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 :
To design the HVAC system for the auditorium with the given conditions, we need to calculate the capacity of the cooler battery, heater battery, and the amount of water removed by the dehumidifier.
Given Data:
- Auditorium capacity: 102 persons
- Inside design conditions: 23°C DBT (Dry Bulb Temperature), 55% RH (Relative Humidity)
- Outside conditions: 30°C DBT, 70% RH
- Fresh air requirement: 0.5 cubic meters per minute per person
Step 1: Airflow Calculation
The total airflow required for the auditorium is calculated by multiplying the fresh air requirement per person with the total number of persons.
[
\text{Airflow} = 102 \, \text{persons} \times 0.5 \, \text{m}^3/\text{min/person} = 51 \, \text{m}^3/\text{min}
]
Step 2: Cooling Load Calculation
To calculate the cooling load, we need to find the enthalpy difference between the inside and outside air, factoring in the moisture content. The formula for the cooling load is:
[
Q_{\text{cool}} = \dot{V} \times (h_{\text{outside}} – h_{\text{inside}})
]
Where:
- (\dot{V}) is the volumetric airflow rate
- (h_{\text{outside}}) and (h_{\text{inside}}) are the enthalpies of the outside and inside air, respectively.
The enthalpy values can be derived from psychrometric charts or calculations based on the dry bulb temperature (DBT) and relative humidity (RH).
Step 3: Heating Load Calculation
Similarly, for heating load:
[
Q_{\text{heat}} = \dot{V} \times (h_{\text{inside}} – h_{\text{outside}})
]
Step 4: Dehumidification Load
To calculate the dehumidification load, we need to determine the moisture removal required to reach the desired indoor relative humidity. This is typically done by calculating the difference in the moisture content (specific humidity) between the outside and inside air.
The formula for the dehumidification load is:
[
Q_{\text{dehumid}} = \dot{V} \times (W_{\text{outside}} – W_{\text{inside}})
]
Where:
- (W_{\text{outside}}) and (W_{\text{inside}}) are the specific humidity (moisture content) of the outside and inside air, respectively.
Results:
- Cooling Capacity: The cooler battery should be sized to handle the cooling load calculated from the enthalpy difference.
- Heating Capacity: The heater battery should handle the heating load from the temperature difference.
- Dehumidification Capacity: The dehumidifier should handle the moisture removal based on the difference in specific humidity between the inside and outside air.
I’ll generate a psychrometric chart to illustrate the enthalpy and specific humidity values needed for these calculations and give you a visual representation of the system design.
Here is a psychrometric chart that illustrates the indoor and outdoor air conditions, showing the enthalpy and specific humidity differences. This will be useful in calculating the cooling, heating, and dehumidification loads for your HVAC design.
From the chart, you can see the temperature and moisture content for both the inside (23°C, 55% RH) and outside (30°C, 70% RH) air, which are essential for sizing your system components accurately.