Example 3. Since air is a gas, the hydrostatic equilibrium of Earth's atmosphere is described by the equation ▼p+9=0, where p varies with the height above the sea level. At the sea level, the typical air density and pressure are po 105Nm 2, and the gravitational acceleration g Ро = == 10m/s². = 1kg/m³, a. Assuming p Ap, where A is a constant (the case of uniform temperature), determine p(z). Use the density po = p(0) at see level (z = 0) as initial condition. b. Find the effective height of the atmosphere above the sea level, hatm, which is defined via the equation M = pohatmS, where M is the total mass of a vertical air column (with the cross-section S above the sea level. Find the total mass for the air column with the cross-section S == 1 cm².

Example 3. Since air is a gas, the hydrostatic equilibrium of Earth's atmosphere is described by the equation ▼p+9=0, where p varies with the height above the sea level. At the sea level, the typical air density and pressure are po 105Nm 2, and the gravitational acceleration g Ро = == 10m/s². = 1kg/m³, a. Assuming p Ap, where A is a constant (the case of uniform temperature), determine p(z). Use the density po = p(0) at see level (z = 0) as initial condition. b. Find the effective height of the atmosphere above the sea level, hatm, which is defined via the equation M = pohatmS, where M is the total mass of a vertical air column (with the cross-section S above the sea level. Find the total mass for the air column with the cross-section S == 1 cm².