and viscosities at operating conditions.
- Set elevation change and total minor-loss coefficient if applicable.
- Choose C handling: automatic by Reynolds, forced TT, or manual value.
- Click Calculate or try Quick TT-only for TT mode.
- Export results via Download CSV or Download PDF.
Heuristic flow-pattern hints use superficial velocities and X dominance; consult detailed maps for design-critical decisions.
FAQs
Inputs display in SI or US units. Internally, calculations use SI after conversion. Outputs show Pa and psi so you can cross-check readily.
It forces turbulent–turbulent assumption (C=20) immediately and calculates. Useful for first-pass screening when both phases are expected turbulent.
They are rule-of-thumb suggestions based on superficial velocities and Martinelli dominance. For critical designs, use detailed maps or experiments.
Churchill’s explicit correlation covers laminar through turbulent regimes and includes roughness effects. The result is the Darcy friction factor.
Yes. Choose “Manual C” and enter your value based on data, standards, or conservative practice.
No. The calculator focuses on frictional losses and adds static and minor terms. Include acceleration effects separately when flashing or significant quality change occurs.
CSV and PDF include SI values; key pressures also appear in psi for convenience.