Magnitude of Force on a Submarine Hatch

In summary, the magnitude of the force acting on the rectangular hatch on the deck of a submarine operating at 100 m below the surface of the ocean is 1.96 * 10^6 Pa. This is determined by taking into account the atmospheric pressure and the pressure exerted by the water above the hatch.
  • #1
NeRdHeRd
12
0

Homework Statement



A submarine is operating at 100 m below the surface of the ocean. If the air inside the submarine is maintained at a pressure of 1 atmosphere, what is the magnitude of the force that acts on the rectangular hatch 2.0 x 1.0 m on the deck of the submarine?

Homework Equations



Force = Pressure* Area
Pressure = density*gravity*height
?

The Attempt at a Solution



If atmospheric pressure is 1.013 x 10^5 Pa and Area of hatch = width * height Then,

Area = 2*1 = 2 m^2
Force = (1.013 x 10^5 Pa)(2 m^2) = 202600

This doesn't seem right to me and I know I'm missing something. I just can't seem to put my finger on it. Please help.
 
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  • #2
I think you forgot about the 100m of water above the hatch...
 
  • #3
Proggle said:
I think you forgot about the 100m of water above the hatch...

Wouldn't I need to know the density of the water to determine the pressure thai it is exerting on the hatch?
 
  • #4
Yes, you would- look it up! The pressure is the weight of water above the hatch divided by the area of the hatch. Since the weight of the water itself is the density of water times its height times the area, the pressure is just the density of water times the height of the column of water above the hatch.
 
  • #5
Yes, you need the density.

I believe the commonly accepted value is 998 kg / m^3.
 
  • #6
I guess I could assume that the density of the water is 1.000 * 10^3. If that is the case then:

the pressure of the water is (1.000 * 10^3)(9.8)(100) = 980000

So the force is 980000*2 = 1960000

I guess then I would subtract 202600 from 196000 giving me 1757400...

I think
 
  • #7
There's a small detail you're missing. If you think about it, on top of the water "column", there is air, which means that the water itself is having the atmospheric pressure added to its own, and exerting the sum of both.

On the sub, you know that there is atmospheric pressure pushing on the hatch from the other side. Think about what this means.
 
  • #8
Proggle said:
On the sub, you know that there is atmospheric pressure pushing on the hatch from the other side. Think about what this means.

The cancel each other because they are pointing in opposite directions. Which means the force acting on the hatch is 1960000 or 1.96 * 10^6
 

1. What is the magnitude of force on a submarine hatch during a dive?

The magnitude of force on a submarine hatch during a dive varies depending on the depth of the dive and the size and integrity of the hatch. However, on average, the force can range from 100 to 300 pounds per square inch.

2. How does the shape of the submarine hatch affect the magnitude of force?

The shape of the submarine hatch can have a significant impact on the magnitude of force during a dive. A round or oval-shaped hatch will distribute the force more evenly, while a rectangular or square-shaped hatch can create areas of higher pressure, increasing the overall force.

3. What materials are used to withstand the magnitude of force on a submarine hatch?

Submarine hatches are typically made of strong and durable materials such as steel or titanium. These materials are able to withstand the high pressures and forces experienced during a dive without compromising the integrity of the hatch.

4. Can the magnitude of force on a submarine hatch be controlled?

The magnitude of force on a submarine hatch can be controlled to some extent by adjusting the air pressure inside the submarine and using specially designed hatches with pressure relief valves. However, during emergency situations, the force may be too great to control.

5. Are there safety measures in place to prevent the hatch from failing under high magnitude of force?

Yes, submarine hatches undergo rigorous testing and are designed to withstand forces well above what they would typically experience during a dive. Additionally, regular maintenance and inspections are conducted to ensure the hatches are in good condition and able to withstand high magnitudes of force.

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