Calculating Wet Bulb Temperature

Iterative Solution Of Psychrometric Equation:

\[ T_w = T - \frac{(2430.0 \times (q - q_s))}{(cp + (2430.0 \times (dq_s/dT)))} \]

Wet Bulb Temperature (Tw):

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1. What Is Wet Bulb Temperature?

Wet bulb temperature (Tw) is the lowest temperature that can be reached by evaporating water into the air. It represents the temperature read by a thermometer covered in water-soaked cloth with air flowing past it.

2. How Does The Calculator Work?

The calculator uses an iterative solution of the psychrometric equation:

\[ T_w = T - \frac{(2430.0 \times (q - q_s))}{(cp + (2430.0 \times (dq_s/dT)))} \]

Where:

\( T \) — Dry bulb temperature (°C)
\( q \) — Specific humidity (kg/kg)
\( q_s \) — Saturation specific humidity at wet bulb temperature (kg/kg)
\( dq_s/dT \) — Derivative of saturation specific humidity with respect to temperature
\( cp \) — Specific heat of air at constant pressure (1005 J/kg·K)
2430.0 — Latent heat of vaporization of water (kJ/kg)

Explanation: The equation is solved iteratively using the Newton-Raphson method to find the wet bulb temperature that satisfies the energy balance.

3. Importance Of Wet Bulb Temperature

Details: Wet bulb temperature is crucial in meteorology, HVAC design, and industrial processes. It helps determine human comfort levels, predict evaporation rates, and assess potential heat stress conditions.

4. Using The Calculator

Tips: Enter dry bulb temperature in °C and relative humidity in percentage (0-100%). The calculator will compute the corresponding wet bulb temperature using psychrometric relationships.

5. Frequently Asked Questions (FAQ)

Q1: How is wet bulb temperature different from dew point?
A: Wet bulb temperature is always between dew point and dry bulb temperature. It represents evaporative cooling potential, while dew point indicates moisture content.

Q2: Why is wet bulb temperature important for human health?
A: High wet bulb temperatures (above 35°C) can be dangerous as they limit the body's ability to cool through sweating, potentially leading to heat stroke.

Q3: How accurate is this calculation?
A: The iterative method provides high accuracy (typically within 0.1°C) for standard atmospheric conditions.

Q4: Does elevation affect wet bulb temperature?
A: Yes, the calculation assumes standard sea-level pressure. For high elevations, pressure correction would be needed for maximum accuracy.

Q5: Can this be used for freezing conditions?
A: The calculation works for temperatures above freezing. For sub-freezing conditions, different formulas accounting for ice phase would be needed.