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Chapter 2: Problem 2

The deepest known spot in the oceans is the Challenger Deep in the Mariana Trench of the Pacific Ocean and is approximately \(11,000 \mathrm{m}\) below the surface. Assume that the salt water density is constant at \(1025 \mathrm{kg} / \mathrm{m}^{3}\) and determine the pressure at this depth.

Short Answer

Expert verified
The pressure at the depth of the Challenger Deep in the Mariana Trench is 110495 kPa.

Step by step solution

01

Identify the given values

The depth of the trench, \( h \), is given as 11,000 m, the density of the salt water, \( ρ \), is given as 1025 kg/m³ and the acceleration due to gravity, \( g \), is generally taken to be 9.8 m/s².
02

Substitute the values into the formula

Substitute these values into the equation \( P = ρgh \) to get \( P = 1025 \, \mathrm{kg/m^3} * 9.8 \, \mathrm{m/s^2} * 11000 \, \mathrm{m} \)
03

Solve for Pressure

By calculating this, the pressure \( P \) at the depth of 11,000 m is found to be 110495000 Pascal or 110495 kPa.

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Most popular questions from this chapter

When the Tucurui Dam was constructed in northern Brazil, the lake that was created covered a large forest of valuable hardwood trees. It was found that even after 15 years underwater the trees were perfectly preserved and underwater logging was started. During the logging process a tree is selected, trimmed, and anchored with ropes to prevent it from shooting to the surface like a missile when cut. Assume that a typical large tree can be approximated as a truncated cone with a base diameter of \(8 \mathrm{ft},\) a top diameter of \(2 \mathrm{ft}\), and a height of \(100 \mathrm{ft}\). Determine the resultant vertical force that the ropes must resist when the completely submerged tree is cut. The specific gravity of the wood is approximately 0.6.

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The deepest known spot in the oceans is the Challenger Deep in the Mariana Trench of the Pacific Ocean and is approximately \(11,000 \mathrm{m}\) below the surface. For a surface density of \(1030 \mathrm{kg} / \mathrm{m}^{3},\) a constant water temperature, and an isothermal bulk modulus of elasticity of \(2.3 \times 10^{9} \mathrm{N} / \mathrm{m}^{2},\) find the pressure at this depth.

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