(a) Calculate the absolute pressure at an ocean depth of 1000 m . Assume the density of seawater

step 1 In this particular case, if over here the pressure is P1 and at a depth the pressure is P2, then

(a) Calculate the absolute pressure at an ocean depth of...

(a) Calculate the absolute pressure at an ocean depth of 1000 $\mathrm{m}$ . Assume the density of seawater is 1030 $\mathrm{kg} / \mathrm{m}^{3}$ and the air above exerts a pressure of 101.3 $\mathrm{kPa}$ . (b) At this depth, what is the buoyant force on a spherical submarine having a diameter of 5.00 $\mathrm{m}$ ?

Key Concepts

Volume of a Sphere

The volume of a sphere is a geometric concept essential for determining the amount of fluid displaced by a spherical object. It is calculated using the formula V = (4/3)?r^3, where r is the radius of the sphere. This calculation is key when applying Archimedes' principle to determine the buoyant force on spherical bodies.

Archimedes' Principle

Archimedes' principle states that any object fully or partially submerged in a fluid is buoyed up by a force equal to the weight of the fluid that the object displaces. This principle is fundamental in fluid mechanics and is used to calculate the buoyant force acting on submerged bodies, which is critical for understanding their stability and behavior in the fluid.

Absolute Pressure

Absolute pressure is the total pressure at a specific point in a fluid and is determined by adding the atmospheric pressure to the hydrostatic pressure. This gives a complete measure of the pressure experienced beneath the surface of the fluid, taking into account both the pressure due to the atmosphere and the weight of the fluid above.

Hydrostatic Pressure

This concept refers to the pressure exerted by a fluid at a given depth due to the weight of the overlying fluid. It is calculated using the formula ?gh, where ? is the fluid density, g is the gravitational acceleration, and h is the depth. It explains how pressure increases linearly with depth in a fluid at rest.

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