HVAC duct pressure differential

Anyone good with HVAC here ... I am adding a duct/fan to bring hot air from a loft area down to the floor of the main level, in order to help reduce heating costs (and possibly, in summertime, to make the loft area more livable. So this is separate of my main HVAC ductwork.

I'm trying to figure the pressure the fan (probably a Fantech FR series) is going to be working against. The CFM of the fan drops off as the pressure head increases, but it doesn't get too significant until about 0.5" H2O, so I'm trying to figure out how much. The duct calculator says I should be below 0.2" or so, just based on the length and diameter of the flexduct. But since I'm sucking quite hot air downwards about 15ft, that's going to add some pressure over and above the friction loss in the ductwork. But I have no idea how to figure out how much. Thanks.

.5 inches wc is a lot of pressure for a short air transfer. I dont know your set up but i dont see you getting anywhere near that. You could always can the flex and just use pipe and that will greatly cut down on friction loss if thats what your worried about. Me personally i hate the stuff and hard pipe everything. Since you have a duct calculator just use the fans max cfm and then use a conservative velocity in the 600-800 fpm range and just size accordingly.

Stack effect on a house, top to bottom , when it is freezing out is ~2-3 Pascals, which works out to be ~0.01-0.015" WC.

I think you can safely neglect it relative to duct loss.

The calculator I found, a spreadsheet from Hart&Cooley, I'm using a form where you give it duct diameter, length, and number of bends, and CFM, and it gives you friction loss. So it figures the velocity when doing the calc I guess.

Ah yes, "stack effect" must be the correct term for what I'm asking about - the fact that the hot air in the loft wants to rise and instead I'm sucking it downwards 15ft or so. Is there some calculator that I can use to get this number directly ? But you're right, even if it's 0.02"WC it is insignificant relative to the friction losses.

These hearth forums are amazing - the wealth and knowledge and helpfulness of the people here !

the formula would be: delta_P = delta_rho * g * h, where g is 9.8 m/s^2, h is in meters, delta_rho is the difference in air density at the two temps, in kg/m^3, and delta_P is in Pascals. rho for air = ~1.3 kg/m^3, and inversely proportional to absolute temp. So it is prob about delta_rho = 1.3 * delta_T(°F) / 500, assuming your average temp is 500°F above absolute zero.

More or less.

Cool stuff, thanks. For 20-degreeF delta-T and 5 meters, I get about 2.5 pascals, or 0.01" WC like you said. Insignificant compared to friction loss in ductwork. Thanks.

That's why passive vents to move hot air have to be so large.

Any thoughts about how many air-changes per hour I should be aiming for ?

Your question is hard. IF you are just dumping the hot air at the bottom of a big space, it will just rise up again without effect. IF you want to mix a big space you should get a ceiling fan for maximum CFM/Watt and mixing. IF you are sending the heat to a more distant locations, figure how much heat you want to move, and use: BTU delivered is ~ 1 BTU/h * CFM * Delta_T(°F).

I'll have a ceiling fan for sure. But the hot air is being sucked from a separate space (a loft in the "great" room, where my Blaze King sits), hence the transfer duct; so a calculation like you suggest makes sense.

I don't understand the first factor in your formula though. I don't think you mean to be saying it takes 1 btu to heat a cubic-foot of air by 1°F. I believe the specific heat of air is about 0.24 btu per lb per °F. Air weighs roughly 0.8oz/ft^3. So it's about 0.012 btu per cu-ft per °F.

So if I'm moving 200cfm and the temperature diff'al is 20°F, I'm only moving aboiut 3000 btu/hr. Yikes. Does my arithmetic look right ?

Yup. The formula is for 'power', BTU/h and I think the prefactor is something like 1.06. These is a 60 in there to convert minutes to hours.
Your prefactor would be something like 0.012 BTU/cuft°F*min * 60 min/h = 0.72 (vs my 1.06). We differ by 30%.

I would have estimated 200 cfm and 20°F to give something like 1.06*200*20 = 4240 BTU/h, ~1250W.

Its hard to move heat with warm rather than hot air.