Atmospheric pressure

The AP tables of information list one atmosphere of pressure as $1.0 \times 10^5\ \text{N/m}^2 = 1.0 \times 10^5\ \text{Pa}$, so that is the number to use when a question says "open to the air" and gives you nothing else.

Its job in the fluid equations is to be $P_0$. In $P = P_0 + \rho g h$, the term $P_0$ is whatever pressure exists at the level you measure $h$ from. For a bucket, a lake or a swimming pool that surface is open to the air, so $P_0 = P_{\text{atm}}$. For a sealed tank with compressed gas above the liquid, $P_0$ is the gas pressure instead, and substituting atmospheric out of habit is the error the setup is testing for.

One of the CED's essential questions for Unit 8 is why we do not feel the miles of air above us pushing us down. The answer is in the scalar nature of pressure: the air pushes inward on you from every direction at once, and the fluids inside you push back at the same pressure, so there is no net force and nothing to feel. A barometer makes it visible by removing the air from one side.

At altitude the value drops, which is why the CED suggests reading air density off the slope of a pressure versus elevation graph.