Humidity Ratio (x)

Detailed Explanation

Humidity ratio (x or W) is the standard thermodynamic descriptor of moist-air absolute humidity: how many grams (or kg) of water vapour accompany 1 kg of dry air. The SI unit is kg_water/kg_dry_air but g/kg is more practical (so "8 g/kg" means 0.008 kg_water/kg_dry_air). The maximum value occurs at saturation and is temperature-dependent: 3.8 g/kg at 0°C, 14.7 g/kg at 20°C, 49 g/kg at 40°C.

Formula: x = 0.622 × (p_vapour / (p_atm − p_vapour)); p_vapour is the partial pressure of water vapour (Pa), p_atm the total atmospheric pressure (101,325 Pa standard). On the psychrometric chart it is shown on the right-hand vertical axis as a linear scale; constant-RH curves intersect x at each temperature. Unlike RH, x is unaffected by temperature change — that is what makes it the master reference for humidification/dehumidification capacity calculations.

Why It Matters

In humidification/dehumidification capacity calculations, x (humidity ratio) is the only valid input for absolute humidity; using an RH difference directly is mathematically wrong. Typical capacity formula:

m_water (kg/h) = ρ_air × V_air × Δx = ρ_air × V_air × (x_target − x_current)

Example: turning 22°C / 30% RH (x ≈ 5 g/kg) into 22°C / 50% RH (x ≈ 8.5 g/kg) needs Δx = 3.5 g/kg = 0.0035 kg/kg. At 10,000 m³/h, capacity = 1.2 × 10,000 × 0.0035 = 42 kg/h. Doing the same calculation with the (wrong) RH difference of 50% − 30% = 20% yields a meaningless number, because RH difference is dimensionless and has no mass interpretation.

Most engineering software and OEM tools (NKT Portal, humidifier control software, Trane Trace) operate on x values. A quick on-site estimate "every 10% RH @ 22°C ≈ 1.7 g/kg" works roughly, but a real calculation should always use a table or a tool.

Practical Example

A data centre in Izmir, supply-air analysis: summer design outdoor 35°C / 45% RH → x ≈ 16 g/kg; indoor target 24°C / 50% RH → x ≈ 9.3 g/kg. The incoming outdoor air therefore carries Δx = 16 − 9.3 = 6.7 g/kg of excess moisture; the system needs dehumidification, not humidification. When the cooling coil drops the air to 9°C (saturation @ 9°C ≈ 7.2 g/kg), condensation removes 16 − 7.2 = 8.8 g/kg. The air is then reheated to 24°C; final x = 7.2 g/kg and RH = 38%. So 8.8 g/kg of moisture is removed and the resulting overcool is corrected by reheat — this classical DX cooling-plus-reheat psychrometric process is driven entirely by the x calculation.

Engineering Note

Caveats for humidity-ratio calculation: (1) Atmospheric pressure is taken as the standard 101,325 Pa, but at altitudes above 1500 m it drops 15–20%; the x value for the same RH at the same Tdb shifts accordingly — for high-altitude designs such as Erzurum (≈1,850 m) the correction is mandatory, and it should also be applied for Kayseri and Konya (≈1,000 m, pressure ≈ 11% lower). (2) Air density (ρ) is 1.2 kg/m³ at sea level but drops 15–20% at altitude; in the capacity formula the two corrections act in opposite directions (ρ falls while x rises for the same RH) and largely cancel out; applying only one of them and ignoring the other introduces a 15–20% error. (3) At very high temperatures (> 50°C), use ASHRAE Fundamentals tables rather than approximate formulas.

Quick Turkish-condition reference values (sea level, x in g/kg): winter outdoor (−5°C / 75% RH) ≈ 1.8 g/kg; spring/autumn (15°C / 60% RH) ≈ 6.4 g/kg; summer outdoor (32°C / 55% RH) ≈ 16.5 g/kg; indoor comfort target (22°C / 50% RH) ≈ 8.4 g/kg; indoor process target (22°C / 30% RH) ≈ 5.0 g/kg.

NKT Application Link

For this application NKT – Nem Kontrol Teknolojileri supplies the Neptronic SKE4 resistive steam humidifier, the Neptronic SKS4 steam-to-steam humidifier and the Neptronic SKH high-pressure atomisation system. It supports unit selection with capacity calculation and technology matching based on space conditions, target temperature and RH (or dew point) and moisture load, and provides technical service and spare parts. Design, installation and commissioning remain within the scope of the facility's designer and contractor.