I have been investigating the requirements for students to be able to weld on campus, which is needed for our Baja SAE team, for projects for our Engineering Senior Design course, and for other various engineering projects.  One of the requirements is, naturally, adequate ventilation.   Specifically¹

Adequate ventilation providing 20 air changes per hour, such as a suction hood system should be provided to the work area.

We have considered several shop rooms as a possible welding space, but it’s not clear if they already have sufficient ventilation or what it would take to add enough ventilation capacity.   What I realized today is that it is useful to turn the question around and ask:  for a “standard” amount of ventilation, how big a space can be properly ventilated to obtain 20 air changes per hour?

What is a “standard” unit of ventilation?   I have a regular old box fan in my lab, and I was able to measure the speed of the exiting air using a borrowed anemometer.  Fans like this are ubiquitous on a college campus, so I’ll chose that as the standard.   The dimension are 19″ × 18.5″, for a total area of 2.44 square feet.   I could compute the flow rate (volume/time) by multiplying the area by the speed of the air exiting the fan (in the same linear units!),  but this anemometer was so smart that if I enter the area it automatically gives me the flow rate in cubic feet per minute (CFM).  The flow rate varied with position around the fan, so I took what seemed like a representative average of measurements all over  (we could do this better, but I just need a ball-park estimate).   There are three speeds: low, medium, and high.   The results were:

Low: 1750 CFM,   Medium: 2250 CFM,   High: 2650 CFM

Just to use a rough order-of-magnitude estimate I will use 2000 CFM in what follows (mostly).

Next, I need a unit of volume.   One of the rooms that is being considered for welding is room 008 in the basement of Resnick Hall (RH 008).   That room has a roll-up door which happens to be exactly 8 feet wide and 8 feet tall.  I need a unit of volume, not area, so I’ll imagine a cube that goes 8 feet back from that door, for a total of 8’× 8′ × 8′ = 512 cubic feet.    This is about the size of the smallest PODS storage container, so I will call this a “pod”² (their container is actually 8′ × 7′ × 7, but this is close enough for our estimate).

The questions then are 1) how many “pods” can a single box fan ventilate (at 20 air changes per hour), and 2) how many pods does it take to match the volume of the room in question?  If the numbers are wildly mis-matched then we  know we can stop there.  If they are close, then we can refine our calculations, or just make sure we add an “engineering margin” to be sure we are over the required capacity.

First, how many “pods” can a single box fan ventilate?  Let’s call that unknown N, and compute it by setting the required ventilation rate equal to the measured rate:

On the left we have the required flow rate for 20 times the volume of N pods (in cubic feet) every 60 minutes.  On the right we have a representative flow rate for a box fan, in cubic feet per minute.  I’ve taken care to use the same units everywhere for time and volume.  Setting these equal and solving for N gives:

The numerical value comes out to be 11.718, which I will round up to 12 pods. (Using 2250 CFM for the “Medium” setting on the fan would give 13 pods.)

But I have to take into account that the ceilings in RH 008 are rather high.   They are certainly more than 8 feet, probably more than 12 feet, and maybe even 16 feet.   Since this is only an estimate, I’m happy to perhaps go over a bit and guess 16 foot ceilings, which means we have to imagine two of these pods stacked on top of each other.   Then the corresponding floor area we can ventilate with one box fan ends up being half the number, or 6 pod “footprints” of 8′ by 8′.

If the floor area of RH 008 is about the same as 6 of these 8′ by 8′ pods, then we are okay with just one box fan.   If it’s twice as large, then we can use two box fans.  If it’s as much as as four times this then we could put 4 box fans across the bottom of the sliding door and have enough ventilation.

If we need multiple box fans across the opening then I imagine they might be in a frame, perhaps with wheels to make it easier to move in and out of place.   The box fans are 19″ wide, and with some allowance for the frame that means we could get as many as 4 across the opening.   That would cover 4×6 = 24 pod “footprints”.

And note that the estimated 2000 CFM for one box fan was closest to (and under) the “Medium” setting.   We can easily re-work this estimate with the fan(s) set on “High”  if needed.  This will give us an estimate for the upper bound of possibility.  Using 4 box fans set to “High” at 2500 CFM would give 24 × 2500/2000 = 30 pod footprints.

My purpose here was to make an estimate to see if we could use one or a few box fans to ventilate a particular room, but the method can easily be applied to any other room, because a box fan provides a reasonable standard of ventilation, and a “pod” of 8’× 8′ × 8′  or with a footprint of 8’× 8′ is a representative unit of volume which one can easily picture in any room – no tape measure required.  We can use this to quickly rule in or out the possibility of ventilating any candidate space.