Air Pressure and Water Pressure

[vrobins1]

Homework Statement

"At the surface of a freshwater lake the air pressure is 1.1 atm. At what depth under water in the lake is the water pressure 4.5 atm?"

Homework Equations

I used the equation P_gauge = Dgh

The Attempt at a Solution

I converted my atm to Pascals--> (4.5)(100000) = 450000 Pa
P_guage = Dgh
P_guage = (1000)(9.8)(h)

-I used 1000, the density of water, but I'm not sure that is the right info to use for D!

Then I solved for h.

h = 450000/ (10000x9.8)
h = 45.92
I got it incorrect though. Can anyone offer any insight? Thanks!

 

[PhanthomJay]

Homework Statement

"At the surface of a freshwater lake the air pressure is 1.1 atm. At what depth under water in the lake is the water pressure 4.5 atm?"

Homework Equations

I used the equation P_gauge = Dgh

The Attempt at a Solution

I converted my atm to Pascals--> (4.5)(100000) = 450000 Pa
P_guage = Dgh
P_guage = (1000)(9.8)(h)

-I used 1000, the density of water, but I'm not sure that is the right info to use for D!

Then I solved for h.

h = 450000/ (10000x9.8)
h = 45.92
I got it incorrect though. Can anyone offer any insight? Thanks!

That would have been OK if the problem asked for the gauge pressure. I think it's looking for the depth at an absolute pressure of 4.5 atm, which includes the atmospheric pressure.

 

[thomate1]

Your attempt at solving the problem is correct, however, there are a few errors in your calculations. Firstly, the density of water is 1000 kg/m^3, not 1000 kg. So the value for D should be 1000 kg/m^3. Secondly, when converting atm to Pa, you should multiply by 101325, not 100000. This gives a value of 454725 Pa. Finally, in your calculation for h, you have used 10000 instead of 1000, resulting in an incorrect value for h.

The correct calculation should be:

h = 454725 / (1000 x 9.8)
h = 46.41 meters

Therefore, at a depth of 46.41 meters under the surface of the freshwater lake, the water pressure would be 4.5 atm. This shows that as the depth increases, the water pressure also increases due to the weight of the water above. This is a fundamental concept in fluid mechanics and is important to understand in various applications such as scuba diving, submarine operations, and even weather forecasting.