Fluid Mechanics seventh edition by Frank M. White · Problem 2.26

Pressure Distribution in a Fluid — Frank M. White

Physics — Fluid Mechanics · the-atmosphere

Problem

For gases that undergo large changes in height, the linear approximation, Eq. (2.14), is inaccurate. Expand the troposphere power-law, Eq. (2.20), into a power series, and show that the linear approximation p≈pa−ρagzp \approx p_a - \rho_a gz is adequate when δz≪2T0(n−1)Bwhere n=gRB\delta z \ll \frac{2T_0}{(n-1)B} \quad \text{where } n = \frac{g}{RB}

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