Isothermal and Non-Isothermal Fluids

Isothermal and Non-Isothermal Fluids Isothermal Fluid (Constant Temperature Solution) Recap equation (1.7) The equation of state for a compressible system generally relates its density to its pressure and temperature. If the fluid is a perfect gas at rest at constant temperature, it can be written from eq (1.7) that Since ,                                                                    = constant   (3.17) Where po and ro are the pressure and density at some reference horizontal plane. With the help of Eq. (3.17), Eq. (3.14) becomes, (3.18) (3.19) where z and z0 are the vertical coordinates of the plane concerned for pressure p and the reference plane respectively from any fixed datum. Non-isothermal Fluid The temperature of the atmosphere up to a certain altitude is frequently assumed to decrease linearly with the altitude z as given by (3.20) where T0 is the absolute temperature at sea level and the constant a is known as lapse rate. For the standard atmosphere, a = 6.5 K/km and T0= 298 K. With the help of p =rRT and (3.20), the Eq. (3.14) can be written as, (3.21) Integration of Eq. (3.21) yields Hence, (3.22) The altitude z in Eq. (3.22) is measured from the sea level where the pressure is po.