A scuba diver searches for treasure at a depth of 20.0m below the surface of the sea. at what pressure must the scuba device deliver air to the diver? (density of sea water= 1030kg/m^3;atmospheric pressure= 1.013x10^5 pa)
p= ρ•g•h + p (atm) =1000•9.8•20 + 101325 =2.97•10^5 Pa,
To find the pressure at a depth of 20.0m below the surface of the sea, you can use the formula for pressure due to the depth of a fluid. The formula is:
Pressure = Density × gravitational acceleration × depth
Given:
Density of sea water = 1030 kg/m^3
Depth = 20.0m
Gravitational acceleration = 9.8 m/s^2
First, substitute the given values into the formula:
Pressure = 1030 kg/m^3 × 9.8 m/s^2 × 20.0m
Next, calculate the pressure:
Pressure = 202,800 Pa or 2.028 × 10^5 Pa
However, this pressure value represents the total pressure at that depth, including atmospheric pressure. To find the pressure that the scuba device must deliver to the diver, you need to subtract the atmospheric pressure.
Given:
Atmospheric pressure = 1.013 × 10^5 Pa
Subtract the atmospheric pressure from the total pressure:
Pressure = 2.028 × 10^5 Pa - 1.013 × 10^5 Pa
Pressure = 1.015 × 10^5 Pa
Therefore, the scuba device must deliver air to the diver at a pressure of 1.015 × 10^5 Pa.