Max Depth of Submarine Modeling: 80kpa

[HighHoAg]

Hello, I'm working on a project, and my teacher gave me something to think about, but I am at a loss. He wants me to come up with an equation to model the maximum height a submarine can go underwater, if it can withstand a maximum pressure of 80kpa. I started thinking it was an integral problem, integ(dP/dz) but I'm not sure. Any help would be much appreciated.

 

[Doc Al]

How does hydrostatic pressure depend on depth? (It's simpler than you think.)

 

[Deathcrush]

it would be very cool if you solve that with integrals, but its a lot more than you need, really

 

[CWatters]

What they said. No integrals required.

1m head of water = 0.1bar = 10kpa

 

[PJC01]

Hello there, it's great that you are working on a project involving submarine modeling. I can provide some insights to help you come up with an equation for the maximum depth a submarine can go underwater.

Firstly, it is important to understand the relationship between pressure and depth in water. As a submarine goes deeper into the water, the pressure around it increases due to the weight of the water above it. This increase in pressure is directly proportional to the depth, which means that the deeper the submarine goes, the higher the pressure it will experience.

Now, let's consider the maximum pressure of 80kpa that the submarine can withstand. This pressure is equivalent to a depth of approximately 800 meters (assuming a density of 1000 kg/m^3 for seawater). This means that the submarine can safely go up to a depth of 800 meters without experiencing any damage due to pressure.

To model this relationship mathematically, we can use the hydrostatic equation: P = ρgh, where P is the pressure, ρ is the density of the fluid (seawater in this case), g is the gravitational acceleration, and h is the depth.

Rearranging this equation, we get h = P/(ρg). Substituting the maximum pressure of 80kpa and the density of seawater, we get h = 80kpa / (1000 kg/m^3 * 9.8 m/s^2) = 8.16 meters.

Therefore, the maximum depth that the submarine can go is 8.16 meters, which is equivalent to 800 meters of seawater.

I hope this helps you in coming up with an equation for your project. Remember to always consider the relevant physical principles and equations when modeling a real-life scenario. Good luck with your project!