Cooling load calculation for13-story building

 

13-story building involves estimating the heat gain from various sources such as walls, windows, occupants, lighting, equipment, and ventilation. This is typically done using the ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers) methods.

Step 1: Gather Building Information

1. Total Area: 30,000 sq. ft.

2. Number of Floors: 13

3. Area per Floor: $\frac{30,000}{13}\approx 2,308\text{sq. ft. per floor}$

4. Building Orientation: Assume standard orientation (for solar heat gain calculations).

5. Occupancy: Assume 10 people per 1,000 sq. ft. → $30,000\times \frac{10}{1,000}=300\text{people}$.

6. Lighting Load: Assume 2 W/sq. ft.

7. Equipment Load: Assume 3 W/sq. ft.

8. Ventilation: Assume 1 air change per hour (ACH).

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Step 2: Cooling Load Components

The total cooling load ($Q_{total}$) is the sum of:

1. Heat gain through walls and roofs ($Q_{walls}$).

2. Heat gain through windows ($Q_{windows}$).

3. Heat gain from occupants ($Q_{occupants}$).

4. Heat gain from lighting ($Q_{lighting}$).

5. Heat gain from equipment ($Q_{equipment}$).

6. Heat gain from ventilation ($Q_{ventilation}$).

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Step 3: Calculations

3.1 Heat Gain Through Walls and Roofs

Assume:

• Wall area per floor: $2,308\text{sq. ft.}\times 0.5=1,154\text{sq. ft.}$ (50% of floor area).

• Roof area: $2,308\text{sq. ft.}$.

• $U$-value for walls: $0.2$.

• $U$-value for roof: $0.15$.

• Temperature difference ($\mathrm{\Delta }T$): $20\mathrm{°}F$ (indoor at 75°F, outdoor at 95°F).

$$Q_{walls}=U\cdot A\cdot \mathrm{\Delta }T=0.2\cdot 1,154\cdot 20=4,616\text{Btu/hr per floor}$$$$Q_{roof}=0.15\cdot 2,308\cdot 20=6,924\text{Btu/hr}$$

Total for 13 floors:

$$Q_{walls+roof}=(4,616\cdot 13)+6,924=66,008+6,924=72,932\text{Btu/hr}$$

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3.2 Heat Gain Through Windows

Assume:

• Window area per floor: $2,308\times 0.3=692\text{sq. ft.}$ (30% of floor area).

• $U$-value for windows: $0.5$.

• Solar heat gain coefficient (SHGC): $0.25$.

• Solar radiation: $200$.

$$Q_{windows}=(U\cdot A\cdot \mathrm{\Delta }T)+(SHGC\cdot A\cdot \text{Solar Radiation})$$$$Q_{windows}=(0.5\cdot 692\cdot 20)+(0.25\cdot 692\cdot 200)$$$$Q_{windows}=6,920+34,600=41,520\text{Btu/hr per floor}$$

Total for 13 floors:

$$Q_{windows}=41,520\cdot 13=539,760\text{Btu/hr}$$

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3.3 Heat Gain from Occupants

Assume:

• Heat gain per person: $250\text{Btu/hr}$ (sensible) + $200\text{Btu/hr}$ (latent).

• Total occupants: 300.

$$Q_{occupants}=300\cdot (250+200)=135,000\text{Btu/hr}$$

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3.4 Heat Gain from Lighting

Assume:

• Lighting load: $2\text{W/sq. ft.}$.

• Conversion: $1\text{W}=3.412\text{Btu/hr}$.

$$Q_{lighting}=2\cdot 30,000\cdot 3.412=204,720\text{Btu/hr}$$

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3.5 Heat Gain from Equipment

Assume:

• Equipment load: $3\text{W/sq. ft.}$.

$$Q_{equipment}=3\cdot 30,000\cdot 3.412=307,080\text{Btu/hr}$$

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3.6 Heat Gain from Ventilation

Assume:

• Air change rate: $1\text{ACH}$.

• Volume per floor: $2,308\text{sq. ft.}\times 10\text{ft}=23,080\text{cu. ft.}$.

• Total volume: $23,080\cdot 13=300,040\text{cu. ft.}$.

• Air density: $0.075\text{lb/cu. ft.}$.

• Specific heat of air: $0.24$.

$$Q_{ventilation}=\text{Volume}\cdot \text{Air Density}\cdot \text{Specific Heat}\cdot \mathrm{\Delta }T\cdot \text{ACH}$$$$Q_{ventilation}=300,040\cdot 0.075\cdot 0.24\cdot 20\cdot 1=108,014\text{Btu/hr}$$

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Step 4: Total Cooling Load

$$Q_{total}=Q_{walls+roof}+Q_{windows}+Q_{occupants}+Q_{lighting}+Q_{equipment}+Q_{ventilation}$$$$Q_{total}=72,932+539,760+135,000+204,720+307,080+108,014$$$$Q_{total}=1,367,506\text{Btu/hr}$$

Convert to tons of cooling (1 ton = 12,000 Btu/hr):

$$\text{Cooling Load}=\frac{1,367,506}{12,000}\approx 114\text{tons}$$

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Summary

• Total Cooling Load: 1,367,506 Btu/hr (~114 tons).