(b) What pressure, in atmospheres, is exerted on the body of a diver if she is 10 m below the surface of the water when the atmospheric pressure is 100 kPa? Assume that the density of the water is 1.00 5 1.00 3 103 kg/m3. The gravitational constant is 9.81 m/s2, and 1 Pa 5 1 kg/ms2

Verified step by step guidance

1. Identify the known values: depth (h) = 10 m, atmospheric pressure (P_atm) = 100 kPa, density of water (\( \rho \)) = 1.00 \times 10^3 \text{ kg/m}^3, gravitational constant (g) = 9.81 \text{ m/s}^2.
2. Calculate the pressure due to the water column using the formula \( P_{water} = \rho \cdot g \cdot h \).
3. Convert the atmospheric pressure from kPa to Pa by multiplying by 1000 (since 1 kPa = 1000 Pa).
4. Add the atmospheric pressure to the pressure due to the water column to find the total pressure exerted on the diver: \( P_{total} = P_{water} + P_{atm} \).
5. Convert the total pressure from Pascals to atmospheres using the conversion factor 1 atm = 101325 Pa.

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases with depth in a fluid and can be calculated using the formula P = ρgh, where P is the pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the height of the fluid column above the point in question.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the atmosphere above a given point. At sea level, this pressure is approximately 101.3 kPa (or 1 atm). When calculating the total pressure experienced by a diver, both the atmospheric pressure and the hydrostatic pressure from the water must be considered.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, it is important to convert pressures from kilopascals (kPa) to atmospheres (atm) for consistency, using the conversion factor where 1 atm is approximately equal to 101.3 kPa. This ensures that all pressure values are in the same units for accurate calculations.