The Hydrostatic Equation

Hydrostatic Equation:

Hydrostatic Balance is when the net upwards force is equal to the downward force, requiring that the balance of forces in the vertical…

The pressure at height, z, is equal to the weight of the air in the vertical column of unit cross-section lying about that level.

Hydrostatic Equilibrium is when vertical pressure gradient force and the force of gravity are normally of nearly equal value and operate in opposite directions when…

─     Gravitational force = vertical pressure gradient force in magnitude à no vertical acceleration occurs

─     Gravitational force > vertical pressure gradient force à downward motion

─     Gravitational force < vertical pressure gradient force à updrafts can develop that are associated with powerful thunderstorms.

Physical Principles: The Hydrostatic Equation

Understanding Weather and Climate (7th Edition) (MasteringMeteorology Series) by Edward Aguado, James E. Burt.

►   Hydrostatic Balance = if the net upwards force is equal to the downward force

─     For an atmosphere in hydrostatic balance, the balance of forces in the vertical requires that…

►   Or, the Hydrostatic Equation:

─     The negative sign ensures that the pressure decreases with increasing height

─     Because

 we can rearrange the hydrostatic equation to give…

►   Above a fixed point on Earth…

─     That is, the pressure at height z is equal to the weight of the air in the vertical column of unit cross-sectional are lying about that level.

Hydrostatic Equilibrium

►   Pressure gradient force causes wind to flow from high to low pressure

►   Air pressure rapidly decreases with altitude

►   Gravity pulls all mass, including the atmosphere, downward.

►   Hydrostatic Equilibrium = vertical pressure gradient force and the force of gravity are normally of nearly equal value and operate in opposite directions

─     When, gravitational force = vertical pressure gradient force in magnitude à no vertical acceleration occurs

─     When, gravitational force > vertical pressure gradient force à downward motion

When, gravitational force < vertical pressure gradient force à updrafts can develop that are associated with powerful thunderstorms

Physical Principles: Earth's Equilibrium Temperature

Understanding Weather and Climate (7th Edition) (MasteringMeteorology Series) by Edward Aguado, James E. Burt