An auditorium is be designed for a capacity of 102 persons. Inside design conditions are 23 degrees celcius DBT and 55% RH, outside conditions 30 degrees celcius DBT and 70% RH, amount of required for one person 0.5 cubic meter per minute. Design equipment; capacity of the cooler battery, capacity of heater battery and amount of water removed by the dehumidifier.
The correct answer and explanation is :
Designing an HVAC system for an auditorium with a capacity of 102 persons requires careful consideration of airflow, temperature control, and humidity management. Here’s a detailed breakdown:
1. Airflow Requirements:
Each person requires 0.5 cubic meters of air per minute. For 102 persons, the total airflow is:
[ 102 \, \text{persons} \times 0.5 \, \frac{\text{m}^3}{\text{min/person}} = 51 \, \frac{\text{m}^3}{\text{min}} ]
Converting this to cubic feet per minute (CFM):
[ 51 \, \frac{\text{m}^3}{\text{min}} \times 33.48 \, \frac{\text{CFM}}{\text{m}^3/\text{min}} \approx 1,709 \, \text{CFM} ]
2. Cooling Load Calculation:
The sensible heat gain due to temperature difference between outside and inside air can be calculated using the formula:
[ Q = \dot{V} \times \Delta T \times 1.08 ]
Where:
- ( \dot{V} ) is the airflow rate in CFM.
- ( \Delta T ) is the temperature difference between outside and inside air (30°C – 23°C = 7°C).
- 1.08 is a constant that accounts for air density and specific heat.
Calculating the cooling load:
[ Q = 1,709 \, \text{CFM} \times 7 \, \text{°C} \times 1.08 \approx 12,900 \, \text{W} ]
Converting to tons of refrigeration (1 ton = 3,412 W):
[ \frac{12,900 \, \text{W}}{3,412 \, \text{W/ton}} \approx 3.78 \, \text{tons} ]
3. Heating Load Calculation:
Assuming the heating is required during colder periods, the heating capacity should match the cooling capacity to maintain comfort. Therefore, the heater battery should have a capacity of approximately 3.78 tons.
4. Dehumidification Requirement:
The amount of water to be removed by the dehumidifier depends on the moisture content of the air. Given the outside air at 30°C DBT and 70% RH, and inside design conditions at 23°C DBT and 55% RH, the dehumidifier must handle the latent load. While precise calculations require psychrometric analysis, a rough estimate can be made based on the airflow and the difference in moisture content between outside and inside air.
Assuming a latent heat removal factor of 0.3 L per CFM per hour:
[ \text{Water Removal} = 1,709 \, \text{CFM} \times 0.3 \, \frac{\text{L}}{\text{CFM} \cdot \text{hr}} \approx 513 \, \text{L/hr} ]
Summary of Equipment Capacities:
- Cooler Battery Capacity: Approximately 3.78 tons of refrigeration.
- Heater Battery Capacity: Approximately 3.78 tons of heating capacity.
- Dehumidifier Capacity: Approximately 513 liters of water removal per hour.
These calculations provide a foundational understanding of the HVAC requirements for the auditorium, ensuring a comfortable environment for all occupants.