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.

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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.
Transcribed Image Text: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.
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