Thermodynamics, Statistical Physics, and Quantum Mechanics

106 SOLUTIONS

4.19 Rocket in Drag (Princeton)

Use dimensionalanalysis toderive thedragforceFon the rocket:

We thenhave

So and

This formula is generally correct for high Reynolds numbers; for low

Reynoldsnumbers we haveStokes’ law:

where is theviscosity and is the radius.

b) For an isothermal atmosphere, take a column of air of height andarea

A. The pressure difference between top and bottom should compensate the

weight of thecolumn:

or

Using

where is the molar weight of the air, and substituting(S.4.19.6) into

(S.4.19.5), we obtain

a)