Air Conditioner and Windows

I have a indoor heating question for you guys.
I have a 2 story house that gets hot in the upper floor and stays pretty cool on the ground floor. I have air conditioning which I only use on really hot days. By the way I installed eyebrow vents that don't seem to be doing a whole lot. I also have a high ceil living room and it takes the AC quite a while to really cool the house.
Anyway, I know the theory is to keep all the windows closed when using the AC, but......... I have hot air trapped on the second floor. Wouldn't it make sense to open the upper windows to push the hot air out while the cool AC air is pumped in? Is this true or am I way off base?

You have two forms of convection in your house, forced and static. Static convection is caused by cold dense air flowing down and lighter warm Air being forced up, this is known as the STACK effect and means the upper floors will always be warmer. Forced convection is created by the supply and return air flow of the A/C unit. Air conditioning units not only cool the Air but also remove moisture and this Latent load can use up to 33% of the unit capacity. So its not just the temperature of the outside air which has to be considered but also it's relative humidity. The Duct layout has to be considered but extract fans in the bathroom or toilet with the windows closed would probably improve the second floor temperature.
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Put a ceiling fan in the living room- that will help a bunch. Like the other guy said, balancing upper and lower floor can be a PITA. I'd get a good HVAC company in for a site survey of the ductwork and system capacity. You made need a zoned system. Not sure what you mean by 'eyebrow vents'- something in the attic? Attic venting and insulation is crucial on the upper floor, otherwise attic gets superheated on sunny days, and radiates back down into the living space, until well after dark. Adding another six inches in this place made a noticable difference in comfort, and on the power bill.
aem sends...

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Way off base.

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One reason it can take a long time to cool off a house when the A/C is first turned on is that often the air is moist and hot and the home (walls furniture etc.) are hot so the A/C first have to remove the moisture and then as it tries to cool the air it is also cooling the walls, floors and furniture. Sometimes it is more energy efficient to run the A/C all the time and not try and vent the house. (note this would generally only be the case when the humidity was high)
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No. Remember that when you are running the A/C the air outside is hotter than the air inside. You are replacing hot air with hotter air.
Now if you were to block off the upstairs from the downstairs then venting the upstairs would make sense.
Frankly if you want to cool the whole house you would start with the upstairs.

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By opening the window, you will vent some of the hot air, but you will also replace it with hotter moister air that will get mixed in and make matters worse.
Sounds like your system needs to be balanced. Be sure you have proper return vents, partially close some of the outlets on the first floor to force more of the cooker air to the second floor.
Be sure you have clean filters and are getting proper air through the system to start with.

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Thanks for the replies.
So if I understand correctly, if the air is hotter outside than inside, keep the windows closed, venting it out with the AC will not work. It almost sounds as if a fan is more effective than the AC.

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Fans do not cool at all, they just move air around and you may feel a little cooler in the breeze. Fans do not remove humidity.
Get the AC working right and you'll be happy with it.