Home Back

Mass Flow Rate of Added Water (Humidification) Calculator

Mass Flow Rate of Added Water

1. What is a Mass Flow Rate of Added Water (Humidification) Calculator?

Definition: This calculator computes the mass flow rate of water (\( \dot{m}_w \)) added during a humidification process in heating or evaporative cooling, based on the change in humidity ratio and the mass flow rate of dry air.

Purpose: It is used in HVAC systems to determine the amount of water needed for humidification, aiding in the design and sizing of humidifiers for heating or evaporative cooling processes.

2. How Does the Calculator Work?

The calculator uses the following formula for the mass flow rate of added water:

Mass Flow Rate of Added Water: \[ \dot{m}_w = \dot{m}_a (W_2 - W_1) \]

Where:

  • \( \dot{m}_w \): Mass flow rate of added water (lb_m/hr, convertible to kg/hr)
  • \( \dot{m}_a \): Mass flow rate of dry air (lb_m/hr, kg/hr)
  • \( W_1 \): Entering humidity ratio (lb_v/lb_da, kg_v/kg_da)
  • \( W_2 \): Leaving humidity ratio (lb_v/lb_da, kg_v/kg_da)

Unit Conversions:

  • Mass Flow Rate (\( \dot{m}_a \), \( \dot{m}_w \)): lb_m/hr, kg/hr (1 kg/hr = 2.20462 lb_m/hr, 1 lb_m/hr = 0.453592 kg/hr)
  • Humidity Ratios (\( W_1 \), \( W_2 \)): lb_v/lb_da, kg_v/kg_da (numerically the same, label changes for clarity)

Steps:

  • Enter the mass flow rate of dry air (\( \dot{m}_a \)), entering humidity ratio (\( W_1 \)), and leaving humidity ratio (\( W_2 \)), and select their units.
  • Convert mass flow rate to lb_m/hr and ensure humidity ratios are consistent.
  • Calculate the mass flow rate of added water using the formula.
  • Convert the result to the selected unit (lb_m/hr or kg/hr).
  • Display the result with 5 decimal places, or in scientific notation if the value is greater than 10,000 or less than 0.00001.

3. Importance of Mass Flow Rate of Added Water Calculation

Calculating the mass flow rate of added water in a humidification process is crucial for:

  • HVAC Design: Determines the amount of water required for humidification, aiding in the sizing of humidifiers and water supply systems.
  • Energy Efficiency: Helps optimize humidification processes by ensuring the correct amount of water is added, avoiding over- or under-humidification.
  • System Performance: Ensures the system can achieve the desired humidity levels for comfort or process requirements in heating or evaporative cooling applications.

4. Using the Calculator

Examples:

  • Example 1: For \( \dot{m}_a = 9508 \, \text{lb_m/hr} \), \( W_1 = 0.002 \, \text{lb_v/lb_da} \), \( W_2 = 0.016 \, \text{lb_v/lb_da} \), mass flow rate in lb_m/hr:
    • \( \dot{m}_w = 9508 \times (0.016 - 0.002) \)
    • \( \dot{m}_w = 9508 \times 0.014 = 133.11200 \)
    • Since 133.11200 < 10000 and > 0.00001, display with 5 decimal places: \( 133.11200 \)
  • Example 2: For \( \dot{m}_a = 1000000 \, \text{kg/hr} \), \( W_1 = 0.005 \, \text{kg_v/kg_da} \), \( W_2 = 0.020 \, \text{kg_v/kg_da} \), mass flow rate in kg/hr:
    • Convert: \( \dot{m}_a = 1000000 \times 2.20462 = 2204620 \, \text{lb_m/hr} \)
    • \( \dot{m}_w = 2204620 \times (0.020 - 0.005) \)
    • \( \dot{m}_w = 2204620 \times 0.015 = 33069.30000 \, \text{lb_m/hr} \)
    • Convert to kg/hr: \( 33069.30000 \times 0.453592 = 14996.42877 \)
    • Since 14996.42877 > 10000, use scientific notation: \( 1.49964e+4 \)
  • Example 3: For \( \dot{m}_a = 0.01 \, \text{lb_m/hr} \), \( W_1 = 0.003 \, \text{lb_v/lb_da} \), \( W_2 = 0.0035 \, \text{lb_v/lb_da} \), mass flow rate in lb_m/hr:
    • \( \dot{m}_w = 0.01 \times (0.0035 - 0.003) \)
    • \( \dot{m}_w = 0.01 \times 0.0005 = 0.000005 \)
    • Since 0.000005 < 0.00001, use scientific notation: \( 5.00000e-6 \)

5. Frequently Asked Questions (FAQ)

Q: What is humidification in HVAC processes?
A: Humidification in HVAC processes involves adding moisture to the air, typically during heating or evaporative cooling, to increase the humidity ratio for comfort or process requirements.

Q: Why is the mass flow rate of added water important?
A: The mass flow rate of added water determines the amount of water a humidifier must supply, which is critical for system design, water supply planning, and ensuring the desired humidity level is achieved.

Q: How do I determine the humidity ratio values if I don’t have a psychrometric chart?
A: Humidity ratios (\( W_1 \), \( W_2 \)) can be calculated using psychrometric equations or software, based on temperature, pressure, and humidity conditions, or approximated using standard air properties.

Mass Flow Rate of Added Water (Humidification) Calculator© - All Rights Reserved 2025