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

 

[rdl]

I would approach this problem by first identifying the known values and the unknown value. The known values are the density of seawater, the gravitational acceleration, and the pressure requirement for human occupancy. The unknown value is the depth at which the submarine can safely descend.

Next, I would use the given density and gravitational acceleration to calculate the pressure at the surface of the water using the pressure formula (P = pgh). This would give me the pressure at the surface, which is equal to the gauge pressure (Pg) since atmospheric pressure (Pat) is assumed to be zero at the surface.

Then, I would use the gauge pressure formula (Pg = P - Pat) to calculate the total pressure (P) at the depth that the submarine can safely descend. This would give me the total pressure required for human occupancy.

Finally, I would use the pressure formula (P = F/A) to calculate the force (F) required to withstand this pressure. Since the area (A) is not given, I would assume a conservative estimate of the area of the submarine's hull.

Using this calculated force, I would then consider the design and structural integrity of the submarine to determine the maximum depth it can safely descend.

In summary, to calculate the maximum depth the Deep View 66 can safely descend to, we would need to use the pressure formula and take into consideration the density of seawater, gravitational acceleration, and the pressure requirement for human occupancy. We would also need to consider the design and structural integrity of the submarine.