Refrigerant Capillary Tube Calculator
An engineering estimator for adiabatic capillary tube length — R134a, R600a, R290, R404A, R32 — from cooling capacity, condensing / evaporating temperatures, and bore size. It uses a published homogeneous-equilibrium flow model with every assumption exposed below. It is not a substitute for vendor sizing software (see scope boundary).
Subcooling sensitivity
How the estimated length changes with liquid subcooling (same duty and bore):
| Subcooling | Est. length | Regime |
|---|
Standard bore comparison
Estimated length for common capillary bores at your duty. Rows highlighted red are far too restrictive; amber rows are choke-limited (normal for capillaries).
| ID (mm) | ID (inch) | Est. length | Regime |
|---|
How the math works
- Mass flow from the cycle.
ṁ = Q / Δh, withΔh = hg(Tevap) − (hf(Tcond) − cp,l·ΔTsub). Saturation enthalpies come from the curated internal tables below. - Single-phase leg. From the condensing pressure down to the flashing pressure
Psat(Tcond−ΔTsub), Darcy–Weisbach with the Churchill (1977) friction factor and a sharp-entrance lossK = 0.5. - Two-phase leg. The steady-flow momentum equation is marched in 300 pressure steps:
ΔL = (ΔP − G²·Δv)·2D / (fm·G²·vm). At each step the quality follows from the stagnation-enthalpy balanceh + G²v²/2 = const(50-iteration bisection), mixture viscosity from McAdams (1942), friction from Churchill on the mixture Reynolds number. - Choking. When
ΔP ≤ G²·Δvover a step, the Fanno maximum-entropy (sonic) point is reached: the march stops and the result is flagged choke-limited. The reported length is then the choking length — extending the tube further would reduce flow, not drop more pressure.
Assumptions and limits
- Adiabatic, horizontal, straight tube of constant bore; coiled tubes need a curvature correction (not applied).
- Homogeneous equilibrium flow: no slip between phases, no delayed (metastable) flashing. HEM is documented to predict choking conservatively (earlier than measured).
- Oil-free refrigerant; drawn-copper roughness 1.5 µm.
- Vapor specific volume from the ideal-gas relation (deviation up to ~15% near the dome at high pressure).
- R404A treated with bubble-line liquid / dew-line vapor properties (glide ≈ 0.75 K disclosed).
- R600a / R290 saturation enthalpies use the Watson (1943) latent-heat correlation fitted to published anchors, with linear liquid enthalpy and density — approximate, disclosed per refrigerant below.
- Valid input envelope: Tcond 20–65 °C, Tevap −40–15 °C, bore 0.5–3.0 mm, subcooling 0–15 K.
Property data sources
- R134a — Baehr (1994) international formulation, tabulated at 5 K steps; viscosity/cp representative textbook values.
- R32 — saturated tables (pressure, enthalpy, volume at 5 K steps), viscosity and cp at 25 °C from the manufacturer property overview.
- R404A — saturated tables (bubble/dew lines) from the manufacturer property overview.
- R600a — anchor at −40 °C from ASHRAE Handbook 2001 SI; saturation pressures from the published PT chart;
hfg(T) = 54.486·(134.7−T)0.38(Watson 1943, fitted to ASHRAE −40 °C and published 0/40 °C latent heats); linear liquid enthalpy/density. - R290 — anchor at −40 °C from ASHRAE Handbook 2001 SI; saturation pressures from the published PT chart;
hfg(T) = 65.843·(96.7−T)0.38(Watson 1943, fitted to ASHRAE −40 °C and published 0/40 °C latent heats); linear liquid enthalpy/density.
Method references: Wongwises & Pirompak, Flow characteristics of pure refrigerants and refrigerant mixtures in adiabatic capillary tubes, Applied Thermal Engineering 21 (2001); the HEM selection-chart paper validating against Mikol (1963), Wijaya (1992), Melo et al. (1999), Fiorelli et al. (2002), HVAC&R Research (2006); Churchill, Friction-factor equation spans all fluid-flow regimes, Chemical Engineering (1977); McAdams et al., Trans. ASME 64 (1942).
Scope boundary & engineering disclaimer
- This is an empirical estimator, not a substitute for vendor sizing software (Danfoss Coolselector, Emerson, Tecumseh data) or laboratory testing.
- Do not use it for safety-critical, medical, food-safety-critical, or large-charge systems without validation by a qualified refrigeration engineer.
- Flammable refrigerants (R290, R600a, R32/A2L): charge limits, ventilation, component approvals, and leak safety are governed by standards such as IEC 60335-2-24 / 2-89 and EN 378 — this tool covers thermodynamics only.
- Real installations differ through oil circulation, suction-line heat exchange, coiling, manufacturing tolerances on bore (±5% bore ≈ ±25% length), and charge variation. Always confirm the final capillary selection by test over the applicable temperature range.
Frequently asked questions
What is a capillary tube and how does it work?
A capillary tube is the simplest refrigeration expansion device: a long, narrow-bore copper tube, typically 0.5 to 2.5 mm inside diameter, connecting the condenser outlet to the evaporator inlet. High-pressure liquid refrigerant enters, loses pressure to wall friction, and begins flashing into vapor partway along the tube. That pressure drop meters the refrigerant flow automatically, with no moving parts and no adjustment. Because the flow depends on the coupled balance of friction and flashing, the length and bore must be matched to the refrigerant, the capacity, and the operating temperatures.
How do I size a capillary tube with this calculator?
Select the refrigerant, enter the required cooling capacity in W or BTU/h, the condensing and evaporating temperatures, the tube inside diameter, and the liquid subcooling. The tool first computes the required refrigerant mass flow from the cycle enthalpy difference, then marches a homogeneous-equilibrium flow model from the condensing pressure down to the evaporating pressure to find the tube length that develops that pressure drop. Use the standard-bore comparison table to try several diameters before choosing one.
What calculation method does this tool use?
A one-dimensional homogeneous-equilibrium model, or HEM: mass, stagnation-enthalpy, and momentum balances integrated in small pressure steps from condenser to evaporator pressure, following the formulation of Wongwises and Pirompak (2001). Single-phase friction uses the Churchill (1977) correlation with a sharp-entrance loss; two-phase friction uses Churchill on the mixture Reynolds number with the McAdams (1942) mixture viscosity. Flow is assumed adiabatic, horizontal, oil-free, and in thermodynamic equilibrium, with no delayed flashing. Choking is detected at the Fanno maximum-entropy point, where the flow reaches the local equilibrium speed of sound.
How accurate is the length estimate?
For R134a the underlying model was checked against published laboratory data: it reproduces the measured mass flow rates of Melo et al. (1999) within minus 8 percent to plus 1 percent and those of Wijaya (1992) within minus 9 percent, across several subcoolings. The same model family was validated to about plus or minus 15 percent against independent experiments in the source literature. Treat results as a plus-or-minus 20 to 30 percent engineering estimator, not a manufacturing specification, and always confirm the final selection by test, as the source papers themselves recommend.
What does 'choke-limited' mean in the results?
It means the refrigerant reaches sonic velocity before the end of the tube, so making the tube longer would reduce the flow instead of dropping more pressure; the reported length is the choking length. This is normal for capillary tubes, and most real capillaries operate choked or near-choked at the exit. A 'severely choked' flag, where choking occurs within the first half of the pressure drop, means the bore is far too small for the required duty: choose a larger inside diameter from the comparison table.
Which refrigerant needs the longest capillary tube?
It depends on the operating point, but as a rule the low-pressure refrigerants, R600a first and then R134a, need longer tubes than the high-pressure ones, R32, R404A, and R290, for the same duty and bore. Their larger specific volumes produce higher velocities and more friction per unit of mass flow. Use the comparison table to see the exact ranking for your temperatures, since the tool computes all five refrigerants consistently with the same model.
How does subcooling change the required length?
Increasing subcooling lengthens the tube required for a given mass flow: colder liquid starts flashing later, so a larger share of the fixed total pressure drop must be developed in the low-friction single-phase liquid region, which needs more meters per kilopascal than the high-friction two-phase region. Conversely, for a fixed tube, more subcooling increases the mass flow rate, which is why subcooling boosts the capacity of an existing system. The results panel shows the estimated length at 2, 5, and 8 K subcooling for your duty; typical design practice targets 3 to 8 K of subcooling.
Can this replace Danfoss Coolselector or other vendor sizing software?
No. Vendor tools are built on proprietary test data and additionally account for oil circulation, non-adiabatic heat-exchanger effects, and coil geometry, validated across thousands of operating points. This estimator is transparent and educational instead: every assumption is exposed and the method is published and cited. Use it for learning, quick feasibility checks, and understanding sensitivities, then validate the final selection with vendor software or laboratory testing, especially for production designs.
What bore size should I choose?
Start from the comparison table: bores that give 'friction-limited' or mildly 'choke-limited' results with practical lengths, roughly 1 to 5 m for small systems, are candidates. Avoid bores flagged 'severely choked', which are far too restrictive, and lengths above about 10 m or below about 0.2 m, which are impractical to coil or cut accurately. Standard capillary bores are sold in inch sizes such as 0.031 in (0.79 mm), 0.042 in (1.07 mm), 0.055 in (1.40 mm), and 0.064 in (1.63 mm); the table lists metric and inch equivalents.
Why does the tool say my bore is too small?
Because the required mass flow would choke almost immediately after flashing begins: the homogeneous choking criterion is met within the first half of the pressure drop, so no practical length of that bore can pass the flow. Physically, the vapor volume generated overwhelms the small cross-section. Increase the inside diameter; the required length grows steeply with bore, roughly with the fifth power of diameter for a fixed pressure drop, so the comparison table will show a longer but feasible tube.
How is the R404A temperature glide handled?
R404A is a zeotropic blend with about 0.75 K of glide. The tool uses bubble-line properties for the liquid on the condenser side and dew-line properties for the vapor on the evaporator side, following the ASHRAE convention for blends. The glide is small enough that the error from this treatment is negligible next to the model's overall uncertainty, and it is disclosed here rather than hidden.
Does the model account for compressor oil in the refrigerant?
No. The model assumes oil-free refrigerant, like the laboratory correlations it is built on. In real systems a small oil fraction circulates and slightly changes viscosity and pressure drop. For typical oil circulation rates of 1 to 3 percent the effect on capillary length is a few percent, well within this estimator's uncertainty band. Systems with oil separators or flooded operation need dedicated analysis.
Should I use a capillary tube or a thermostatic or electronic expansion valve?
Capillary tubes suit small, stable-load systems such as domestic refrigerators, bottle coolers, and small freezers: they are cheap, have no moving parts, and need no adjustment. They cannot adapt to varying loads or ambients, so the refrigerant charge must be correct. Thermostatic and electronic expansion valves suit larger or variable-load systems such as air conditioning and commercial refrigeration because they actively control superheat across conditions, at higher cost and complexity. This tool only sizes fixed-bore capillary tubes; it does not select expansion valves.
Are R290 and R600a safe to use? They are flammable.
R290 (propane) and R600a (isobutane) are ASHRAE safety class A3, meaning flammable. They are used safely in millions of factory-built appliances under standards such as IEC 60335-2-24 and IEC 60335-2-89, which limit charge sizes, commonly 150 g, and require specific construction and labeling. This calculator covers thermodynamics only: flammability, charge limits, ventilation, and leak safety must be handled per the applicable standards by qualified personnel. Never retrofit a flammable refrigerant into equipment that was not designed for it.
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