Assuming that your lungs can function when under a pressure of 11 kPa, what is the deepest you could be under water and still breathe through a tube to the surface?
To determine the deepest you can be under water and still breathe through a tube to the surface, we need to consider the relationship between pressure and depth.
The pressure exerted by a liquid (in this case, water) increases with depth due to the weight of the fluid above it. The pressure can be measured in units such as pascals (Pa) or kilopascals (kPa).
First, let's convert the pressure of 11 kPa to pascals for consistency. Since 1 kPa = 1000 Pa, 11 kPa would be equal to 11,000 Pa.
Next, we need to determine the pressure exerted by the water at various depths. The pressure at a given depth can be calculated using the formula:
Pressure (Pa) = Density (kg/m³) × Acceleration due to gravity (m/s²) × Depth (m)
The density of fresh water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².
Now, we can rearrange the formula to solve for depth:
Depth (m) = Pressure (Pa) / (Density (kg/m³) × Acceleration due to gravity (m/s²))
Plugging in the values:
Depth (m) = 11,000 Pa / (1000 kg/m³ × 9.8 m/s²)
Calculating the equation:
Depth (m) = 11,000 Pa / 9800 kg*m/s²
Depth (m) ≈ 1.122 meters
Therefore, assuming your lungs can function under a pressure of 11 kPa, you can be approximately 1.122 meters (or about 3.68 feet) deep under water and still breathe through a tube to the surface.