Calculating changes in Fan Power

[StudYMA]

I have a question regarding the relationship between airflow restriction and fan power. If the pressure drop across an airflow restrictor (filter bank, heat exchanger coils, etc.) is known by measuring with a magnehelic differential pressure gage and that dP changes (filter replacement/removal, etc), how will that affect fan speed/fan power?

I am talking about a variable speed fan which aims to maintain a constant duct static pressure downstream of said obstructions, so I believe that the fan speed would decrease, but how do I calculate how much?

To find power reduction I initially used an extended bernoulli equation ignoring kinetic and potential energy factors which reduced to [(pressure reduction)*(mass flowrate)]/(air density), or (pressure reduction)*(CFM) but this is coming out lower than I expected.

I'm also aware than fan power varies with the cube of fan speed, so maybe I'm skipping an intermediate step?


Thanks in advance to anybody who can assist me!

-Brian

 

[russ_watters]

Use the fan affinity laws, not Bernoulli's equation. Have a look at them and let me know if you have trouble applying them to this situation - I do this exact problem several times a week.

Google them - I'm posting from a blackberry and can't give much help right now.

 

[StudYMA]

OK, I can see how fan affinity laws would be preferred. In fact, that's where I came up with fan power being proportional to the cube of fan speed. I see that head or pressure is proportional to the square of fan speed, so that will allow me to get from change in pressure to change in fan power.

The question I have is applying the change in pressure. I'm looking at a large hospital AHU whose duct static pressure setpoint is 2" wg. The final filter bank reads 0.7" wg drop across it. I am stuck here - the only next step I can see is using 2 and 1.3 for P1 and P2 and then calculating the change in fan speed, but that doesn't seem right...

 

[russ_watters]

The trick here is to split it into two problems. The basic affinity laws are good for changing one parameter at a time - but you are changing resistance and then fan speed to compensate. So calculate a new CFM due to the change in resistance, then the new rpm needed to get you back to the original CFM.

If you just want power loss due to the restriction, that's easier. The equation is just SP*CFM/(6356*%Eff)=HP

 

[russ_watters]

Also, supply static is just a control parameter. What matters is the typical operating CFM and the SP loss across the filter for energy loss or total static rise across the fan for total fan energy.

 

[StudYMA]

First off, thanks for your patience and assistance. I'm less than a year out of school working my first engineering job so applying the concepts learned in school is still a struggle. Much easier when a textbook tells you exactly the variables you need.

Here's what I found for fan affinity laws:

CFM 1 / CFM 2 = RPM 1 / RPM 2

Delta P 1 / Delta P 2 = [RPM 1 / RPM 2]^2

Power 1 / Power 2 = [RPM 1 / RPM 2]^3


Knowing anyone of the fractions will allow me to solve for any other. The equation that stands out to me is the second one since I'm dealing with a known pressure drop across a filter bank. However I believe this equation is relating pressure differential across a fan (or head across a pump) for two different settings, and then outputting the change in fan speed given those delta P's.

You say to calculate a new CFM based on resistance - what is this relationship? I was assuming that the CFM delivered by the fan would stay the same, it just would not have to work as hard to supply it.

Finally, the equation of power loss due to restriction SP*CFM/(6356*%Eff)=HP is essentially what I came up with so that is relieving. Would it also apply to removing airflow restrictors such as sound attenuators downstream of the fan in the ductwork? Also, is the 6356 just a coefficient to get power into units of HP based on inputting pressure in units of "h2o and flowrate in units of CFM?


Again, thanks so much
-Brian

 

[karthikane]

How do you arrive to the equation SP*CFM/(6356*%Eff)=HP and how do we write this equation in SI units??