A submarine rests on the ocean floor at a depth of 800 m. Calculate A) the pressure at this depth and B) the force acting on a 0.6 m² hatch on the conning tower of the submarine, assuming that the pressure inside the hatch is 1 atmosphere.
A submarine rests on the ocean floor at a depth of 800 m. Calculate A) the pressure at this depth and B) the force acting on a 0.6 m² hatch on the conning tower of the submarine, assuming that the pressure inside the hatch is 1 atmosphere.
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![**Problem Statement:**
A submarine rests on the ocean floor at a depth of 800 meters. Calculate:
A) The pressure at this depth.
B) The force acting on a 0.6 m² hatch on the conning tower of the submarine, assuming that the pressure inside the hatch is 1 atmosphere.
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**Detailed Explanation:**
To solve this problem, we need to consider the concepts of pressure in fluids and forces exerted on surfaces due to pressure differences.
**Part A: Calculating Pressure at Depth**
The pressure at a certain depth in a fluid is given by the formula:
\[ P = P_0 + \rho g h \]
Where:
- \( P \) is the pressure at depth.
- \( P_0 \) is the atmospheric pressure at the surface (1 atmosphere = 101,325 Pa).
- \( \rho \) is the density of seawater (approx. 1025 kg/m³).
- \( g \) is the acceleration due to gravity (9.81 m/s²).
- \( h \) is the depth (800 m).
Substitute these values to find the pressure at 800 meters.
**Part B: Calculating the Force on the Hatch**
Once the pressure at 800 meters is found, the force on the hatch can be determined using:
\[ F = (P - P_{\text{inside}}) \cdot A \]
Where:
- \( F \) is the force acting on the hatch.
- \( P_{\text{inside}} \) is the pressure inside the hatch (1 atmosphere = 101,325 Pa).
- \( A \) is the area of the hatch (0.6 m²).
Calculate the difference in pressure between the outside and the inside of the hatch, and then multiply by the area to get the force.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3738e16a-10fd-4378-b4a3-b8733d2d5bb5%2Faa3597f7-7ca6-428c-8646-b479e88e1ddf%2Fc89am8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A submarine rests on the ocean floor at a depth of 800 meters. Calculate:
A) The pressure at this depth.
B) The force acting on a 0.6 m² hatch on the conning tower of the submarine, assuming that the pressure inside the hatch is 1 atmosphere.
---
**Detailed Explanation:**
To solve this problem, we need to consider the concepts of pressure in fluids and forces exerted on surfaces due to pressure differences.
**Part A: Calculating Pressure at Depth**
The pressure at a certain depth in a fluid is given by the formula:
\[ P = P_0 + \rho g h \]
Where:
- \( P \) is the pressure at depth.
- \( P_0 \) is the atmospheric pressure at the surface (1 atmosphere = 101,325 Pa).
- \( \rho \) is the density of seawater (approx. 1025 kg/m³).
- \( g \) is the acceleration due to gravity (9.81 m/s²).
- \( h \) is the depth (800 m).
Substitute these values to find the pressure at 800 meters.
**Part B: Calculating the Force on the Hatch**
Once the pressure at 800 meters is found, the force on the hatch can be determined using:
\[ F = (P - P_{\text{inside}}) \cdot A \]
Where:
- \( F \) is the force acting on the hatch.
- \( P_{\text{inside}} \) is the pressure inside the hatch (1 atmosphere = 101,325 Pa).
- \( A \) is the area of the hatch (0.6 m²).
Calculate the difference in pressure between the outside and the inside of the hatch, and then multiply by the area to get the force.
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