CIVE 3209 Assignment 2 Solutions Winter 2020
1. A condominium unit has a single exterior surface of 60 m2 facing the south orientation in Ottawa.
The window-to-wall area ratio is 0.5. The R-SI of the wall is 5 m2·K/W. The infiltration rate is 0.25
L/s·m2 of the exterior wall surface area. Thickness of the concrete floor slab is 0.2 m. The floor
area is 100 m2. While selecting the window U-SI value, you want to make sure that your building is
resilient to a three-day power outage in the winter. Your design objective is that the temperature of
the building will not be less than 10°C after a three-day power outage. Assume that the outdoor
temperature is constant at -10°C for the three-day analysis period. Neglect solar and internal heat
gains. When the power outage starts, assume that the temperature of the unit is 22°C at the onset of
the power outage. Treat the unit as a single lumped capacitance. Assume the density, specific heat,
and thermal conductivity of the concrete slab as 2300 kg/m3, 800 J/kg·K, and 1 W/m·K,
respectively; and the specific heat and density of air as 1.2 kg/m3 and 1000 J/ kg·K, respectively.
Lumped capacitance of 𝐶 = 𝑐𝑐𝑜𝑛𝑐 ∙ 𝑣𝑐𝑜𝑛𝑐 ∙ 𝜌𝑐𝑜𝑛𝑐
concrete slab:
= 800 𝐽⁄𝑘𝑔𝐾 ∙ (100𝑚2 × 0.2𝑚) ∙ 2300 𝑘𝑔⁄𝑚3
𝐶 = 36,800,000 𝐽/𝐾
Total system resistance: −𝑡
𝑇(𝑡) = 𝑇𝑜𝑎 + (𝑇𝑡=0 − 𝑇𝑜𝑎 )𝑒 𝑅𝐶 where t @ 3 days = 259,200s
−259200𝑠
10℃ = −10℃ + (22℃ − (−10℃))𝑒 𝑅×36,800,000 𝐽/𝐾
𝑅 = 0.015 𝐾/𝑊
U-SI of window: −1
𝐴𝑤𝑎𝑙𝑙
𝑅=( + 𝐴𝑤𝑖𝑛 𝑈𝑤𝑖𝑛 + 𝑐𝑎𝑖𝑟 ∙ 𝑞𝑖𝑛𝑓 ∙ 𝐴𝑤𝑎𝑙𝑙 ∙ 𝜌𝑎𝑖𝑟 )
𝑅𝑤𝑎𝑙𝑙
30𝑚2 1𝑚3
0.015 𝐾/𝑊 = (5𝑚2 𝐾⁄𝑊 + 30𝑚2 × 𝑈𝑤𝑖𝑛 + 1000 𝐽⁄𝑘𝑔𝐾 ∙ 0.25 𝐿⁄𝑠𝑚2 × (1000𝐿) ∙ 60𝑚2 ∙
−1
1.2 𝑘𝑔⁄𝑚3 )
𝑈𝑤𝑖𝑛 = 1.42 𝑊 ⁄𝑚2 𝐾
Therefore, the window would need to have a maximum U-SI of 1.42 W/m2K to ensure the temperature does not drop
below 10˚C during the three-day power outage.
1
, CIVE 3209 Assignment 2 Solutions Winter 2020
2. You are hired to commission one of the two air handling units in Canal Building. During a site visit
on a cold winter day, you took the measurements indicated in the figure below. For simplicity,
assume that the density of air 1.2 kg/m3 in all your calculations.
(i) In less than 200 words, define what an air handling unit is and explain its four modes of
operation (i.e., heating, economizer, economizer with cooling, cooling).
(ii) Determine the outdoor air fraction. Compare it to the outdoor and return air damper
positions. Interpret your results from this comparison.
(iii) Determine the outdoor airflow rate in L/s.
(iv) Determine the sensible and latent heating rate in kW.
(v) Determine the humidification rate in g/s.
(vi) Assuming that heating and humidifier coils can linearly control the sensible and latent
heating rates, determine the coils’ capacity.
(vii) If we need to provide 10 L/s-person outdoor air for ventilation purposes and if the
building is used by 250 occupants, comment on the outdoor airflow rate calculated in (iii).
(viii) Without changing the supply airflow rate, temperature, and humidity, what would you do
to change the outdoor airflow rate to 2,500 L/s (250 x 10 L/s)? Estimate the reduction in
sensible and latent heating rate in kW and percentage points.
(i) Definitions:
An air handling unit (AHU) is the main component of a forced-air system that conditions the supply air to adequate
temperature and IAQ requirements. This is achieved by bringing in a combination of fresh outdoor and return air into a
mixing plenum via a series of dampers, where this air is filtered, heated/cooled, and humidified. An AHU is supported
by a chiller and boiler to provide cooling or heating via coils in the unit. In the heating mode, AHUs bring in the
minimum outdoor air required to meet IAQ requirements, with the heating coil operating to bring the colder mixed air
up to temperature. In the economizer mode, outdoor air is brought in as required to meet the target supply air
temperature without the use of heating or cooling coils. In the economizer/cooling mode, the unit brings in 100%
outdoor air and cools this air with the cooling coil as needed. In the mechanical cooling mode, outdoor air is once again
brought in at a minimum and conditioned entirely by the cooling coil.
2
1. A condominium unit has a single exterior surface of 60 m2 facing the south orientation in Ottawa.
The window-to-wall area ratio is 0.5. The R-SI of the wall is 5 m2·K/W. The infiltration rate is 0.25
L/s·m2 of the exterior wall surface area. Thickness of the concrete floor slab is 0.2 m. The floor
area is 100 m2. While selecting the window U-SI value, you want to make sure that your building is
resilient to a three-day power outage in the winter. Your design objective is that the temperature of
the building will not be less than 10°C after a three-day power outage. Assume that the outdoor
temperature is constant at -10°C for the three-day analysis period. Neglect solar and internal heat
gains. When the power outage starts, assume that the temperature of the unit is 22°C at the onset of
the power outage. Treat the unit as a single lumped capacitance. Assume the density, specific heat,
and thermal conductivity of the concrete slab as 2300 kg/m3, 800 J/kg·K, and 1 W/m·K,
respectively; and the specific heat and density of air as 1.2 kg/m3 and 1000 J/ kg·K, respectively.
Lumped capacitance of 𝐶 = 𝑐𝑐𝑜𝑛𝑐 ∙ 𝑣𝑐𝑜𝑛𝑐 ∙ 𝜌𝑐𝑜𝑛𝑐
concrete slab:
= 800 𝐽⁄𝑘𝑔𝐾 ∙ (100𝑚2 × 0.2𝑚) ∙ 2300 𝑘𝑔⁄𝑚3
𝐶 = 36,800,000 𝐽/𝐾
Total system resistance: −𝑡
𝑇(𝑡) = 𝑇𝑜𝑎 + (𝑇𝑡=0 − 𝑇𝑜𝑎 )𝑒 𝑅𝐶 where t @ 3 days = 259,200s
−259200𝑠
10℃ = −10℃ + (22℃ − (−10℃))𝑒 𝑅×36,800,000 𝐽/𝐾
𝑅 = 0.015 𝐾/𝑊
U-SI of window: −1
𝐴𝑤𝑎𝑙𝑙
𝑅=( + 𝐴𝑤𝑖𝑛 𝑈𝑤𝑖𝑛 + 𝑐𝑎𝑖𝑟 ∙ 𝑞𝑖𝑛𝑓 ∙ 𝐴𝑤𝑎𝑙𝑙 ∙ 𝜌𝑎𝑖𝑟 )
𝑅𝑤𝑎𝑙𝑙
30𝑚2 1𝑚3
0.015 𝐾/𝑊 = (5𝑚2 𝐾⁄𝑊 + 30𝑚2 × 𝑈𝑤𝑖𝑛 + 1000 𝐽⁄𝑘𝑔𝐾 ∙ 0.25 𝐿⁄𝑠𝑚2 × (1000𝐿) ∙ 60𝑚2 ∙
−1
1.2 𝑘𝑔⁄𝑚3 )
𝑈𝑤𝑖𝑛 = 1.42 𝑊 ⁄𝑚2 𝐾
Therefore, the window would need to have a maximum U-SI of 1.42 W/m2K to ensure the temperature does not drop
below 10˚C during the three-day power outage.
1
, CIVE 3209 Assignment 2 Solutions Winter 2020
2. You are hired to commission one of the two air handling units in Canal Building. During a site visit
on a cold winter day, you took the measurements indicated in the figure below. For simplicity,
assume that the density of air 1.2 kg/m3 in all your calculations.
(i) In less than 200 words, define what an air handling unit is and explain its four modes of
operation (i.e., heating, economizer, economizer with cooling, cooling).
(ii) Determine the outdoor air fraction. Compare it to the outdoor and return air damper
positions. Interpret your results from this comparison.
(iii) Determine the outdoor airflow rate in L/s.
(iv) Determine the sensible and latent heating rate in kW.
(v) Determine the humidification rate in g/s.
(vi) Assuming that heating and humidifier coils can linearly control the sensible and latent
heating rates, determine the coils’ capacity.
(vii) If we need to provide 10 L/s-person outdoor air for ventilation purposes and if the
building is used by 250 occupants, comment on the outdoor airflow rate calculated in (iii).
(viii) Without changing the supply airflow rate, temperature, and humidity, what would you do
to change the outdoor airflow rate to 2,500 L/s (250 x 10 L/s)? Estimate the reduction in
sensible and latent heating rate in kW and percentage points.
(i) Definitions:
An air handling unit (AHU) is the main component of a forced-air system that conditions the supply air to adequate
temperature and IAQ requirements. This is achieved by bringing in a combination of fresh outdoor and return air into a
mixing plenum via a series of dampers, where this air is filtered, heated/cooled, and humidified. An AHU is supported
by a chiller and boiler to provide cooling or heating via coils in the unit. In the heating mode, AHUs bring in the
minimum outdoor air required to meet IAQ requirements, with the heating coil operating to bring the colder mixed air
up to temperature. In the economizer mode, outdoor air is brought in as required to meet the target supply air
temperature without the use of heating or cooling coils. In the economizer/cooling mode, the unit brings in 100%
outdoor air and cools this air with the cooling coil as needed. In the mechanical cooling mode, outdoor air is once again
brought in at a minimum and conditioned entirely by the cooling coil.
2
