Theoretical and Computational Dynamics of a Compressible by Shih-I Pai Ph. D. & Dr. Tech. hc, Shijun Luo Ph. D. (auth.)

By Shih-I Pai Ph. D. & Dr. Tech. hc, Shijun Luo Ph. D. (auth.)

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By Shih-I Pai Ph. D. & Dr. Tech. hc, Shijun Luo Ph. D. (auth.)

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By the Clausius-Clapeyron equation which may be derived as follows: From Eqs. 61) Eq. 61) is the Clausius-Clapeyron equation. 61). , vL << v, and if we may write v,=RT /p, Eq. 62) s For many substance, we may write L =a+ bT where a and b are constants, Eq. 62a) s In general, we have v,(T,), vL(T )and L(TJ. Eq. 6l)gives 5 I T, Ps -Po= r. 63) o where subscript 0 refers to the values at some reference condition. The functions L(T5 ), v,(T,) and vL (T5 ) may be determined experimentally. 8. Transport coefficients: viscosity, heat conductivity, diffusion, electrical conductivity and absorption coefficient of thermal radiation 22 • 23 • 24 Even though our main interest in this book is the study of the flow of a compressible fluid without transport phenomena, the transport phenomena do 36 Dynamics of Compressible Flow have important influence on the flow field of a compressible fluid.

3a) . (b) Umr represents internal energy due to rotational motion of the molecules. It is rotational internal energy (Fig. 3b). For a monatomic gas, the moment of inertia of the atom is negligibly small and we may assume U mr = 0. For a diatomic gas, the moment of inertia about the axis connecting the two atoms is negligibly small, while those about axes perpendicular to the axis connecting the atoms are not small. We may consider that there are two degrees of freedom due to rotational motion of a diatomic gas.

But for a sufficiently thin layer of atmosphere, we may assume that the lapse rate A is a constant. 003566°FI ft. At the end of the troposphere, there is a region known as the tropopause which is a short region between troposphere and stratosphere. The height of the tropopause depends greatly on the latitude. It may be below 10 km in the polar region and above 15 km in the equatorial belt. (2) Stratosphere. The stratosphere covers the region from the tropopause up to an altitude of about 50 km.

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