The atmospheric air at 40°C dry bulb temperature is flowing at the rate of 100 m³/min through the space at the rate of 48 kg/h. Determine the specific humidity of leaving air using... The atmospheric air at 40°C dry bulb temperature is flowing at the rate of 100 m³/min through the space at the rate of 48 kg/h. Determine the specific humidity of leaving air using the psychometric chart.
Understand the Problem
The question involves determining the specific humidity of air given its dry bulb temperature and the conditions of water being injected into the air stream. It likely requires the use of a psychrometric chart for the calculations.
Answer
The specific humidity is found through the mixture of the existing air’s specific humidity and the humidity introduced by the injected water at 18°C. Specific humidity is calculated in kg/kg.
Answer for screen readers
The specific humidity of the air can be determined through the above calculations, combining the effects of both the existing air and the moisture introduced from the injected water.
Steps to Solve
- Determine the specific volume of air
Using the provided information, the specific volume of the moist air can be found using the formula:
$$ V_{a} = \frac{1}{P} \cdot V_{specific} $$
- Calculate the mass flow rate of the air
The total volume flow rate of air is given as 100 m³/min. To convert it into kg/s, use:
$$ \text{mass flow rate} = \text{density} \times \text{flow rate} $$
- Find the specific humidity of the injected water
Using the condition of water injected at 18°C, we can find the specific humidity ($\omega_w$) using the formula:
$$ \omega_w = \frac{0.622 \times P_{v}}{P - P_{v}} $$
Where $P_{v}$ is the vapor pressure at 18°C. Refer to the psychrometric chart to find this value.
- Calculate the resultant specific humidity in the air
After determining the specific humidity of both the dry air ($\omega_a$) and the injected water, use the overall mixing formula:
$$ \omega_{total} = \frac{m_{a} \cdot \omega_a + m_{w} \cdot \omega_w}{m_{a} + m_{w}} $$
- Use psychrometric chart for final adjustments
Finally, reference the psychrometric chart for any adjustments and confirm your calculations.
The specific humidity of the air can be determined through the above calculations, combining the effects of both the existing air and the moisture introduced from the injected water.
More Information
Specific humidity is a measure of the amount of water vapor present in the air and is expressed as the mass of water vapor per unit mass of dry air. This value is essential for understanding and controlling humidity in various engineering applications.
Tips
- Confusing specific volume with density—ensure you use the correct terms and units.
- Not converting units properly (e.g., from m³/min to kg/s) can lead to significant errors.
- Misreading the psychrometric chart or using incorrect data from it can result in inaccurate specific humidity calculations.
AI-generated content may contain errors. Please verify critical information
