because both ends are connected to the same atmosphere cancelling out any weight pressure. this is unlike open water loops where water (which is heavier than iar) is connected to atmosphere.
Thanks all for your answers.
If you have a 10m vertical duct with 300m3/hr the height pressure is about 12 mm H2O, this can be important in relation with the friction pressure loss, depending of the type of duct. Is this wrong? If you only have a straight duct, then according to my calculations it could be important.
I'm not sure how, even if negligible it would matter at all. since the air in the duct has same density as the atmosphere, the height pressure isn't only negligible, it is nonexistent. unless you move warm or cold air, then you have some stack effect working for or against the fan, but that is little. but if yo move air at same tamp s the surrounding, you have exactly 0 gravity pressure, not negligible, 0.
Ades: if your duct is in a vacuum your assumptions is correct because then you need energy to lift the air. but the air floats in air, and moving it around only requires to overcome friction. 10 m duct vertical or horizontal doesn't' matter.
Same way in hydronic systems, in closed loops we don't take height into account. but in open loops.
If you apply Bernoulli at the inlet, berore the fan, and at the outlet, you will have:
v1=0, v2=v (v=velocity inside the duct, suposing air comes out at the same velocity it has inside the duct)
p1=p2 + SP(z2-z1) SP: Specific Weight of air
Therefore substituting in the Bernoulli formula you will have that the work needed by the fan is only the friction losses plus velocity pressure.
Is this correct?
Thermal Gravity Effect calculation is usually taken into consideration when the temperature difference and the height of the vertical duct are significantly high. In most cased it is usually negligible.
Here is an example:
THERMAL GRAVITY EFFECT CALCULATION
D Pse : Thermal Gravity Pressure Differential, in.wc
ra: Ambient (Room) air density, lb/ft3. 0.0745 lb/ft3 for 75 oF
r: Density of the air in the duct, lb/ft3. 0.08 lb/ft3 for 40 oF
Dh: Elevation difference between the air intake and discharge, 4.0 ft.
DPse = 0.192 x (ra - r) x Dh
DPse = 0.192 x (0.0745 - 0.08) x (4.0) = -0.004 in.wc (pressure change due to elevation/density diff.)
Ades: your bernoulli equation ignores buouncy of air, meaning the air displaces as much air as it weighs, so you don't have to overcome gravity. It would apply to vaccuum (not sure you how keep the air in the duct if you had it in a vaccuum......) and fluids with higehr density than atmosphere, like water. Unless you have a very high duct, with high dT, stack effect doesn't matter much.
How much did you sweat last time you had to carry air up the stairs??????? adn how much potential energy could you extract from your airdam power plant (like hydrodam, except filled with air)? If you needed energy to blow air up the duct, then you should be able to run a generator on a windmill in the duct when the air falls back, right?
Use practical formula from ASHRAE Fundamentals to calculate it:
p,st = 0,192 x (ro,a - ro) x (z2 - z1)
ro,a - ambient air density
ro - supply air density.
You have to care about direction: if you supply cold air upwards (fan is at the bottom) ro > ro,a, stack effect is downwards and will act as additional pressure loss. If you supply warm air in the same direction, stack effect will "help" fan. The opposite applies to downward design flow.
To assess whether is negligible or not, calculate, compare with total pressure drop calculated for system and you will see.
When in doubt, it is much more responsible to check it (as you are seemingly attempting) than to find resort in general "rule of thumb" assumptions.
Rules of thumb are good only if you are certain that you can apply them.
I was considering no temperature variation, therefore the density remains the same and there is no stack effect.
I think HerrKarl example of obtaining potential energy from a duct full of air makes clear that the above reasoning of the Bernoulli ecuation for a non compressible fluid is correct: the height pressure diffence is cero. The same thing happens if you pump wáter through a pipe inside water, that is you have water at the outlet of the pipe. It would be different if you exhaust the air, lets say, through a vertical duct, but into another room that is pressurized, then the difference in height pressure (or potential energy) would not cancel.
I cant imagine a situation where you have constantly a vaccum in the duct, but if fan stops, then air will fill the vacuum. On the othe side if you put the fan at the top you would have a negative pressure inside the pipe, but on the outside you will always have the atmospheric pressure, and you would require the same amount of energy.
Drazen's equation and reasoning is correct, if you need to take into account stack effect. If your duct temp ia bout the sane as the air surrounding the duct you will achieve zero. If you have significant dT, you will have some stack effect, but if you calculate it, you will see it is very small compared to your friction loss.
Actually there are solar power plants that work with a tall chimney and hot air rising up, so this can be a significant amount. but you likely don't have a 1000ft tall duct and have hot air at some hundred °F.
Thanks HerrKarl, but my doubt was referring to a duct with constant temperature (no variation in density) and considering incompressible flow. In some handbooks I found they add up height pressure, but I think my error was to consider the atmospheric pressure the same at the inlet in the bottom and the outlet at a diferent altitude. This could be okay, if there is water inside the duct and air outside (the error would be very small), but not if you have air inside and outside.
it has nothing to do with variations in duct temperature - average value is to be used - but with temperature difference between supply air and space air, as mentioned.
