# Calculations

Building Specs
• Building area: 2,420 sf
• No. of occupants allowed (fire code): 92
• Infiltration loss: 1 – 2 ACH (air changes per hour) is typical
• Outdoor air required: 15 – 25% of ventilation air
• Breathing zone
• 3 – 72″ from the floor
• 24″ from the walls or AC equipment
• Humidity: 30 – 35% (< 20% or > 60% is problematic)
• Inside design temperature: 70 – 72˚F (cooling set point)
• T_db is 34.8˚C or 94.6˚F (0.4% extreme)
• Climatological data
Rough Estimation
• 20 cfm/person (common minimum design standard) and a reheat system
• The estimated cooling load is 0.25 – 0.35 tons per 100 sf of total building area

Q = 2,420 sf x 0.35 tons / 100 sf = 8.47 tons

• Q_dot = U x A x (T_i – T_o) or more accurate Q_dot = U x A x (CLTD)
• Cooling Load Temperature Difference gives ~15% error
• T_i = 70˚F
• T_o = 94.6˚F
• ∆T = 24.6
• U = 1/R

Roof

• A = 2,420 sf with 3′ of air space in attic
• R = 1.79 (1/2” acoustical ceiling tile)
• R = 30 (9-1/4” thick R-19 insulation)
• U_total = 1/R_total = 0.03
• CLTD = 28 (L- light construction & ∆T=35˚C, worst case for Jacksonville, FL is 36.6˚C)

Q_roof = 0.03 x 2,420 x 28 = 2,130 Btu/hr

Doors

• Glass door in the front (west wall)
• Qty (2) 1-¾”insulated metal doors in the back (east wall)
• A = 80” x 36” = 20 sf
• U = 0.40 (Btu/hr-sf-°F)
• CLTD = 16 (light construction & 35˚C)

Q_doors = U x A x #_doors x CLTD = 0.40 x 20 x 2 x 16 = 1,220 Btu/hr

Concrete Slab

• 4” thick slab = 0.333’
• ∆T = 5˚F
• Slab edge of N & S walls have zero heat transfer since they abut against neighboring business spaces
• U_slab_face = 0.05
• U_ slab_edge = 0.81
• A_slab_face = 2,420 sf
• A_ slab_edge = 0.333’ x (41’ x 2) = 27.33 sf

Q_slab = (0.05 x 2,420 + 0.81 x 27.33) x 5 = 715 Btu/hr

Exterior Walls

Zero heat transfer from N & S facing walls since they abut against other business spaces

East wall

• Height is 128” high and 41’ long
• Made of 12” CMU (concrete masonry unit), ¾” plywood, and ½” sheetrock
• R = 0.33 (7.5 mph wind outside)
• R = 0.68 – 0.69 (inside air)
• R = 2.04 – 2.56 (12” CMU- LW block not HW block)
• R = 1.08 (3/4” plywood)
• R = 2.22 (1/2” sheetrock)
• CLTD = 16 (light construction & 35˚C)
• Area of East wall = 128’ x 41” = 200 sf
• A_wall = (12’ x 200’) – A_windows – A_E_door = 2,400 – 80 – 60 = 2,260 sf
• U_total = 1/R_tot = 0.15

West wall

• Window wall except parts comprised of 12” CMU, ¾” plywood, ½” sheetrock, and 1” stucco
• R = 4.76 (1” stucco)
• U_total = 1/R_tot = 0.09
• Area of West wall = 24” (above window) x 41’ + 16.5” x 104” x 3 (between windows) = 82 + 36 = 118 sf
• Q_E_wall = 0.15 x 2,260 x 16 = 5,425 Btu/hr
• Q_W_wall = 0.09 x 118 x 16 = 170 Btu/hr

Q_wall_tot = 5,425 + 170 = 5,595 Btu/hr

Windows

• 3 – 5 hours of peak sun per day
• Conduction heat gain through fenestration areas: Q = A x U x CLTD

• Q_fes = (A_s x SHGF + A_sh x SHGF_sh) x SC
• Q_fs = Q_fes x CLF (space cooling load)
• SHGF = Maximum Solar Heat Gain Factor, Btu/hr-ft2 (use latitude 32˚N & June)
• SHGF_sh = Shaded Solar Heat Gain Factor (East/West & May)
• A_s = Unshaded Area of Window Glass
• A_sh = Shaded Area of Window Glass
• SL = Shade Line = Shade Line factor x shadow width beneath edge of the overhang
• SCL = Solar Cooling Load (SCL = SHGF x CLF, where CLF takes into account time lag)
• GLF = Glass Load Factor (GLF = SCL x SC)

Aluminum frame single-pane glass door & windows

• U = 1.27 Btu/hr-sf-°F
• Area of door = 72” x 104” = 52 sf
• Area of window = 66” x 104” = 48 sf
• 6 windows
• Area_tot = 52 + (48 x 6) = 340 sf
• CLTD = 16 (light construction & 35˚C)

Q_windows = 1.27 x 16 = 6,910 Btu/hr (least accurate method)

• Width of the overhang = 101”
• SLF = 0.8 | SL = 0.8 x 101” = 81”
• A_s = (1 – (81/104) x 340) = 75 sf
• A_sh = 340 – 75 = 265 sf
• SHGF = 1,169 Btu/sf-day / 8 hours = 146
• SHGF_sh = 142 W/m2 x 0.0929 m2/sf x 3.41 Btu/h-W = 45
• SC = 0.50 (blinds or translucent roller shade for single pane)

Q_windows = (75 x 146 + 265 x 45) x 0.50 = 11,440 Btu/hr

Lighting

• Q = 3.41 x W x BF x CLF
• 3.41 – conversion coefficient between Watts and Btu/hr
• W – lighting capacity, Watts
• BF – Ballast Factor (heat loss in the ballasts of fluorescent lights)
• CLF – Cooling Load Factor (heat storage in the lighting fixtures)
• Fluorescent lights
• Qty (25) 4’X2’ fixtures with qty (4) 48” T12 lamps, 32 W per bulb, BF = 0.92
• Qty (6) 2’X2’ fixtures with qty (2) 24” T12 u-shaped lamps, 32 W per bulb, BF = 0.94
• CLF (1.0 is often used)

Q_lighting = 3.41 x [(25 x 4 x 32 W x 0.92 x 1.0) + (6 x 2 x 32W x 0.94 x 1.0)] = 11,270 Btu/hr

Occupants

• Qs = qs x n x CLF | Ql = ql x n
• Qs & Ql = Sensible and Latent heat gains, Btu/hr
• qs & ql = Sensible and Latent heat gains per person, Btu/hr-person
• n = Number of People
• CLF = Cooling Load Factor for people (capacity of a space to absorb and store heat is 0.91 – 1.0)
• Activity type: office work
• Activity level: moderate
• Sensible heat gain is 250 Btu/hr-person
• Latent heat gain is 200 Btu/hr-person

Q_occupants: 450 Btu/hr-person x 92 people = 41,400 Btu/hr

Equipment

• Qty (59) computers (21” monitors) running at idle is 30 W and continuously is 130 W
• Refrigerator (15 ft3) = 300 W (there is a small fridge only, so halving this value)
• Laser Printer is 70 W
• Coffee maker is 2,590 Btu/hr
• Qty (2) 50” televisions (Westinghouse) = 151.3 kWh/yr
• Any other office equipment = 25% nameplate
• Q = 3.41 x (59 computers x 130 W) = 26,150 Btu/hr (21” monitors)
• Q = 3.41 x (1 computer x 110 W) = 375 Btu/hr (15” monitor)
• Q = 2 x 151.3 kWh/yr x 0.3895 [(Btu/hr) / (kWh/yr)] = 120 Btu/hr (television)
• Q = 3.41 x 150 W = 510 Btu/hr (refrigerator)
• Q = 3.41 x 70 W = 240 Btu/hr (laser printer)
• Q = 2,590 Btu/hr (coffee maker)
• Q = 2,185 Btu/hr (8 head soda fountain machine)

Q_equipment = 32,170 Btu/hr

Q_l+s_r = 9,800 + 2,130 + 1,220 + 715 + 5,595 + 11,440 + 11,270 + 41,400 + 32,170 = 105,740 Btu/hr

Ventilation

• Rp: 5 cfm/person
• Pz (no. of people): 92
• Ra: 0.06 cfm/ft2
• Az (floor area): 2,420 ft2
• Ez (distribution effectiveness): 1.00
• Single Zone and Dedicated OA (outdoor air) Systems (DOAS)
• V_bz_dot = Rp x Pz x Ra x Az (ventilation rate, breathing zone outdoor air)
• Voz_dot = V_bz_dot / Ez (zone outdoor airflow)
• Voz = (5 x 92 + 0.06 x 2,420) / 1.0 = 605 cfm

Sensible heat in a cooling process of air

• h_s = 1.08 x V_oz x ∆T | ρ = 0.075 lbm/ft3
• T_o = 94.6˚F (dry-bulb) | T_i = 70˚F (dry-bulb) | ∆T = (T_o – T_i) = 24.6
• h_s = 1.08 x 605 ft3/min x 24.6 = 16,075 Btu/hr

Latent heat due to moisture in the air, in a humidification process of air

• h_l = 4,840 x V_oz x dw_lb
• dw_lb = humidity ratio difference (lb water/dry air)
• T_wb = 25.4˚C = 77.7˚F (mean coincident wet bulb)
• dw_lb = 0.0206
• h_l = 4,840 x 605 ft3/min x 0.0206 = 60,320 Btu/hr
• h_t = h_s + h_l = 16,075 + 60,320 = 76,395 Btu/hr

Q_t = Q_l+s_r + h_t = 105,740 + 76,395 = 182,135 Btu/hr / 12,000 = 15.18 tons

Alternative method

• h_t = 4.5 x V_oz x dh
• dh = h_o – h_i (enthalpy difference)
• h_o = 45.5 (using psychrometric chart at T_db = 94.6˚F & dw_lb = 0.0206)
• h_i = 22 (using psychrometric chart at T_db = 70˚F & RH = 30%)
• h_t = 4.5 x 605 x (45.5 – 22) = 63,980 Btu/hr

Q_t = Q_l+s_r + h_t = 105,740 + 63,980 = 169,720 Btu/hr / 12,000 = 14.14 tons