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I own an evaporative air cooler of width 28 inches and height 34 inches, I was wondering if a taller air cooler with lesser width (but same surface area as the one I own) would have been more efficient in cooling the room.

My logic is that a cooler with lesser height would throw the air at a lower height and as cool air tends to sink, taller coolers can be more efficient. But also my bed rests lower on the ground so a cooler with more width and lesser height would throw the cool air horizontally (which would be better) while lowering the direction of the taller cooler would result in throwing the air at a negative angle from the horizontal which intuitively feels to me that more cold air is lost as its basically cooling the ground more.

How do I calculate the difference in efficiency of both the coolers given their surface area and all other factors are same, at different levels of height in the room. Assuming the fan is not turned on i.e there is minimal vertical air flow. What all criteria should be taken into account? How would it affect the calculations if the fan is in fact turned on i.e more vertical air flow?

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Nope, the density difference between hot and cold air, and humid and dry air, is insufficient to make any difference in the efficiency of a swamp cooler. Ditto for the exit angle of the cooled air atream coming out of the cooler.

The reason all of them are more or less cubical in shape is that this minimizes the amount of steel needed to build the cooler housing relative to the surface area of the sides containing the evaporation pads, thereby minimizing the manufacturing cost for the unit.

The primary determinant of the power consumption of a swamp cooler is the size of the motor that drives the fan, and the fan design itself. This is why all but the cheapest coolers use squirrel-cage fans that are direct-driven (no belts, gears, etc. between the motor shaft and the fan assembly). These waste less energy than a propeller-type fan per cubic foot of air delivered. They also generate less noise than a propeller fan, which is an important consideration when the cooler is used in a home or office.

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