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

step 1 Question number 6. The pressure at a depth under water is given as p equal to row G H where H is

(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 1024 $\mathrm{kg} / \mathrm{m}^{3}$ and that the air above exerts a pressure of 101.3 $\mathrm{kPa}$ . (b) At this depth, what force must the frame around a circular submarine porthole having a diameter of 30.0 $\mathrm{cm}$ exert to counterbalance the force exerted by the water?

Key Concepts

Area Calculation for Circular Surfaces

Calculating the area of circular surfaces is important when determining the total force exerted by a fluid on objects like portholes or windows in submerged structures. The area is computed using the formula A = ?r², where r is the radius of the circle, linking geometric properties with physical forces in fluid mechanics.

Force on a Submerged Surface

The force on a submerged surface is determined by the product of the pressure acting on the surface and the area over which it is applied. This concept is used to calculate the net force that must be counterbalanced by structural supports in submerged structures, ensuring their stability and safety.

Fluid Density

Fluid density is a measure of mass per unit volume and is critical in the calculation of hydrostatic pressure. Higher density fluids exert greater pressure at the same depth, and understanding this property is key in engineering designs and calculations involving fluid statics in various environments.

Absolute Pressure

Absolute pressure is the total pressure exerted on a point in a fluid, combining both the atmospheric pressure acting on the surface and the hydrostatic pressure due to the fluid’s weight above that point. It is essential for accurately calculating the forces in deep-water environments and ensuring structural integrity in underwater applications.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It increases linearly with depth according to the relationship p = ?gh, where ? is the fluid density, g is the acceleration due to gravity, and h is the depth. This concept is fundamental in understanding how pressure builds up in fluids, such as in oceans or lakes.

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