How Does Water Pressure Change with Depth and Altitude?

[Devin Longo]

Homework Statement

At the surface of a freshwater lake the pressure is 106 kPa. (a) What is the pressure increase in going 34.5 m below the surface? (b) What is the approximate pressure decrease in going 36 m above the surface? Air at 20°C has density of 1.2 kg/m3.

Homework Equations

Ph20 = pgh
Pabs = Ph20 + Patm

The Attempt at a Solution

I calculated both equations and got 439.4 kPa. I then subtracted 106 from 439.4 to get number one, but it doesn't work! How can I calculate number one? Also, I don't know where to begin for 2!

 

[Doc Al]

The pressure change in both cases can be calculated via ΔP = ρgΔh.

 

[kerimek]

I would first clarify what type of pressure is being referred to in the problem. Based on the given information, it seems that the pressure at the surface of the lake is the absolute pressure, which includes the pressure from the water and the atmosphere. The pressure increase and decrease being asked for in the problem would then be the gauge pressure, which is the difference between the absolute pressure and the atmospheric pressure.

For part (a), the pressure increase in going 34.5 m below the surface can be calculated using the equation P = ρgh, where P is the pressure, ρ is the density of water (1000 kg/m3 for freshwater), g is the acceleration due to gravity (9.8 m/s2), and h is the depth. Plugging in the given values, we get P = (1000 kg/m3)(9.8 m/s2)(34.5 m) = 33900 Pa = 33.9 kPa. This is the gauge pressure, so to get the absolute pressure, we need to add the atmospheric pressure of 106 kPa. Therefore, the absolute pressure at a depth of 34.5 m is 139.9 kPa.

For part (b), the pressure decrease in going 36 m above the surface can be calculated using the same equation. However, in this case, the depth would be negative since we are going above the surface. So P = (1000 kg/m3)(9.8 m/s2)(-36 m) = -35280 Pa = -35.3 kPa. Again, this is the gauge pressure, so to get the absolute pressure, we add the atmospheric pressure of 106 kPa. Therefore, the absolute pressure at a height of 36 m above the surface is 70.7 kPa.

In summary, the absolute pressure at a depth of 34.5 m below the surface is 139.9 kPa and the absolute pressure at a height of 36 m above the surface is 70.7 kPa.