Atmospheric Buoyant Force
Date: winter 2013-14
How much does our atmosphere buoy us up?
The buoyant force on our bodies is the weight of the air we displace. The volume of a 70 kg person is around .07 cubic meters, and air has a density of around 1.2 kg per cubic meter, so our buoyant force is around .07 * 1.2 kg = 84 grams.
The “Law of Bouncy” is this. When an object is weighed while submerged on a fluid, the object’s weight is reduced BY THE MASS OF THE VOLUME OF THE FLUID THAT IS DISPLACED. In most cases the correction is small, but must be made for precise measurements.
Suppose you weigh 100 gm of an object that has a density of 1 gm/cm^3 – about the density of water. The density of air is approximately 0.00118 gm/cm^3.
Of course that number has to be adjusted for the humidity of the air and for the barometric pressure in precise measurements.
Then the “apparent” weight of the object is: 100x[1 – 0.00118 / 1.0] = 100 – [1 – 0.00118] = 0.118 gm less than 100 gm – or 0.118% is the mass that is supported by the displaced air.
A definitive text on the precise measurement of masses is: “Handbook of Mass Measurement” by Frank E. Jones and Randall m. Schooneover published by the Chemical Rubber Company (CRC) (2002) ISBN: 0-8493-2531-5 or visit www.crcpress.com .
What I think you are asking about concerns how much air is displaced by a human body. The weight of that air (based upon your volume) is the buoyancy which reduces your apparent weight under normal atmospheric conditions.
The first question is what is your volume? We could measure that by momentarily submerging you in a large graduated cylinder with water. But the easy way is to take your weight in kilograms, and figuring that humans are mostly water, figure that our volume in liters is pretty close to our weight in kilograms. I know that is close for me, as I float if my lungs are full but sink if my lungs are empty, so I know that my "density" is pretty close to that of water which is about 1 kilogram per liter. A liter is 1000 cubic centimeters = 1000 milliliters. A cubic meter = 1,000,000 cubic centimeters = 1,000,000 milliliters = 1000 liters.
So if you take your weight; see the density of air here: http://en.wikipedia.org/wiki/Density_of_air According to this page, the density of air at 25 degrees C is 1.1839 kilogram per cubic meter.
So if we suppose that your weight might be 75 Kilograms, then your volume is probably close to 75 liters, or 0.075 cubic meters. Then the weight of the air which you displace will be 0.075 x 1.1839 kG = 0.08879 kG = 88.79 grams.
This is all a "rough" calculation. Also, in theory grams and Kg are measures of mass, not weight, so the above calculation is not completely rigorous.
The better answer would be that buoyancy is force, which can be measured in Newtons. On the surface of the earth, 1 kG weighs about 9.8 Newtons or 980,000 dynes. So the buoyant force of air on the 75 kG person would be roughly 0.870 Newtons or 87,000 dynes.
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Update: November 2011