{"id":3447,"date":"2026-10-08T18:18:52","date_gmt":"2026-10-08T10:18:52","guid":{"rendered":"http:\/\/www.circutor-rus.com\/blog\/?p=3447"},"modified":"2026-10-08T18:18:52","modified_gmt":"2026-10-08T10:18:52","slug":"how-to-calculate-the-mass-flow-rate-through-a-copper-capillary-tube-4e05-c13e18","status":"publish","type":"post","link":"http:\/\/www.circutor-rus.com\/blog\/2026\/10\/08\/how-to-calculate-the-mass-flow-rate-through-a-copper-capillary-tube-4e05-c13e18\/","title":{"rendered":"How to calculate the mass flow rate through a copper capillary tube?"},"content":{"rendered":"

If you\u2019ve ever worked with refrigeration systems, heat exchangers, or compact fluid circuits, you know copper capillary tubes are the unsung workhorses of these applications. As a supplier of copper capillary tubes, I get dozens of calls and emails every week asking the same question: \u201cHow do I calculate the mass flow rate through one of these tiny, precise tubes?\u201d It\u2019s not as straightforward as it sounds\u2014capillary flow is a unique mix of laminar flow, friction, and compressibility, depending on what fluid you\u2019re moving, the tube\u2019s specs, and the pressure conditions. Too high a flow rate and your system loses efficiency; too low and you\u2019ll cycle too often, wasting energy. Today, I\u2019m walking you through the exact calculation process, drawing on years of working with engineers, HVAC technicians, and custom system designers who rely on our capillaries daily. Copper Capillary Tube<\/a><\/p>\n

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First, let\u2019s get clear on what a copper capillary tube is, because that context matters. Unlike larger tubes that use turbulent flow to move fluid quickly, copper capillaries are small\u2014typically 0.5 mm to 3 mm in inner diameter (ID) and 100 mm to 3,000 mm long. Their small diameter forces fluid into laminar flow (Reynolds number below 2,300, almost always the case here), where friction dominates the flow behavior. That\u2019s why the calculation isn\u2019t just a matter of velocity times area, like with a big pipe. It also means their mass flow rate depends almost entirely on two things: the pressure drop across the tube (inlet pressure minus outlet pressure) and the tube\u2019s own physical dimensions (ID, length, wall roughness), plus the fluid\u2019s properties (viscosity, density, compressibility).<\/p>\n

Let\u2019s start with the basics you\u2019ll need before you even pull out a calculator. First, you\u2019ll need to define your operating conditions. Are you working with a subcooled liquid, like liquid refrigerant, or a two-phase mixture, which is common in evaporator circuits? For most HVAC and refrigeration applications, that\u2019s the standard use case. You\u2019ll also need the absolute inlet pressure (P_in) to the capillary, the absolute outlet pressure (P_out) after the capillary, the fluid\u2019s dynamic viscosity (\u03bc) at average conditions (midway between inlet and outlet temperature), and the tube\u2019s exact inner diameter and length. Important note: because we work with custom-cut or standard copper capillaries, we always provide verified ID and length for every order\u2014never guess, because a 0.1 mm difference in ID can change flow rate by 30% or more.<\/p>\n

Now, the core equation for laminar flow through a small tube is the Hagen-Poiseuille equation. This is the foundation of all capillary flow calculations, and it\u2019s been tested and refined for copper tubes specifically because their smooth inner walls minimize extra friction. The full Hagen-Poiseuille equation for mass flow rate (\u1e41) is:<\/p>\n

\u1e41 = (\u03c0 * \u03c1 * \u0394P * d\u2074) \/ (128 * \u03bc * L)<\/p>\n

Wait, let\u2019s break that down so it makes sense for your work, because every variable here matters. Let\u2019s define each term clearly, with units you\u2019ll use in industrial settings:<\/p>\n