Compressible Fluids, Properties of Atmosphere

The most common compressible fluid we know is air. Assuming air to behave like a perfect gas, Eqn.2.15 becomes,

$${{dp} \over {dz}} = -\rho g=-{{p \over {RT}}} g$$ or

$${{dp} \over p } ={-{g \over R} {{dz} \over T}}$$ (2.22)

By integrating the above equation we obtain,

$${\int_{p_1}^{p_2}} {{dp} \over p}=\ln {p_2 \over p_1}=-{g \over R} {\int_{z_1}^{z_2}} ~{{dz} \over T}$$ (2.23)

To solve the above equation we need to know how temperature T varies with altitude. For this we rely on the concept of Standard Atmosphere described next.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney