Static Pressure in relation to CFM

[ItsScience]

Hey all, I’ve scoured the internet in search of an answer to no avail, so it’s time to ask the experts!My background is more Chemistry and Biology, not Physics, or specifically fluid dynamics, so bear with me! Also, this is a little long, so I will do my best to make it easy to follow.The Problem:

I am trying to derive a formula to calculate air flow rates (in CFM) based on the static pressure (Inches W.C.) of the HEPA filter I am blowing through for a laminar flow hood that I am building. ( http://en.wikipedia.org/wiki/Laminar_flow_cabinet ) I am trying to figure this out because many HVAC application fans have ratings of their output at certain static pressures, many, many more do not, and it would be really helpful to be able to derive this information on my own.Information I have available to use:

--Standard fan information, from the manufacturer (Brake Horsepower, Fan wheel dimensions, RPM &/or CFM).

--Volume of the Plenum Chamber ( http://en.wikipedia.org/wiki/Plenum_chamber ), in this case >= 4sq.ft. (12in. x 24in. x 24in. as it is generally accepted that the size of an adequate plenum must be >= the volume of the filter).

--The Static Pressure of the HEPA filter, in my case 1in. w.c., and although I don’t know how it relates to anything or what it means, I also have the resistance range of, 0.69.

--The desired volume/rate of air on the intake of the filter, calculated out to 400CFM @ 1.00in. w.c. SP. ( Based upon this formula (Desired FPM Output) x (Volume of HEPA Filter) = Required CFM Input. ( http://www.fungifun.org/English/Flowhood#match ).

--The desired output of the entire unit, 100-200FPM, ideally.Questions developed from research & attempts to solve:

--Some fans are rated at 0.00” SP all the way up through 1..5+” SP. What are the standard conditions for these specs? I.E. in chemistry you have SC = 1.0ATM @ 0degC. If a fan is rated at 500CFM without any information given about Static Pressure, what would be the static pressure? Is it 0.00” w.c.? above, or below?

--I have stared at the Affinity, or Fan Laws ( http://www.greenheck.com/library/articles/10 )for countless hours now. Specifically Law #2. SP2 = SP1( CFM2 / CFM1)sqrd. I was hoping that this would solve my problems, but I have been trying to solve for CFM1, since I know I want SP2 to equal 1.0” and I know I want CFM2 to equal 400 @ SP2. I have been operating under the assumption that a fan, at it’s highest RPM/CFM is operating at 0.0” SP. But then you can’t calculate for the obvious reasons, so this has to be wrong. So back to standard conditions for fans.Thanks!

This has been degrading my life for a week now, any help or insite is very appreciated!

-Science!

 

[russ_watters]

Static pressure drop across an obstruction can indeed be used as a type of flow meter. The problems here are:
1. The filter gathers dust, changing its characterization.
2. The resistance vs flow function isn't necessarily quadratic like Affinity Law #2 says it should be.

The next step for you is to find or select the make and model of the filter and get a copy of the performance curve. Worst case, you can just use the curve directly instead of trying to characterize it in an equation.

 

[ItsScience]

Alright, I'll see if the company has any graphs, but currently all literature is just raw numeric data. (Flanders is the manufacturer)

Does this mean that there is no way to derive a fans performance curve at various static pressure? That seems odd to me.

 

[russ_watters]

Alright, I'll see if the company has any graphs, but currently all literature is just raw numeric data. (Flanders is the manufacturer)

Flanders most definitely provides curves.

Does this mean that there is no way to derive a fans performance curve at various static pressure? That seems odd to me.

Fans have their own performance curves that can be used in the same way (using pressure rise across the fan).

I'm wondering though why you can't just use an actual airflow sensor or better yet hire a balancer for this.

[edit: also, this is mechanical enginering, so I'll move it to that section.]

 

[ItsScience]

Thank you Russ, I appreciate the help, and thanks for moving me to the right section!

Yes, an airflow sensor would work wonders. However I am trying to find a fan to buy that do not all have the appropriate specs, or are not supplied with airflow curves, so I was trying to come up with a mathematical way to figure out what fan would suit my purposes.

Take this one for example: http://www.grainger.com/product/DAYTON-Blower-1XJX7?nls=1&searchQuery=1xjx7
It's not rated at 1.0"" Static, but I'd love to know.

This one: http://www.grainger.com/product/DAYTON-Blower-1C792?nls=1&searchQuery=1c792
Is rated above and below 1.0"

Or an eBay special: http://www.ebay.com/itm/FURNACE-FAN-BLOWER-ASSEMBLY-1-3HP-115-VOLT-/281628262452?pt=LH_DefaultDomain_0&hash=item41925a4034
You get the idea...

 

[jack action]

I'm not sure that you understood exactly how it works, so I'll explain it my way. Don't get offended if I repeat stuff you already understand.

In your duct, you will have components that will create restrictions, i.e. pressure build up. The simple use of straight duct - if long enough - will create a notable restriction. Bends can add huge restrictions. Of course, filters do as well. These restrictions all add up. If you have a filter that creates a pressure build up of 1" and you have a bend in your duct that creates a pressure build up of 1" also, you will get a total pressure build up of 2". That is the pressure drop that your blower will have to go against. So, looking at the blower's chart, it will tell you how much CFM it produces at 2" SP.

These restrictions are dependent on the flow. The bigger the flow, the bigger the restriction. It is generally a good approximation to use the «2nd fan law» equation you mentioned. So if you know that at, say, 400 cfm you get a 1" pressure built up in front of the duct (filter, bend, whatever), then you can estimate that at 566 cfm you will get a 2" pressure build up [ = (566/400)² * 1]. Obviously, using this relation, at 0 cfm you will always have 0" of pressure build up (which you will always experience anyway).

http://india.donaldson.com/en/engine/support/datalibrary/065785.pdf (you can see the square relation in the graphs).

For HEPA filters, http://www.flanders-csc.com/Downloads/hepa.pdf which relates the pressure drop with the air velocity instead of the volumetric flow (Of course, the latter depends on the air velocity times the filter area). On p. 9 of the same document, you have cfm values for particular models calculated at 1" pressure build up. You can again use the «2nd fan law» to determine the actual pressure for your actual volumetric flow need. For example, if I take the first one (12 X 12 X 11½) which is rated at 205 cfm @ 1" would probably give you a pressure of 3.81" if you would actual send 400 cfm through it [ = (400/205)² * 1].

The cfm you get from the blower's chart must match the cfm you used for all your restrictions you calculated. So if you want 400 cfm, you calculate the restrictions for all ducts, bend and filters at that volumetric flow rate and add them up. Then find a blower that will deliver 400 cfm at the total pressure build up you calculated.

 

[russ_watters]

Yes, an airflow sensor would work wonders. However I am trying to find a fan to buy that do not all have the appropriate specs, or are not supplied with airflow curves, so I was trying to come up with a mathematical way to figure out what fan would suit my purposes.

Take this one for example: http://www.grainger.com/product/DAYTON-Blower-1XJX7?nls=1&searchQuery=1xjx7
It's not rated at 1.0"" Static, but I'd love to know.

The curve is provided in tabular form in the specs. You can graph it if you want, or just interpolate from the provided table. Also, if you click-through to the catalog page, you'll find a bunch of different sizes of the same model fan. It's not a great fit for your needs, though.

Keep browsing Grainger: there's even one with a built-in filter rack that looks like it is exactly in the size-range you need.

This one: http://www.grainger.com/product/DAYTON-Blower-1C792?nls=1&searchQuery=1c792
Is rated above and below 1.0"

Looking at the catalog page, it looks like there are versions of that fan that are within the range of what you need.

Or an eBay special: http://www.ebay.com/itm/FURNACE-FAN-BLOWER-ASSEMBLY-1-3HP-115-VOLT-/281628262452?pt=LH_DefaultDomain_0&hash=item41925a4034

Ehh...I wouldn't.

Also, I was assuming the 1" drop from the filter is pretty much all you have, but Jack is right that it may not be. In particular, for a laminar flow hood, the diffuser might have a signficiant pressure drop associated with it. You do have to be sure you added-them up.

 

[MarkJW]

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