Refrigerant Capillary Tube Calculator

Understanding the capillary tube calculator

A capillary tube is a fixed-restriction metering device used in refrigerators, freezers, window air conditioners, and other small sealed refrigeration systems. It is simply a long, narrow-bore copper tube installed between the condenser outlet and the evaporator inlet. As high-pressure liquid refrigerant is forced through the tiny bore, friction against the tube wall — and, further along the tube, flashing into vapor — drops the pressure down to evaporator pressure without any moving parts.

The formula

This calculator estimates the friction-driven pressure drop of the liquid refrigerant using the standard Darcy-Weisbach equation:

ΔP = f × (L / d) × (ρ × V² / 2)

where ΔP is the pressure drop, f is the Darcy friction factor, L and d are the tube length and inner diameter, ρ is the liquid density, and V is the flow velocity found from the mass flow rate divided by density and cross-sectional area (V = ṁ / (ρ × A)). The friction factor itself depends on the Reynolds number, Re = 4ṁ / (π × d × μ), where μ is the liquid's dynamic viscosity: for laminar flow (Re < 2300) it uses the Hagen-Poiseuille relation f = 64/Re, and for turbulent flow in a smooth tube it uses the Blasius correlation f = 0.316/Re^0.25.

Understanding the inputs

Tube diameter and length come from the physical capillary tube (or the size you are considering). Mass flow rate is set by the system's cooling capacity. Liquid density and viscosity are refrigerant-property values at the condensing temperature — check a refrigerant property table or manufacturer data sheet for the exact refrigerant in the system; the defaults shown are reasonable mid-range values for common HFC refrigerants near typical condensing conditions.

Interpreting the results

The pressure drop and velocity are the two practical outputs — a low velocity relative to the tube's expected range can signal an oversized bore, while a pressure drop far below the actual condenser-to-evaporator pressure difference is expected, because this model only accounts for single-phase liquid friction (see the FAQ below). Reynolds number tells you whether the flow is laminar or turbulent, which determines which friction factor formula applies; the friction factor itself is mainly useful for verifying the calculation by hand.

Frequently Asked Questions

What does a capillary tube do in a refrigeration system?

A capillary tube is a fixed-restriction metering device: a long, narrow-bore copper tube installed between the condenser outlet and the evaporator inlet. Its small diameter and length create the friction needed to drop high-pressure liquid refrigerant down to evaporator pressure, replacing a thermostatic expansion valve in simpler systems like refrigerators and window air conditioners.

What formula does this calculator use?

It applies the Darcy-Weisbach pressure drop equation for flow through a tube: pressure drop equals the friction factor times length-over-diameter times velocity-squared-times-density-over-two. The friction factor comes from the Hagen-Poiseuille relation (f = 64/Re) when flow is laminar, or the Blasius correlation (f = 0.316/Re^0.25) for turbulent flow in a smooth tube, where Re is the Reynolds number computed from the refrigerant's mass flow rate, tube diameter, and liquid viscosity.

Why might the real pressure drop across a capillary tube be higher than this result?

This calculator models single-phase liquid flow only. In an actual capillary tube, the refrigerant partially flashes into vapor partway along the bore as pressure falls below the saturation point, and that two-phase flow accelerates and adds extra pressure drop beyond simple liquid friction. Treat this result as the liquid-friction component of the restriction, useful for comparing tube sizes, not as a substitute for manufacturer selection charts or full two-phase design calculations.

How do tube diameter and length affect the pressure drop?

For a fixed mass flow rate, pressure drop scales roughly with length divided by diameter to the fifth power, because velocity itself scales with one over diameter squared. A small reduction in bore diameter produces a large increase in restriction, which is why capillary tubes are manufactured to tight diameter tolerances and why length is the easier dimension to adjust when fine-tuning a system's charge.