Applied Thermodynamics for Meteorologists by Sam Miller

Author:Sam Miller [Miller, Sam]
Language: eng
Format: epub, pdf
Publisher: Cambridge University Press
Published: 2015-06-29T23:00:00+00:00

where m is the mass of the object [kg], g is the effective gravity acting on it [m/s2], and zi is the (initial) altitude of the object before it’s dropped [m]. The LHS of (9.22) is kinetic energy, and the RHS is the potential energy of position in a gravitational field. Canceling the mass on both sides of (9.22) and solving for final velocity results in:

(9.23)

We have seen that g varies by about 1 percent from pole to equator, which means that the final velocity of an object dropped from a fixed altitude would vary as a function of latitude. A straightforward example will illustrate this very nicely. Let’s assume we are at latitude 45° and elevation 10 km. To compute vf using (9.23), we need a representative value of g, which can be estimated using Table 9.1. To begin, let’s estimate the value of g at the surface by taking the arithmetic mean of g at 40 and 50°:

(9.24a)

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