# Application Problem: Ventilation Rate

• Dec 6th 2008, 03:49 PM
chrozer
Application Problem: Ventilation Rate
Quote:

The model
$\displaystyle y=80.4 - 11\ln x$, $\displaystyle 100\leq x\leq 1500$
which approximates the minum required ventilation rate in terms of the air space per child in a publich classroom. In the model, $\displaystyle x$ is the air space per child in cubic feet and $\displaystyle y$ is the ventilation rate per child in cubic feet per minute.

A classroom is designed for 30 students. The air conditioning system in the room has the capacity of moving 450 cubic feet of air per minute.

(a) Determine the ventilation rate per child, assuming that the room is filled to capacity.
(b) Estimate the air space require per child.
(c) Determine the mininum number of square feet of floor space required for the room if the ceiling height is 30 feet.
(a) Wouldn't that be just $\displaystyle \frac {450}{30} = 15$ cubic feet of air per minute per child?

(b) Have no idea how to do this one. Any ideas?

(c) Don't know how to work this one either. Any ideas?
• Dec 7th 2008, 01:04 AM
CaptainBlack
Quote:

Originally Posted by chrozer
(a) Wouldn't that be just $\displaystyle \frac {450}{30} = 15$ cubic feet of air per minute per child?

yes

Quote:

(b) Have no idea how to do this one. Any ideas?

(c) Don't know how to work this one either. Any ideas?
There is insufficient information to answer these, are you supposed to be using some form of space standard to supplement the question.

CB
• Dec 7th 2008, 06:02 AM
chrozer
Quote:

Originally Posted by CaptainBlack
yes

There is insufficient information to answer these, are you supposed to be using some form of space standard to supplement the question.

CB

Srry I forgot to add one more thing.

Quote:

The model
$\displaystyle y=80.4 - 11\ln x$, $\displaystyle 100\leq x\leq 1500$
which approximates the minum required ventilation rate in terms of the air space per child in a publich classroom. In the model, $\displaystyle x$ is the air space per child in cubic feet and $\displaystyle y$ is the ventilation rate per child in cubic feet per minute.
• Dec 7th 2008, 06:57 AM
CaptainBlack
Quote:

Originally Posted by chrozer
Srry I forgot to add one more thing.

We have the ventilation rate per child and so if $\displaystyle x$ is the minimum air volume per child we have:

$\displaystyle 15=80.5-11\ln(x)$

Solve this for x to get the answer for part b.

CB
• Dec 7th 2008, 07:57 AM
chrozer
Quote:

Originally Posted by CaptainBlack
We have the ventilation rate per child and so if $\displaystyle x$ is the minimum air volume per child we have:

$\displaystyle 15=80.5-11\ln(x)$

Solve this for x to get the answer for part b.

CB

Ok. I got $\displaystyle x$ to be $\displaystyle \approx 382$ cubic feet per child.

I'm stuck on part (c) though. What do I do for it?