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Partial Pressure of Water Vapor Calculator

Partial Pressure of Water Vapor

1. What is a Partial Pressure of Water Vapor Calculator?

Definition: This calculator computes the partial pressure of water vapor (\( P_v \)) using Carrier's equation, based on dry-bulb and wet-bulb temperatures, total pressure, and saturation pressure at the wet-bulb temperature.

Purpose: It is used in HVAC systems to determine the partial pressure of water vapor in moist air, aiding in psychrometric calculations for air conditioning and ventilation systems.

2. How Does the Calculator Work?

The calculator uses Carrier's equation to calculate the partial pressure of water vapor:

Above 32°F (over water): \[ P_v = P_w - \frac{(P - P_w)(T - T_w)}{2831 - 1.43 T_w} \]

Below 32°F (over ice): \[ P_v = P_w - \frac{(P - P_w)(T - T_w)}{3160 - 0.09 T_w} \]

Saturation Pressure (\( P_w \)) Calculation (if not provided): \[ P_w = 0.61078 \exp\left(\frac{17.27 T_w}{T_w + 237.3}\right) \, \text{(kPa, where \( T_w \) is in °C)} \] Converted to psia for calculation.

Where:

  • \( P_v \): Partial pressure of water vapor (psia, inHg, Pa)
  • \( P_w \): Saturation pressure at wet-bulb temperature \( T_w \) (psia, inHg, Pa)
  • \( P \): Total pressure (psia, inHg, Pa)
  • \( T \): Dry-bulb temperature (°F, °C, K)
  • \( T_w \): Wet-bulb temperature (°F, °C, K)

Unit Conversions:

  • Temperatures (\( T \), \( T_w \)): °F, °C (°F = °C × 9/5 + 32), K (°F = (K - 273.15) × 9/5 + 32)
  • Pressures (\( P_v \), \( P_w \), \( P \)): psia, inHg (1 inHg = 0.491154 psia), Pa (1 Pa = 0.000145038 psia)

Steps:

  • Enter the dry-bulb temperature (\( T \)), wet-bulb temperature (\( T_w \)), and total pressure (\( P \)), and select their units.
  • Indicate whether you have \( P_w \) from Table 2-3 or need to calculate it from the wet-bulb temperature.
  • If calculating \( P_w \), the calculator uses the wet-bulb temperature to compute it; otherwise, input \( P_w \) directly.
  • Convert all temperatures to °F and pressures to psia.
  • Select the appropriate formula based on the wet-bulb temperature (\( T_w \geq 32^\circ \text{F} \) or \( T_w < 32^\circ \text{F} \)).
  • Calculate the partial pressure of water vapor using the selected formula.
  • Convert the result to the selected unit (psia, inHg, or Pa).
  • Display the result with 4 decimal places.

3. Importance of Partial Pressure of Water Vapor Calculation

Calculating the partial pressure of water vapor is crucial for:

  • HVAC Design: Determines the moisture content in air, aiding in the design of air conditioning, dehumidification, and ventilation systems.
  • Comfort and Health: Ensures appropriate humidity levels for occupant comfort and indoor air quality.
  • System Performance: Enables accurate psychrometric calculations for HVAC system efficiency.

4. Using the Calculator

Examples:

  • Example 1 (Using \( P_w \) from Table 2-3): For \( T = 80^\circ \text{F} \), \( T_w = 70^\circ \text{F} \), \( P = 14.681 \, \text{psia} \), \( P_w = 0.3632 \, \text{psia} \), result in psia:
    • Since \( T_w = 70^\circ \text{F} \geq 32^\circ \text{F} \), use formula over water.
    • Denominator: \( 2831 - 1.43 \times 70 = 2831 - 100.1 = 2730.9 \)
    • \( P_v = 0.3632 - \frac{(14.681 - 0.3632)(80 - 70)}{2730.9} = 0.3632 - \frac{14.3178 \times 10}{2730.9} \approx 0.3632 - \frac{143.178}{2730.9} \approx 0.3632 - 0.0524 \approx 0.3108 \, \text{psia} \)

    Note: The example output in the prompt (\( P_v = 0.3107 \, \text{psia} \)) is slightly different due to rounding differences in intermediate steps. The calculator's result of 0.3108 is consistent with the provided values.

  • Example 2 (Calculating \( P_w \)): For \( T = 25^\circ \text{C} \), \( T_w = 15^\circ \text{C} \), \( P = 101325 \, \text{Pa} \), result in Pa:
    • Convert: \( T = (25 \times 9/5) + 32 = 77^\circ \text{F} \), \( T_w = (15 \times 9/5) + 32 = 59^\circ \text{F} \), \( P = 101325 \times 0.000145038 = 14.6956 \, \text{psia} \)
    • Calculate \( P_w \): \( T_w = 15^\circ \text{C} \), \( P_w = 0.61078 \times \exp\left(\frac{17.27 \times 15}{15 + 237.3}\right) \approx 0.61078 \times \exp(1.0272) \approx 1.7058 \, \text{kPa} \), \( P_w = 1.7058 \times 0.145038 \approx 0.2474 \, \text{psia} \)
    • Since \( T_w = 59^\circ \text{F} \geq 32^\circ \text{F} \), use formula over water.
    • Denominator: \( 2831 - 1.43 \times 59 = 2831 - 84.37 = 2746.63 \)
    • \( P_v = 0.2474 - \frac{(14.6956 - 0.2474)(77 - 59)}{2746.63} \approx 0.2474 - \frac{14.4482 \times 18}{2746.63} \approx 0.2474 - 0.0946 \approx 0.1528 \, \text{psia} \)
    • Convert to Pa: \( 0.1528 \times 6894.76 \approx 1053.52 \, \text{Pa} \)

5. Frequently Asked Questions (FAQ)

Q: What is the partial pressure of water vapor?
A: The partial pressure of water vapor (\( P_v \)) is the pressure exerted by the water vapor in a moist air mixture, a key parameter in psychrometric calculations.

Q: Why is this calculation important in HVAC systems?
A: It determines the moisture content in air, which is essential for designing systems that control humidity for comfort, health, and equipment performance.

Q: How do I determine the saturation pressure (\( P_w \)) if I don’t have Table 2-3?
A: The calculator uses the Magnus-Tetens formula to estimate \( P_w \) based on the wet-bulb temperature, or you can provide \( P_w \) directly if known from external sources like psychrometric tables.

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