Calculations

Cooling Load Calcs

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

Cooling Load

  • 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

Solar Radiation through glass

  • 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
  • SC = Shading Coefficient
  • 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)
  • 0.25 for white shades, 1.0 for no shades

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

Ventilation Air Cooling Load

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