Question 1178476: According to the American Society of Heating, Refrigerating
and Air-Conditioning Engineers, Inc. (ASHRAE), a nonsmoking classroom
should have a ventilation rate of 15 ft3 per min for each person in the room.
(a) Write an equation that models the total ventilation V (in cubic feet per hour)
necessary for a classroom with x students.
(b) A common unit of ventilation is air change per hour (ach). One ach is equivalent
to exchanging all the air in a room every hour. If x students are in a classroom
having volume 15,000 ft3, determine how many air exchanges per hour (A) are
necessary to keep the room properly ventilated.
(c) Find the necessary number of ach (A) if the classroom has 40 students in it.
(d) In areas like bars and lounges that allow smoking, the ventilation rate should
be increased to 50 ft3 per min per person. Compared to classrooms, ventilation
should be increased by what factor in heavy smoking areas?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step by step:
**(a) Equation for Total Ventilation (V)**
* **Ventilation per person:** 15 ft³/min
* **Number of students:** x
* **Total ventilation per minute:** 15x ft³/min
* **Convert to cubic feet per hour:** 15x ft³/min * 60 min/hour = 900x ft³/hour
Therefore, the equation is:
* **V = 900x**
**(b) Air Exchanges per Hour (A)**
* **Total ventilation per hour:** V = 900x ft³/hour
* **Classroom volume:** 15,000 ft³
* **Air exchanges per hour (A):** A = (Total ventilation per hour) / (Classroom volume)
* **A = (900x) / 15,000**
* **A = 9x / 150 = 3x / 50**
Therefore, the number of air exchanges per hour is:
* **A = 3x / 50**
**(c) Necessary Air Exchanges with 40 Students**
* **Number of students (x):** 40
* **A = 3x / 50**
* **A = 3(40) / 50**
* **A = 120 / 50**
* **A = 12 / 5 = 2.4**
Therefore, with 40 students, 2.4 air exchanges per hour are necessary.
**(d) Ventilation Increase in Smoking Areas**
* **Ventilation in classrooms:** 15 ft³/min per person
* **Ventilation in smoking areas:** 50 ft³/min per person
* **Factor increase:** (Ventilation in smoking areas) / (Ventilation in classrooms)
* **Factor increase:** 50 / 15
* **Factor increase:** 10 / 3 ≈ 3.33
Therefore, ventilation should be increased by a factor of 10/3 or approximately 3.33 in heavy smoking areas.
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