Buoyant Forces Are Everywhere

In 212 B.C., Archimedes discovered the law for buoyant force:

Any object immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by the object.

Although this phenomenon is most apparent in the case of liquids, it holds true for gases as well.

Buoyant force acts on us all the time, since we displace the air around us. Estimate the buoyant force experienced by the average human being standing at sea level, surrounded by air.

Assume that the density of air is 1.23 kg/m 3 1.23 \text{ kg/m}^3 .

0.000 1 N \SI{0.0001}{\newton} 0.01 N \SI{0.01}{\newton} 1 N \SI{1}{\newton} 100 N \SI{100}{\newton}

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1 solution

Pranshu Gaba
Sep 24, 2016

Let the volume of the average human be v v . This is the volume of air that the human displaces. The mass of air displaced is then ρ v \rho v , where ρ \rho is the average density of air. The weight of air displaced is ρ v g \rho v g , and this is the amount of buoyant force experienced by the human being.

We can assume our body's density to be equal to density of water since our body is mostly made of water. If the mass of the human being is 75 kg \SI{75}{\kilogram} , then the volume occupied is 75 75 litres, or 75 × 1 0 3 m 3 \SI{75e-3}{\meter ^3} . The density of air is about 1.23 kg/m 3 1.23 \text{ kg/m} ^3 . Hence the weight of air displaced is 1.23 × 75 1000 × 9.81 1.23 \times \dfrac{75}{1000} \times 9.81 = 0.905 N = \SI{0.905}{\newton}

The average human being experiences a buoyant force of about 0.905 N \SI{0.905}{\newton} . This is of the order of magnitude of 1 N \SI{1}{\newton} .

insufficient data on the question

Anom Ahmed - 4 years, 8 months ago

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This is an estimation question, where one can get a good approximate of a quantity by making reasonable assumptions. If you think any information is missing, then you can make a reasonable guess for it and proceed forward.

Pranshu Gaba - 4 years, 8 months ago

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how do you guess average human weight is 75 kg??? @Pranshu Gaba

Anom Ahmed - 4 years, 8 months ago

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@Anom Ahmed Never wondered how they come up with Max people and with in an elevator? Thats how you estimate 75 kg. If you did it with 80 kg or even 100 kg you still would have gotten a good appriximation. With 100 kg you would end up around 1.3 N, which is still in the same order of magnitude.

Peter van der Linden - 4 years, 8 months ago

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@Peter van der Linden And weight should be added in my first sentence

Peter van der Linden - 4 years, 8 months ago

How did u take 75 kg equal to 75 liter?

Khushin Lakhara - 4 years, 8 months ago

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The density of water is 1 kg per liter. So, if mass of person is 75 kg, then its volume is mass density \frac{\text{mass}}{\text{density}} = 75 liters

Pranshu Gaba - 4 years, 8 months ago

Hello sir! I'm appearing for KVPY SA on Nov6.Will enjoy ur company from Nov7 .Plz help me if u've some time.I wish to join the IISc after 10+2

Kaushik Chandra - 4 years, 7 months ago

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