Serway & Jewett — Fluid Mechanics: Problem 37

Evangelista Torricelli was the first person to realize that we live at the bottom of an ocean of air. He correctly surmised that the pressure of our atmosphere is attributable to the weight of the air. The density of air at \(0^\circ\text{C}\) at the Earth’s surface is \(1.29\text{ kg/m}^3\). The density decreases with increasing altitude (as the atmosphere thins). On the other hand, if we assume the density is constant at \(1.29\text{ kg/m}^3\) up to some altitude \(h\) and is zero above that altitude, then \(h\) would represent the depth of the ocean of air. (a) Use this model to determine the value of \(h\) that gives a pressure of \(1.00\text{ atm}\) at the surface of the Earth. (b) Would the peak of Mount Everest rise above the surface of such an atmosphere?