Derive Eq. (4.13) for pressure variation in the atmosphere with elevation. Find the pressure at Shangri-La, which is about \(3000 \mathrm{~m}\) above the sea level. (In the Tibetan language Shangri-La means the Sun and Moon at heart.)

The temperature variation with elevation is small, and is usually represented as a linear relation:

\[T=T_{0}(1-\alpha z)\]

Incorporate this into the calculation of density and then solve the hydrostatic equation to find a relation for the pressure variation with height including the above temperature correction.

The change in temperature is about \(6.4{ }^{\circ} \mathrm{C}\) for a change in height of \(1000 \mathrm{~m}\). Using this, find \(\alpha\) defined above and recalculate the pressure at Shangri-La.

Transcribed Image Text:

22 Po = exp Mw Z RGT (4.13)