Calculation of the capillary tube of the refrigerator: exact formula and table

Replacement capillary tube in a household refrigerator is one of the most difficult and important operations that a technician faces when repairing a refrigeration unit. Unlike industrial equipment, where throttling parameters are often adjusted, in home equipment, the length and internal diameter of the tube are the only factors that ensure the correct pressure ratio in the circuit. An error in the calculations at this stage can lead to the compressor working with overload, and the temperature in the chambers will not drop to the required values.

The main function of this element is to create hydraulic resistancewhich is necessary to divide the circuit into a high and low pressure zone. It is thanks to this resistance that the refrigerant, leaving the condenser, is throttled, expands sharply and boils at a low temperature, absorbing heat from the evaporator. An incorrectly selected length or diameter will lead to an imbalance in mass flow, which is critical for the efficiency of the entire system.

In this article we will analyze the physical essence of the process, provide specific formulas for engineering calculations and provide reference tables that will help you choose the optimal tube size for a specific refrigerator model. Understanding these processes will allow you to avoid common mistakes, such as “underfilling” freon or overheating of the compressor due to high discharge pressure.

Physics of the throttling process and the role of the capillary

The capillary tube is a long copper tube with a very small internal diameter, usually ranging from 0.5 to 2.0 mm. The moment high-pressure liquid refrigerant enters a narrow opening, its speed increases sharply and static pressure drops. This process is called throttling. As a result of the pressure drop, part of the liquid instantly evaporates, forming a vapor-liquid mixture, which enters the evaporator.

The length and diameter of the tube are selected in such a way that the flow resistance corresponds to the performance of the particular one. compressor. If the resistance is too great (the tube is too long or narrow), the compressor will not be able to push through the entire volume of gas, and there will not be enough refrigerant in the evaporator for effective cooling. If the resistance is too low, the liquid freon may not have time to completely evaporate and will enter the compressor suction, causing a water hammer.

⚠️ Attention: The capillary tube does not dynamically regulate the refrigerant flow, like a thermostatic expansion valve (TRV). It is designed to operate in a certain range of temperatures and pressures. A sudden change in conditions (for example, extreme heat in a room) can shift the operating point, so the accuracy of the initial calculation is critical.

The flow process in a capillary is complicated in that as freon moves and pressure drops, the volume of steam increases and the flow rate increases. At some point, the speed can reach the speed of sound, and the flow will become “choked” (choked flow). Further reduction in outlet pressure will not increase the mass flow through the tube. That is why geometric parameters must be strictly coordinated with the type of refrigerant (R134a, R600a, R12) and motor power.

Why can’t you just take the tube by eye?

The inner diameter of the tube can differ by a fraction of a millimeter, but this drastically changes the throughput. A tube with a diameter of 0.6 mm and 0.8 mm with the same length will have a difference in flow rate of up to 40-50%. Using the tube “by eye” without recalculating the length is guaranteed to lead to incorrect operation of the refrigerator.

Key parameters for accurate calculation

Before starting mathematical calculations, it is necessary to collect accurate initial data. Without knowing the characteristics of your of the refrigeration unit any calculation will be meaningless. The main variables are the type of refrigerant, the cooling capacity of the compressor and the operating temperature.

The tube diameter is a fixed parameter, which is often dictated by the availability of material or design features of the factory design. Most often, craftsmen use tubes with an internal diameter 0.66 mm, 0.71 mm or 0.79 mm. A change in diameter requires a proportional change in length to maintain the same hydraulic resistance.

Condensation and boiling temperatures also play a role. For household refrigerators, standard conditions are usually accepted: boiling temperature -23,3°C (for freezers) or -10°C (for refrigerators), and the condensation temperature depends on the ambient temperature (usually +55°C). These parameters are included in empirical formulas.

• 🔹 Refrigerant type: R134a requires different parameters than isobutane (R600a) due to different viscosity and density.
• 🔹 Compressor power: The higher the performance (in W or kcal/h), the shorter the tube should be or the larger its diameter.
• 🔹 Condenser condition: A condenser clogged with dust increases the condensation pressure, which changes the operating mode of the capillary.

It is important to understand that the internal surface The tube must be perfectly smooth. Any burrs or contamination change the friction coefficient, which introduces an error into the calculations. Therefore, when replacing, it is always used new tube, and soldering is done with care so as not to melt or deform the thin walls of the copper.

Engineering formula for calculating the length

For professional selection of the length of a capillary tube, there are a number of empirical formulas derived from experimental data. One of the most common methods used by technical engineers is based on the dependence of the length on the internal diameter and mass flow of the refrigerant.

The basic formula for recalculating the length when changing the diameter is as follows:

L2 = L1 * (D1 / D2)^4.75

Where:

• L1 is the known length of the tube (base, for example, factory).
• D1 —the known internal diameter of the base tube.
• L2 —the required length of the new tube.
• D2 —the internal diameter of the new tube that you plan to install.

This formula shows how critical the influence of diameter is on the length. Degree 4.75 means that even a minimal change in diameter requires a drastic change in length. For example, if you replace a tube with a diameter of 0.66 mm by 0.71 mm, the length of the new tube must be significantly shorter to maintain the same resistance.

There is also a formula for the initial calculation if the compressor parameters are known:

L = K * (Q / d^4.75)

Here Q is the cooling capacity, d is the diameter, and K is a coefficient depending on the type of refrigerant and units of measurement. For R134a and R600a the coefficients will be different. The exact values of the coefficients are often a trade secret of manufacturers, so in practice they often use the method of recalculation from a known analogue or selection from tables.

Reference table for sizing

Using ready-made tables can significantly simplify the process and avoid complex mathematical calculations. Below are averaged data for household refrigerators of average power (compressors like Danfoss/NSEC or Aspera with a power of about 1/5 - 1/4 hp).

The data in the table is relevant for refrigerant R134a. When using R600a, the length can be increased by 10-15% with the same diameter due to differences in viscosity.

Please note that the length indicated is for a straight tube. If the tube is wound in a spiral (which is often done for compactness), its effective length does not change, but the heat exchange with the environment may be different. In the factory, the capillary is often glued to the suction tube for heat exchange, which increases the efficiency of the cycle.

⚠️ Attention: The tabular data is a starting point. Actual length may vary depending on the specific condenser and evaporator design. Always start at the top of the recommended length, leaving room for trimming during the adjustment process.

Practical instructions for replacement and adjustment

The process of replacing a capillary tube requires not only calculations, but also careful execution. Incorrect soldering or moisture ingress will invalidate all calculations. Before starting work, make sure that the system is completely evacuated and the new capillary is protected from dust and moisture.

First you need to dismantle the old capillary. If it is glued to the evaporator or suction tube, be careful not to damage the aluminum. The new capillary is sealed into the filter drier and into the evaporator. The depth of insertion into the filter should be 15-20 mmso that the end of the tube does not rest against the bottom and does not block the flow.

After assembly circuit and evacuation, refrigerant is charged. At this stage the final setup begins. If you used the estimated length, the system should work immediately. However, it is often required (fine tuning). If the suction pressure is too low and the overheating is high, the tube must be shortened. If the pressure is high and liquid is possible at the suction, the tube is too short (or wide), and it needs to be replaced with a longer (or narrow) one.

Shortening is done in stages: the lower end is unsoldered, cut off 5-10 cm, the tube is resoldered, and a repeat test is carried out. This cycle is repeated until optimal operating parameters are achieved.

Typical errors and problem diagnosis

Even experienced craftsmen can make mistakes during calculations or installation. The most common problem is using a tube with a diameter different from the original without recalculating the length. This leads to a mismatch between the compressor performance and the throttle capacity.

If the capillary is selected incorrectly, you will encounter characteristic symptoms. If the tube is too long (high resistance), the compressor will operate with low current, the suction pressure will be lower than normal, and the evaporator will not be completely filled with freon. The refrigerator will “underfreeze.”

• 🔸 Overheating of the compressor: Often a consequence of high discharge pressure due to a blockage or too narrow capillary.
• 🔸 Freezing of the suction tube: A sign that the liquid freon does not have time to evaporate (the capillary is too short or wide).
• 🔸 Pressure pulsation: May indicate the presence of an air lock or incorrect capillary length causing unstable boiling.

Neglect is also a common mistake replacing the filter drier. When replacing the capillary required the filter is also changed, since the old one could absorb moisture and become contaminated with oil breakdown products. Installing a new capillary in a dirty system will lead to rapid re-clogging.

⚠️ Attention: When working with flammable refrigerants (R600a), all soldering must be done with extreme caution. Make sure there are no leaks before first soldering. Use only tools that do not produce sparks.

What to do if you do not have a tube of the required diameter?

If you do not have a tube with the required diameter, you can use the length conversion method. For example, if you need a 0.66 mm tube 3 meters long, but only have 0.71 mm, use the formula from the section above. Most likely you will need a 0.71 mm tube about 2 meters long. However, it is better to stick to factory diameters to minimize risks.

Frequently asked questions (FAQ)

Is it possible to clean the old capillary instead of replacing it?

Theoretically, it is possible to blow with nitrogen under high pressure, but in practice this rarely gives a long-term result. The internal diameter of the capillary is so small that microscopic particles of oxides or paraffin sludge (when using mineral oil with the wrong freon) are almost impossible to completely remove. The risk of re-clogging in a week or month is 90%. Replacing with a new element is the only professional solution.

How does the temperature in the room affect the operation of the capillary?

The capillary tube has no moving parts, but its throughput depends on the viscosity of the refrigerant, which changes with temperature. In a hot room, the condensation pressure increases, which increases the pressure drop across the capillary and, consequently, the freon consumption. This can lead to an excess of refrigerant in the evaporator. In a cold room (below +16°C), the flow rate will drop and the refrigerator may stop turning off. To work in cold climate zones, special modifications to the system are required (thermal film, winter kit).

Why is the capillary often soldered to the return tube?

This is called a “pipe-in-pipe” heat exchanger or simply external heat exchange. The capillary transfers heat to the cold gas moving from the evaporator to the compressor. This leads to additional supercooling of liquid freon before throttling (which increases cooling capacity) and heating of steam in front of the compressor (which prevents the liquid phase from entering the crankcase). It is not recommended to break this thermal contact during repairs.

What length margin should be left during the first installation?

When using calculated data or tabular values, it is recommended to leave a length margin of around 10-15%. That is, if the calculation showed 200 cm, it is better to weld 220-230 cm. It is easy to shorten the tube during the setup process (unsoldered, cut, soldered), but extending a short tube without losing the tightness and quality of the soldering is extremely difficult. The margin allows you to flexibly adjust the system to real conditions.

Does the roughness of the internal surface affect the calculation?

Yes, it does. The formulas use the friction coefficient, which depends on the roughness. Copper tubes for refrigerators have a very smooth inner surface. The use of copper water pipes or low-quality pipes with burrs inside will result in the actual length required being less than the calculated length, since the roughness will create additional resistance. Always use specialized refrigeration tubes.