# Find the maximum safe depth of a submarine

• motp44
In summary, the conversation discusses the maximum safe depth of an ocean-going research submarine with a 40.0 cm-diameter window that is 9.00 cm thick and can withstand forces up to 1.20×106 N. Using the equations p = F/A and p = p0 + ρseawatergd, the attempt at a solution calculates a safe depth of 936m, but the actual answer is 947m. It is suggested that the force on the window may be proportional to the pressure difference between the inside and outside.
motp44

## Homework Statement

An ocean-going research submarine has a 40.0 cm -diameter window 9.00 cm thick. The manufacturer says the window can withstand forces up to 1.20×106 N . What is the submarine's maximum safe depth? The pressure inside the submarine is maintained at 1.0 atm.

ρseawater = 1030 kg/m3
r = .2 m
g = 9.8 m/s2

## Homework Equations

p = F/A
p = p0 + ρseawatergd
A = πr2

## The Attempt at a Solution

p0 = 1 atm = 101,300 Pa

p = (1.2*106 N)/(π*.22 m) = 9549296.586 Pa

9549296.586 Pa = 101300 Pa + (1030 kg/m3)(9.8 m/s2)d

d = (9549296.586 Pa - 101300 Pa)/((1030 kg/m3)(9.8 m/s2))

d = 936m

But the actual answer is 947m so I'm pretty sure I did something wrong or I'm missing something at some point because that is a significant difference. I'm pretty sure there's some point where I'm supposed to be using the volume of the window when I'm not but I'm not quite sure where I'm supposed to use it.

motp44 said:

## Homework Statement

An ocean-going research submarine has a 40.0 cm -diameter window 9.00 cm thick. The manufacturer says the window can withstand forces up to 1.20×106 N . What is the submarine's maximum safe depth? The pressure inside the submarine is maintained at 1.0 atm.

ρseawater = 1030 kg/m3
r = .2 m
g = 9.8 m/s2

## Homework Equations

p = F/A
p = p0 + ρseawatergd
A = πr2

## The Attempt at a Solution

p0 = 1 atm = 101,300 Pa

p = (1.2*106 N)/(π*.22 m) = 9549296.586 Pa

9549296.586 Pa = 101300 Pa + (1030 kg/m3)(9.8 m/s2)d

d = (9549296.586 Pa - 101300 Pa)/((1030 kg/m3)(9.8 m/s2))

d = 936m

But the actual answer is 947m so I'm pretty sure I did something wrong or I'm missing something at some point because that is a significant difference. I'm pretty sure there's some point where I'm supposed to be using the volume of the window when I'm not but I'm not quite sure where I'm supposed to use it.
Wouldn't the force on the window be proportional to the pressure difference between the inside and the outside?

motp44 said:
p = p0 + ρseawater g d
p is the pressure difference across the window
p0 is the pressure inside the window
ρseawater g d is the pressure outside the window

Does the equation match the physical situation?

## 1. How is the maximum safe depth of a submarine determined?

The maximum safe depth of a submarine is determined by various factors, including the design and construction of the submarine, the materials used, and the capabilities of its propulsion and life support systems. It is also influenced by the depth of the water and the conditions of the surrounding environment.

## 2. What could happen if a submarine goes beyond its maximum safe depth?

If a submarine goes beyond its maximum safe depth, it could experience extreme pressure and potentially implode, causing serious damage or even sinking the submarine. The crew could also experience physiological effects such as decompression sickness.

## 3. How do scientists and engineers calculate the maximum safe depth of a submarine?

Scientists and engineers use mathematical models and simulations to calculate the maximum safe depth of a submarine. They consider factors such as the water pressure at different depths, the structural integrity of the submarine, and the effects of compression on the materials used.

## 4. Can the maximum safe depth of a submarine change over time?

Yes, the maximum safe depth of a submarine can change over time. As technology advances, submarines may be able to withstand greater depths. Additionally, as a submarine ages, its structural integrity may weaken, causing a decrease in the maximum safe depth.

## 5. Are there different maximum safe depths for different types of submarines?

Yes, different types of submarines have different maximum safe depths. This is because they are designed and built for specific purposes and may have different capabilities and features that affect their maximum safe depth. Factors such as size, shape, and propulsion systems can also impact the maximum safe depth of a submarine.

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