What is the buoyant force exerted on it by the air?

Question

An empty storage tank has a volume of 8,000 ft³. What is the buoyant force exerted on it by the air? (Assume the air is at 0°C and 1 atm.)

Answer 1

I am assuming that by "empty tank" it is meant that there is vacuum in the tank.

If my assumption is wrong and there is ambient atmospheric pressure inside the tank, then air provides no buoyancy.

Let

V = 8000ft³ be the volume of the tank,

g = 9.8m/s² be gravitational acceleration,

r = 1.225 kg/m³ be density of air at 0°C and 1 atm.

By the law of Archimedes, the buoyant force is equal to the weight of air with volume V:

g r V =

9.8m/s² x 1.225 kg/m³ x 8000ft³ =

96040 kg ft³ / (s² m²) =

96040 kg 0.3048³ m³ / (s² m²) =

2720 kg m / s² =

2720 N

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I am not sure which calculation you are referring to,

so let me explain all the lines.

Line 1: g r V =

Line 2: 9.8m/s² x 1.225 kg/m³ x 8000ft³ =

Line 3: 96040 kg ft³ / (s² m²) =

Line 4: 96040 kg 0.3048³ m³ / (s² m²) =

Line 5: 2720 kg m / s² =

Line 6: 2720 N

Line 1 is the expression for the Law of Archimedes.

Line 2 is obtained from line 1 by substituting numbers for symbols.

Line 3 is obtained from line 2 by multiplying all the numbers together,

and by multiplying (i.e., combining) all the units.

Line 4 is obtained from line 3 by replacing ft = 0.3048 m.

Line 5 is obtained from line 4 by multiplying the two numbers.

Line 6 is obtained from line 5 by the substitution N = kg m / s².