Total Cooling Load (W):

The Library Cooling Calculator helps determine the cooling requirements for a library based on its dimensions, occupancy, and other factors. This calculator is useful for architects, engineers, and facility managers to design effective HVAC systems for libraries.

## Inputs:

**Length of Library (L)**: The length of the library in meters or feet.**Width of Library (W)**: The width of the library in meters or feet.**Height of Library (H)**: The height of the library in meters or feet.**Number of Occupants (N)**: The number of people typically present in the library.**Lighting Load (W/m² or W/ft²)**: The lighting power density of the library.**Equipment Load (W/m² or W/ft²)**: The equipment power density of the library.

## Formulas and Calculations:

## Cooling Load Calculation:

The formula to calculate the total cooling load (Q) is:

[ Q = Q_{\text{walls}} + Q_{\text{roof}} + Q_{\text{occupants}} + Q_{\text{lighting}} + Q_{\text{equipment}} ]

Where:

- ( Q_{\text{walls}} ): Cooling load from walls
- ( Q_{\text{roof}} ): Cooling load from roof
- ( Q_{\text{occupants}} ): Cooling load from occupants
- ( Q_{\text{lighting}} ): Cooling load from lighting
- ( Q_{\text{equipment}} ): Cooling load from equipment

## Detailed Component Calculations:

**Cooling Load from Walls (Q_walls)**:

[ Q_{\text{walls}} = U_{\text{walls}} \times A_{\text{walls}} \times \Delta T ]

Where:

- ( U_{\text{walls}} ): Thermal transmittance of the walls
- ( A_{\text{walls}} ): Surface area of the walls
- ( \Delta T ): Temperature difference between inside and outside

**Cooling Load from Roof (Q_roof)**:

[ Q_{\text{roof}} = U_{\text{roof}} \times A_{\text{roof}} \times \Delta T ]

Where:

- ( U_{\text{roof}} ): Thermal transmittance of the roof
- ( A_{\text{roof}} ): Surface area of the roof
- ( \Delta T ): Temperature difference between inside and outside

**Cooling Load from Occupants (Q_occupants)**:

[ Q_{\text{occupants}} = N \times Q_{\text{person}} ]

Where:

- ( N ): Number of occupants
- ( Q_{\text{person}} ): Heat gain per person (typically 100-150 W/person)

**Cooling Load from Lighting (Q_lighting)**:

[ Q_{\text{lighting}} = A_{\text{floor}} \times LPD ]

Where:

- ( A_{\text{floor}} ): Floor area of the library
- ( LPD ): Lighting power density

**Cooling Load from Equipment (Q_equipment)**:

[ Q_{\text{equipment}} = A_{\text{floor}} \times EPD ]

Where:

- ( A_{\text{floor}} ): Floor area of the library
- ( EPD ): Equipment power density

## Example Calculation:

**Inputs**:

- Length of Library (( L )): 30 meters
- Width of Library (( W )): 20 meters
- Height of Library (( H )): 4 meters
- Number of Occupants (( N )): 50
- Lighting Load (( LPD )): 10 W/m²
- Equipment Load (( EPD )): 5 W/m²
- U-value of Walls (( U_{\text{walls}} )): 0.5 W/m²K
- U-value of Roof (( U_{\text{roof}} )): 0.3 W/m²K
- Temperature Difference (( \Delta T )): 10°C

## Step-by-Step Calculation:

**Calculate Floor Area (A_floor)**:

[ A_{\text{floor}} = L \times W = 30 \times 20 = 600 \, \text{m}^2 ]**Calculate Surface Area of Walls (A_walls)**:

[ A_{\text{walls}} = 2 \times H \times (L + W) = 2 \times 4 \times (30 + 20) = 2 \times 4 \times 50 = 400 \, \text{m}^2 ]**Calculate Surface Area of Roof (A_roof)**:

[ A_{\text{roof}} = L \times W = 30 \times 20 = 600 \, \text{m}^2 ]**Calculate Cooling Load from Walls (Q_walls)**:

[ Q_{\text{walls}} = U_{\text{walls}} \times A_{\text{walls}} \times \Delta T = 0.5 \times 400 \times 10 = 2000 \, \text{W} ]**Calculate Cooling Load from Roof (Q_roof)**:

[ Q_{\text{roof}} = U_{\text{roof}} \times A_{\text{roof}} \times \Delta T = 0.3 \times 600 \times 10 = 1800 \, \text{W} ]**Calculate Cooling Load from Occupants (Q_occupants)**:

[ Q_{\text{occupants}} = N \times Q_{\text{person}} = 50 \times 120 = 6000 \, \text{W} ]**Calculate Cooling Load from Lighting (Q_lighting)**:

[ Q_{\text{lighting}} = A_{\text{floor}} \times LPD = 600 \times 10 = 6000 \, \text{W} ]**Calculate Cooling Load from Equipment (Q_equipment)**:

[ Q_{\text{equipment}} = A_{\text{floor}} \times EPD = 600 \times 5 = 3000 \, \text{W} ]**Calculate Total Cooling Load (Q)**:

[ Q = Q_{\text{walls}} + Q_{\text{roof}} + Q_{\text{occupants}} + Q_{\text{lighting}} + Q_{\text{equipment}} = 2000 + 1800 + 6000 + 6000 + 3000 = 18800 \, \text{W} ]

## Summary:

For a library with the given dimensions and inputs, the total cooling load required is 18,800 W (or 18.8 kW).

## Conclusion:

The Library Cooling Calculator is an essential tool for accurately estimating the cooling requirements of a library. By inputting key parameters such as the library’s dimensions, number of occupants, lighting, and equipment loads, this calculator provides a comprehensive calculation of the total cooling load. This information is crucial for designing efficient and effective HVAC systems, ensuring a comfortable environment for library users.