Decrease in Pressure Above a Lake

[dvolpe]

Homework Statement

What is the approximate decrease in pressure in going 31 m above the surface of the lake? Air at 20 degrees C has density of 1.2 kg/mcubed. The pressure at the surface of the lake is 104 kPa

Homework Equations

Pressure = F/Area
Force = density*area*height*g
Pressure = density*height*g = pgh

The Attempt at a Solution

P = 1.2 * 9.8 * 31 m = 364.56 Pa

These doesn't seem right in comparison to the surface of lake. What about atmospheric pressure? Does that need to be considered here as there is a pressure decrease?

 

[Filip Larsen]

You have calculate the change in pressure from 31 meter of air, so if you start at 104 kPa and move up 31 meter, then what is the absolute pressure there?

 

[dvolpe]

Does this mean that the pressure at 31 m above lake = atm pressure + pressure on surface area of lake? How do I calculate atmospheric pressure?

So if P = Patm + Plake then isn't P atm = pgh and that is the decrease?

 

[Filip Larsen]

Does this mean that the pressure at 31 m above lake = atm pressure + pressure on surface area of lake? How do I calculate atmospheric pressure?

So if P = Patm + Plake then isn't P atm = pgh and that is the decrease?

No, the pressure at the lake surface is the atmospheric pressure (here given as 104 kPa). I can see that I probably have added some to you confusion. Given the equations you posted, you have correctly calculated the decrease in pressure going up 31 m, and this is what the problem text is asking.

You then ask if this can be correct since you are not using the 104 kPa information, and I think I probably answered something else on that, sorry. Let me try to do better: No, in the context of the problem text where the density is a given number you do not need to consider the atmospheric pressure of 104 kPa.

In case the density was not given and the pressure at the lake was significantly different from standard pressure (101.3 kPa) it would then be prudent to calculate the density given the absolute pressure and temperature of the air (for instance assuming an ideal gas). If you want to be even more accurate, there are more complex equations for calculating the atmospheric pressure based on gas theory that requires, amongst others, the surface level pressure and temperature (see for instance [1]), but I would guess that would be a fair bit of overkill in this case and the difference most likely wouldn't matter much over 31 m anyway.

[1] http://en.wikipedia.org/wiki/Barometric_formula

 

[rwisz]

As a scientist, it is important to consider all factors and variables in a problem. In this case, the decrease in pressure above a lake is affected by both the height above the surface and the atmospheric pressure. The pressure at the surface of the lake is already taking into account the atmospheric pressure, so we cannot simply subtract it from our calculation.

To calculate the decrease in pressure, we can use the equation P = ρgh, where ρ is the density of air, g is the acceleration due to gravity, and h is the height above the surface. In this case, we have all the necessary information except for the height above the surface.

To find the height, we can use the equation P = ρgh and rearrange it to solve for h, giving us h = P/(ρg). Plugging in the given values, we get h = (104 kPa)/(1.2 kg/m^3 * 9.8 m/s^2) = 8.67 m.

Therefore, the approximate decrease in pressure in going 31 m above the surface of the lake is 104 kPa - 8.67 m * 1.2 kg/m^3 * 9.8 m/s^2 = 94.3 kPa. This is a significant decrease in pressure, which is why it is important to consider all factors when solving scientific problems.