Chapter 2: Atmospheric pressure

Molecular view of atmospheric pressure

EARTH SURFACE

gravity

random

motion

• Weight of all air molecules is propagated to surface by random motion of molecules

​

• Random motion of molecules causes pressure to be applied in all directions

Measurement of atmospheric pressure with the mercury barometer

Atmospheric pressure p = p_A = ρ_Hg gh

Mean sea-level pressure:

p = 1.013x10⁵ Pa = 1013 hPa

= 1013 mb

= 1 atm

= 760 mm Hg (torr)

atmospheric pressure

(weight of atmosphere per unit area of surface)

SI unit for pressure is the Pascal (Pa): 1 Pa = 1 kg m^-1 s^-2

Today’s sea-level pressure map

https://www.wpc.ncep.noaa.gov/basicwx/day0-7loop.html

Pressures are in a narrow range 996-1033 hPa

Why are sea-level pressure gradients so weak?

Consider a pressure gradient at sea level operating on an elementary air parcel dxdydz with mass dm = ρ_adxdydz where ρ_a is the air density:

p(x)

p(x+dx)

Vertical area

dydz

Pressure-gradient force

Acceleration

For pressure difference Δp = 10 hPa over Δx = 100 km, with ρ_a ≈ 1 kg m^-3,

we get a ≈ 10^-2 m s^-2 🢧 100 km/h wind in 3 h!

Wind transports air to from high to low pressure, decreasing Δp

Exerted force

p(x)dydz

So Δp never gets large, except over mountains:

p(z)

p(z+Δz)

p-gradient

gravity

Total mass m_a of the atmosphere

Radius of Earth:

6380 km

Mean pressure at Earth's surface: 984 hPa

(less than 1013 hPa because of elevated land)

Total number of moles of air in atmosphere:

Mol. wt. of air: 29 g mole^-1 = 0.029 kg mole^-1

Molecular weight of air:

9.81 m s^-2 (atmosphere is thin enough that this can be considered constant)

Mean vertical profiles of pressure and temperature�

Troposphere has 85% of atmospheric mass, stratosphere has 15%, little above

Decrease of pressure with altitude: barometric law

Consider elementary slab of atmosphere at equilibrium between gravity and p-gradient forces:

p(z)

p(z+dz)

hydrostatic

equation for fluids

Ideal gas law:

Assume uniform T and integrate:

barometric law

unit area

g

Application of barometric law: the sea-breeze effect