Randall D. Knight — Fluids and Elasticity: Problem Problem_48

It’s possible to use the ideal-gas law to show that the density of the earth’s atmosphere decreases exponentially with height. That is, \(\rho = \rho_0 \exp(-z/z_0)\), where \(z\) is the height above sea level, \(\rho_0\) is the density at sea level (you can use the Table 14.1 value), and \(z_0\) is called the scale height of the atmosphere. a. Determine the value of \(z_0\). Hint: What is the weight of a column of air? b. What is the density of the air in La Paz, Bolivia, at an elevation of 3600 m? What percent of sea-level density is this? c. What is the density of the air in Kampala, Uganda, at an elevation of 1200 m? What percent of sea-level density is this?