Calculating the Rise of Hot Air in a Solar Dehydrator

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To calculate the rise of hot air in a solar dehydrator, one must determine the air density both inside and outside the tube, considering the temperature and humidity levels. The hot air is at 120°F with 30% relative humidity, while the outside air is at 80°F with 60% relative humidity. By multiplying the air density by the volume of the hot air (40 cubic feet) and gravitational acceleration, one can find the total force affecting the air's movement. This force can then be used to account for friction and acceleration within the tube. Accurate calculations will provide a better estimate than an educated guess.
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So for a class I am designing a solar dehydrator and I want to know how fast the hot air will rise out of the dehydrator. For calculation purposes assume the hot air is 120°F @ 30% relative humidity (23 g/m3) and rising through a tube (if necessary assume the tube is 4 in. in diameter), the outside air is 80°F @ 60% relative humidity. In addition assume the hot air has a volume of 40 cubic feet.

If anybody knows how to calculate how fast it will rise through the tube that would be awesome. Otherwise I will most likely doing an educated guess.

Thanks.
 
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How long is the tube?

If you can calculate the air density inside and outside, multiply it with the volume inside and the gravitational acceleration of Earth to get the total force. That will be used for friction and acceleration of the air, with some fraction to determine.
 
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