The deepest place in the ocean is the Marianas Trench in the western Pacific Ocean, which is over \(11.0 \mathrm{km}\) deep. On January \(23,1960,\) the research sub Trieste went to a depth of \(10.915 \mathrm{km},\) nearly to the bottom of the trench. This still is the deepest dive on record. The density of seawater is \(1025 \mathrm{kg} / \mathrm{m}^{3} .\) (a) What is the water pressure at that depth? (b) What was the force due to water pressure on a flat section of area \(1.0 \mathrm{m}^{2}\) on the top of the sub's hull?

Short Answer

Expert verified
Answer: (a) The water pressure at the depth of 10.915 km is approximately 109,565,816.75 Pa. (b) The force due to water pressure on a flat section of area 1.0 m² on the top of the sub's hull is approximately 109,565,816.75 N.

Step by step solution

01

Calculate the water pressure at the depth

Using the formula \(P = hρg\), we can find the water pressure at the depth of \(10.915 \mathrm{km}\). The density of seawater is given as \(1025 \mathrm{kg} / \mathrm{m}^{3}\) and the acceleration due to gravity is approximately \(9.81 \mathrm{m} / \mathrm{s}^{2}\). First, we need to convert the depth from kilometers to meters: \(10.915 \mathrm{km} * 1000 = 10915 \mathrm{m}\). Now we can plug these values into the formula: \(P = (10915 \mathrm{m})(1025 \mathrm{kg} / \mathrm{m}^{3})(9.81 \mathrm{m} / \mathrm{s}^{2})\).
02

Compute the pressure

Perform the calculation to find the pressure: \(P = (10915)(1025)(9.81) \approx 109565816.75 \mathrm{Pa}\). Therefore, the water pressure at the depth of \(10.915 \mathrm{km}\) is approximately \(109,565,816.75 \mathrm{Pa}\).
03

Calculate the force due to water pressure on a flat section of area \(1.0 \mathrm{m}^{2}\)

Using the formula \(F = PA\), we can now find the force due to water pressure on a flat section of area \(1.0 \mathrm{m}^{2}\) on the top of the sub's hull. We have already calculated the pressure, so we just need to multiply it by the area: \(F = (109565816.75 \mathrm{Pa})(1.0 \mathrm{m}^{2})\).
04

Compute the force

Perform the calculation to find the force: \(F = 109565816.75 \mathrm{N}\). Therefore, the force due to water pressure on a flat section of area \(1.0 \mathrm{m}^{2}\) on the top of the sub's hull is approximately \(109,565,816.75 \mathrm{N}\).

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