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KUNDU Fluid Mechanics 2 Episode 2

Tham khảo tài liệu 'kundu fluid mechanics 2 episode 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | to. Sialic Equilibrium of a Compressible Medium 19 where r dT dz is the temperature gradient ra g Cp is called the adiabatic temperature gradient and is the largest rate at which the temperature can decrease with height without causing instability. For air at normal temperatures and pressures the temperature of a neutral atmosphere decreases with height at the rate of g Cp 10 c km. Meteorologists call vertical temperature gradients the lapse rate so that in their terminology the adiabatic lapse rate is 10 C km. Figure 1.9a shows a typical distribution of temperature in the atmosphere. The lower part has been drawn with a slope nearly equal to the adiabatic temperature gradient because the mixing processes near the ground tend to form a neutral atmosphere with its entropy well mixed that is uniform with height. Observations show that the neutral atmosphere is capped by a layer in which the temperature increases with height signify ing a very stable situation. Meteorologists call this an inversion because the temperature gradient changes sign here. Much of the atmospheric turbulence and mi xing processes cannot penetrate this very stable layer. Above this inversion layer the temperature decreases again but less rapidly than near the ground which corresponds to stability. It is clear that an isothermal atmosphere a vertical line in Figure 1.9a is quite stable. Potential Temperature and Density The foregoing discussion of static stability of a compressible atmosphere can be expressed in terms of the concept of potential temperature which is generally denoted by 0. Suppose the pressure and temperature of a fluid particle at a certain height arc p and T. Now tf we take the particle adiabatically to a standard pressure ps say the sea level pressure nearly equal to 100 kPa then the temperature attained by the particle is called its potential temperature. Using Eq. 1.26 it follows that the actual temperature T and the potential temperature 0 arc related by _ y I r T ei . .