# Converting pressure to atomspheres

1. Oct 19, 2014

### dlp248

1. The problem statement, all variables and given/known data
The deepest part of the ocean is about 10,900 meters deep. Calculate the pressure at that depth in units of N/m^2. Mass density for seawater is 1030 kg/m^3. Then convert the pressure to the number of atmospheres given one atmosphere is 1.013x10^5 N/m^2.

2. Relevant equations
pressure = mass density x gravity x height

3. The attempt at a solution
p= (1030 kg/m^3)(9.8 m/s^2)(10,900 m)
p= 1.10x10^8 N/m^2

1 atmosphere = 1.013x10^5 N/m^2

1.10x10^8 N/m^2 / 1.013x10^5 N/m^2 = 1086 atmospheres.

I know that number is wrong. My guess is there are about 1.3 - 1.4 atmospheres of pressure there, but I can't get the math to find an exact number for that conversion. What is the best way to convert pressure to atmospheres?

2. Oct 19, 2014

### NTW

Imagine a column of water with a cross section of 1 m2 and 10900 m high. It's easy to calculate how much does it weigh... At 1030 kg/m3, its mass is 10900 m3 * 1030 kg/m3 = 11,2270 * 106 kg. Ant it weighs 11,2270 * 106 * 9,8 = 1,10025 *108 N. The pressure is the same, in N/m2

Using the equivalence 1 atm = 1.01325 * 105, I get the same figure as you: 1086 atm.

It's a reasonable figure. The pressure at a point 15 m deep, in fresh water, is already 1,5 atm...

3. Oct 19, 2014

### Staff: Mentor

In what way is that number wrong? On what do you base your guess of 1.3 - 1.4 atmospheres?

I note that you didn't account for the fact that the atmosphere itself lies above the ocean surface and presses down with its own pressure...

4. Oct 19, 2014

### SteamKing

Staff Emeritus
This is why one learns physics: so you are not guessing about things so much.

5. Oct 19, 2014

### dlp248

Thanks guys. I guess when I saw the number I questioned myself. It'll come with more practice.

That is the exact why reason I am loving physics! I'm in the base introductory course at my college this semester so I can get my calc done and then off to bigger and better things! Planning on getting a BS in physics!