At what depth will the pressure exerted on a man be twice that of the pressure at the surface if water?

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01-07-2021
Mathematics

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At what depth will the pressure exerted on a man be twice that of the pressure at the surface if water?

Sagot :

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oeerivona oeerivona · Answer 1 · 2021-07-05T22:29:16-04:00

Answer:

The depth of water at which the pressure on a man will be twice that of the pressure at the surface is approximately 10.36 meters

Step-by-step explanation:

The pressure, P, in a fluid (liquid or gas) is given by P = ρ·g·h

Where;

ρ = The density of the fluid

g = The acceleration due to gravity ≈ 9.81 m/s²

h = The depth of the body in the fluid

The pressure at the surface of water = The atmospheric pressure = 101,325 Pa

The pressure on a man in water will be twice the pressure at the water surface (the atmospheric pressure) when the pressure due to the water is equal to the atmospheric pressure as follows;

Pressure on man = Pressure due to water + Atmospheric pressure = Twice the atmospheric pressure

∴ Pressure due to water = 2 × Atmospheric pressure - Atmospheric pressure = Atmospheric pressure

Pressure due to water, P = Atmospheric pressure = 101,325 Pa

The depth of water, h = P/(ρ·g)

The density of water, ρ = 997 kg/m³

∴ h ≈ 101,325 Pa/(997 kg/m³ × 9.81 m/s²) ≈ 10.36 meters

The depth of water at which the pressure on a man will be twice that of the pressure at the surface, h ≈ 10.36 meters.

Sagot :

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