Understanding Wet-Bulb Temperature: Key Concepts and Calculations

The Crucial Role of Wet-Bulb Temperature in Climate Control

Wet-bulb temperature refers to the temperature at which a water surface reaches equilibrium when the rate of heat transfer by convection equals the rate of mass transfer away from the surface. It is a crucial parameter in various applications, including meteorology, HVAC systems, and thermal comfort studies.

Wet-Bulb Temperature, Dry-Bulb Temperature, and Cooling Effectiveness

The wet-bulb temperature is the lowest temperature to which air can be cooled through the evaporation of water into it at constant pressure. It is measured by wrapping a wet wick around the bulb of a thermometer. In contrast, the dry-bulb temperature is the ambient air temperature. The difference between these two temperatures indicates the humidity level in the air: a larger difference suggests lower humidity.

Calculating Humidity and Related Parameters

Given the wet-bulb temperature (Tw), dry-bulb temperature (Ta), and ambient pressure (P), the humidity of the air can be calculated using the following formula:

𝑝=𝑝𝑤−0.00066𝑃(𝑇𝑎−𝑇𝑤)(1+0.0115𝑇𝑤)p=pw​−0.00066P(Ta​−Tw​)(1+0.0115Tw​)

Where:

• 𝑝p is the vapor pressure of water vapor.
• 𝑝𝑤pw​ is the saturated vapor pressure of water vapor at the wet-bulb temperature.
• 𝑃P is the ambient pressure.
• 𝑇𝑎Ta​ is the ambient or dry-bulb temperature.
• 𝑇𝑤Tw​ is the wet-bulb temperature.

The saturated vapor pressure at the wet-bulb temperature (𝑝𝑤pw​) is given by:

𝑝𝑤=6.112×𝑒(17.67×𝑇𝑤𝑇𝑤+243.5)pw​=6.112×e(Tw​+243.517.67×Tw​​)

Similarly, the saturated vapor pressure at the dry-bulb temperature (𝑝𝑠ps​) is:

𝑝𝑠=6.112×𝑒(17.67×𝑇𝑎𝑇𝑎+243.5)ps​=6.112×e(Ta​+243.517.67×Ta​​)

Using these equations, the relative humidity (𝜙ϕ) can be calculated as:

𝜙=(𝑝𝑝𝑠)×100ϕ=(ps​p​)×100

The specific humidity (𝜔ω) can be determined by:

𝜔=0.622×𝑝𝑃−𝑝ω=P−p0.622×p​

The dew point temperature (𝑇𝑑Td​) is calculated as:

𝑇𝑑=243.5×ln⁡(𝑝6.112)17.67−ln⁡(𝑝6.112)Td​=17.67−ln(6.112p​)243.5×ln(6.112p​)​

Evaporative Cooling Systems

A typical evaporative cooling system involves the flow of warm, dry air through a wetted media or fogging chamber, where water is added and evaporates. This process cools the air, increasing its moisture content. The effectiveness of this cooling process, known as cooling effectiveness (𝜖ϵ), is a measure of how closely the temperature of the cooled, moist air (𝑇coolTcool​) approaches the wet-bulb temperature (𝑇𝑤Tw​). It is defined as:

𝜖=𝑇𝑎−𝑇cool𝑇𝑎−𝑇𝑤ϵ=Ta​−Tw​Ta​−Tcool​​

Wetted media and chillers can be positioned either upstream or downstream of a gas turbine inlet filter/plenum. If located upstream, synthetic filters must be used, as paper filters could swell and get damaged in high humidity conditions.

The Bottom Line

Understanding and measuring the wet-bulb temperature is essential in various scientific and engineering applications. It provides valuable insights into air humidity and is crucial for designing effective cooling systems. By accurately calculating related parameters, such as vapor pressure, relative humidity, and specific humidity, one can better manage and optimize environmental conditions.