Pressure scale height
= Pressure scale height
{title2=$H_P=-dr/d\log P$}
A pressure scale height is the local distance over which <pressure> would change by a factor $e$ if its logarithmic gradient were constant. In <hydrostatic equilibrium>, $H_P=P/(\rho g)$; for an <ideal gas> it is $k_BT/(\mu m_ug)$. A small logarithmic pressure interval has depth approximately $H_P\,\Delta\log P$.