(a) Calculate the absolute pressure at the bottom of a...

(a) Calculate the absolute pressure at the bottom of a freshwater lake at a depth of 27.5 $\mathrm{m}$ . Assume the density of the water is $1.00 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$ and the air above is at a pressure of 101.3 $\mathrm{kPa}$ . (b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 35.0 $\mathrm{cm}$ ?

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases with depth and is calculated by multiplying the fluid's density, the gravitational acceleration, and the vertical depth. This concept is fundamental for understanding how pressure changes in liquids, such as water in lakes or oceans.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the Earth's atmosphere. At sea level, it provides a baseline or reference pressure that must be accounted for when calculating absolute pressures in fluids. In many calculations, the hydrostatic pressure due to a fluid is added to the atmospheric pressure to yield the total, or absolute, pressure at a given depth.

Force from Pressure

Force from pressure is determined by multiplying the pressure by the area over which the pressure is acting. This relation shows that a higher pressure results in a greater force on a surface, and it is crucial when analyzing how structures withstand forces from fluids, such as windows on underwater vehicles.

Area Calculation for Circular Surfaces

Calculating the area of a circular surface is necessary when determining the total force acting on that surface due to pressure. This involves using the formula for the area of a circle, which is based on the circle's radius, and links geometric measurements to physical forces.

Unit Conversions

Unit conversions are an essential practice in physical calculations to ensure consistency across the measurement units involved. Common conversions include those for pressure (e.g., converting kilopascals to pascals), length (e.g., centimeters to meters), and ensuring that all units align to avoid calculation errors.

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