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The Hydrostatic Equation

The air pressure at any given height in the atmosphere is due to the force per unit area exerted by the weight of all the air lying above that particular height. It follows then that atmospheric pressure decreases with increasing height above the ground. The downward gravitational force on a thin horizontal slice of air is generally very closely in balance with the net upward force acting on it, due to the decrease in atmospheric pressure with height. If these two forces equal each other the atmosphere is said to be in hydrostatic balance. 

The negative sign just ensures that pressure decreases with increasing height.

© 2015 by UniMet.

* All information on this site has come from lecture notes and the associated course text books: 'Atmospheric Science: An introductory survey, 2nd edition, J. M. Hobbs and P. V. Wallace' and 'Meteorology Today: An Introduction to Weather, Climate and the Environment, 10th edition (International), C. D. Ahrens.' Some sections may have been rephrased and altered slightly but all content came from the above mentioned sources unless otherwise stated. 

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