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basic fluid dynamics solutions tarun deep saini indian institute of science bangalore india tarun physics iisc ernet in 1 ideal fluids 1 hydrostatic equilibrium a plane parallel atmosphere composed of ...
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...Basic fluid dynamics solutions tarun deep saini indian institute of science bangalore india physics iisc ernet in ideal fluids hydrostatic equilibrium a plane parallel atmosphere composed perfect gas is an external gravitational eld z g derive expression for the entropy gradient if isothermal solution condition implies v therefore euler equations take form dp p dz from rst law thermodynamics we have tds du pdv and upon dividing by mass it takes pd or d u dh where used denition specic enthalpy last step note that internal energy depends only on temperature t since equation state k b m clear too function thus obtain now using as ds c earth s lower stratosphere air use to show exp h scale height kt estimate mean molecular weight fact which can be solved pressure proportional density being constant obeys similar pexp calculated km assuming isentropic dt mp here ratio heats gases like nitrogen oxygen why does above vanish expressions mentioned earlier tem perature this gives solving zg weal...