Tour Submarine: Deep View 66 Can Descend to What Depth?

[rijo664]

Homework Statement

A submarine called the Deep View 66 is currently being developed to take 66 tourists at a time on sightseeing trips to tropical coral reefs. According to guidelines of the American Society of Mechanical Engineers (ASME), to be safe for human occupancy the Deep View 66 must be able to withstand a pressure of 10.0 {\rm N} per square millimeter.

To what depth can the Deep View 66 safely descend in seawater?

Homework Equations

p = M/V (density formula)

P = F/A (pressure formula)
P_g = P - P_at (gauge pressure formula)
P₂ = P₁ + pgh (Pressure with Depth)
g = 9.81
density of seawater = 1025 kg/m³

The Attempt at a Solution

Here is what I know about the problem:

I know that p = 1025 kg/m³
I know that g = 9.81
I know that P₁ = 10 N because its given in the problem
But I don't know P₂ or h

I have tried to figure a way to do the problem but I don't know how to start it. Any advice would be greatly appreciated. Just an advice on how to go about the problem on finding P₂.

 

[mgb_phys]

So how high must a column of seawater 1mm *1mm be to weigh 10N?

 

[rijo664]

I am not sure what you are trying to ask. I need to know h. But in order to find h i need a way to find P₂. I don't know how to start the problem.

 

[mgb_phys]

Pressure is pgh

You are looking for a pressure of 10N/mm^2
10N/mm^2 = 1025kg/m^3 * 9.81 N/m/s^2 * h, simply rearrange to get h

Probably helpful to convert the pressure into N/m^2