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.
