Relative Humidity from a Sling Psychrometer

A sling psychrometer is two ordinary thermometers, one with a wetted cotton wick over its bulb, whirled on a handle until both readings stop changing. It is a nineteenth-century instrument, it costs almost nothing, it needs no calibration certificate, and it will still out-measure a cheap capacitive RH sensor that has been drifting in a duct for three years. Understanding what it does is the fastest route into psychrometrics.

The wet bulb reads low because water evaporating off the wick takes its latent heat from the bulb. Evaporation continues until the sensible heat arriving from the passing air exactly balances the latent heat leaving with the vapour, and the temperature at which that balance settles depends on how dry the air is. Dry air pulls water off the wick hard, the depression is large; saturated air pulls none, and the wet bulb equals the dry bulb. The psychrometric equation $p_v = p_{ws}(t_{wb}) - A p (t_{db} - t_{wb})$ is that energy balance written down.

The psychrometer constant $A$ is a property of the instrument, not of nature. This page uses the WMO value of $6.66\times10^{-4}$ K⁻¹, which applies to a properly ventilated psychrometer — air moving at 3 m/s or more across the wick, which is exactly what whirling a sling achieves. A wall-mounted screen hygrometer sitting in stagnant air runs nearer $8\times10^{-4}$ and will read humid. If the wet bulb falls below freezing the wick becomes an ICE bulb, the latent heat changes, and the constant drops to about $5.94\times10^{-4}$; a half-frozen wick reads somewhere between the two and cannot be corrected at all, which is why cold-weather practice is to let it freeze deliberately and note that it has.

Notice that $p$ multiplies the depression. The same two readings mean a different humidity in Denver than in Miami, and a psychrometric slide rule printed for sea level is quietly wrong at altitude. That is the same pressure dependence that shows up everywhere else in this shard.

The wet bulb is not the dew point, and the two get confused constantly. The dew point is where this air would start condensing if you cooled it without changing its moisture. The wet bulb is where this air ends up when it is cooled BY evaporating water into itself, which adds moisture as it goes. The wet bulb therefore always sits between the dew point and the dry bulb, and the three coincide only at saturation. The wet bulb is also the number a cooling tower is chasing — no evaporative device can drive water below the ambient wet bulb, which is why tower performance is quoted as approach to wet bulb and never as approach to air temperature. If you want the wet bulb estimated from dry bulb and relative humidity rather than measured, that is Stull's correlation and it lives on its own page; this one deliberately does not rebuild it.