Saturday, November 23, 2024

Comprehensive Guide to Psychrometric Calculator and concepts Used

Psychrometrics deals with the physical and thermodynamic properties of air-vapor mixtures. The HTML-based psychrometric calculator presented here allows users to compute various properties of moist air, such as enthalpy, humidity ratio, relative humidity, dew point temperature, and others, based on inputs like Dry Bulb Temperature (DBT), Wet Bulb Temperature (WBT), or Relative Humidity (RH). This blog dives into the key formulas, concepts, and the logic used in the calculator.


Core Inputs and Their Significance

  1. Dry Bulb Temperature (DBT):
    The temperature of air measured using a standard thermometer without considering moisture content.

  2. Wet Bulb Temperature (WBT):
    The lowest temperature air can reach through evaporative cooling, measured with a thermometer covered by a wet cloth.

  3. Relative Humidity (RH):
    The ratio of the current vapor pressure of air to its saturation vapor pressure at a given temperature, expressed as a percentage.

  4. Altitude:
    The height above sea level affects atmospheric pressure, which in turn influences psychrometric properties.


Key Calculations and Formulas

1. Saturation Vapor Pressure

The saturation vapor pressure depends on the temperature and is determined using the Hyland-Wexler equation:

  • For T ≥ 0°C (Water):

    Psat, water=eC8Tk+C9+C10Tk+C11Tk2+C12Tk3+C13ln(Tk)P_{\text{sat, water}} = e^{\frac{C_8}{T_k} + C_9 + C_{10}T_k + C_{11}T_k^2 + C_{12}T_k^3 + C_{13}\ln(T_k)}
  • For T < 0°C (Ice):

    Psat, ice=eC1Tk+C2+C3Tk+C4Tk2+C5Tk3+C6Tk4+C7ln(Tk)P_{\text{sat, ice}} = e^{\frac{C_1}{T_k} + C_2 + C_3T_k + C_4T_k^2 + C_5T_k^3 + C_6T_k^4 + C_7\ln(T_k)}

    Here, Tk=T+273.15T_k = T + 273.15 (Kelvin).

2. Humidity Ratio (W):

The ratio of the mass of water vapor to the mass of dry air:

W=0.62198PvaporPatmPvaporW = 0.62198 \cdot \frac{P_{\text{vapor}}}{P_{\text{atm}} - P_{\text{vapor}}}

3. Partial Vapor Pressure (PvaporP_{\text{vapor}}):

Based on RH:

Pvapor=RH100PsatP_{\text{vapor}} = \frac{\text{RH}}{100} \cdot P_{\text{sat}}

4. Dew Point Temperature (TdewT_{\text{dew}}):

Using the logarithmic relation:

α=ln(Pvapor1000)\alpha = \ln\left(\frac{P_{\text{vapor}}}{1000}\right) Tdew={C14+C15α+C16α2+C17α3+C18Pvapor0.1984if Tdew06.09+12.608α+0.4959α2if Tdew<0T_{\text{dew}} = \begin{cases} C_{14} + C_{15}\alpha + C_{16}\alpha^2 + C_{17}\alpha^3 + C_{18}P_{\text{vapor}}^{0.1984} & \text{if } T_{\text{dew}} \geq 0 \\ 6.09 + 12.608\alpha + 0.4959\alpha^2 & \text{if } T_{\text{dew}} < 0 \end{cases}

5. Enthalpy (hh):

The total heat content of moist air:

h=Cp,airT+(Hfg+1.86T)Wh = C_{p, \text{air}}T + (H_{\text{fg}} + 1.86T)W

Where:

  • Cp,air=1.006kJ/kg\cdotpKC_{p, \text{air}} = 1.006 \, \text{kJ/kg·K} (specific heat of air)
  • Hfg=2501kJ/kgH_{\text{fg}} = 2501 \, \text{kJ/kg} (latent heat of vaporization)

6. Air Density (ρ\rho):

Using the ideal gas law:

ρ=PatmRspecific(T+273.15)(1+1.6078W)\rho = \frac{P_{\text{atm}}}{R_{\text{specific}}(T + 273.15)(1 + 1.6078W)}

7. Specific Volume (vv):

The volume occupied by 1 kg of moist air:

v=1ρv = \frac{1}{\rho}

Key Features of the Calculator

Input Types:

  • DBT & WBT: Calculates properties based on dry and wet bulb temperatures.
  • DBT & RH: Computes values using dry bulb temperature and relative humidity.

Altitude Adjustment:

Atmospheric pressure at altitude:

Patm=101325(12.25577×105altitude)5.2559P_{\text{atm}} = 101325 \cdot \left(1 - 2.25577 \times 10^{-5} \cdot \text{altitude}\right)^{5.2559}

Output Parameters Explained

  1. Enthalpy (kJ/kg): Total energy of air, combining sensible and latent heat.
  2. Humidity Ratio (kg/kg): Amount of moisture per unit mass of dry air.
  3. Air Density (kg/m³): Mass per unit volume of air.
  4. Partial Vapor Pressure (Pa): Pressure contributed by water vapor.
  5. Dew Point Temperature (°C): Temperature where air becomes saturated and water vapor condenses.
  6. Specific Volume (m³/kg): Volume occupied by a unit mass of moist air.
  7. Saturated Vapor Pressure (Pa): Maximum pressure water vapor can exert at a given temperature.
  8. Atmospheric Pressure (Pa): Ambient pressure adjusted for altitude.
  9. Calculated RH (%): Relative humidity derived from WBT.
  10. Calculated WBT (°C): Wet bulb temperature inferred from RH.

How It Works

  1. The user selects the input type and provides values for DBT, WBT/RH, and altitude.
  2. The calculator computes intermediate values like saturation pressure and partial vapor pressure.
  3. Core outputs like enthalpy, humidity ratio, and density are calculated.
  4. Results are dynamically displayed in a tabular format.

Advantages of This Calculator

  • User-friendly interface: Simple input forms with validation.
  • Dynamic adjustments: Fields toggle based on input type.
  • Real-world accuracy: Incorporates altitude effects on pressure.
  • Comprehensive outputs: Covers all significant psychrometric properties.

This psychrometric calculator simplifies the complex process of evaluating moist air properties, making it an indispensable tool for HVAC engineers, meteorologists, and anyone working with thermodynamic systems.

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