Fluids Problem

Problem A Coruscant is a world completely covered in city. The buildings are so high and there is so much thermal control, that from the surface to an elevation of 2000m, the temperature is maintained at 21C. Above the city, there is a heat haze-called a "Heat Island Effect" - for 10,000m. Heat rises in this layer and gets caught by a layer of smog caused by incoming starships. The temperature rises 1C every 750m in this haze. The atmosphere of Coruscant is breathable to humans, but has a gas constant of 400 J/kg K. Due to its dense core, the gravity needs to be accounted for using g = Gm/r2 Where the radius of the planet is fe= 3,333 km plus elevation, and its mass is 6.39 E 23 kg, and G is a universal constant equal to 6.67 E-11 N- m/kg Han Solo needs to escape Imperial wrath by making a jump to light speed in the atmosphere, and has asked you to derive an equation for the pressure in the atmosphere as a function of elevation as fast as possible. Starting from Navier Stokes, and showing your assumptions, derive an expression with short explanations for each step for pressure, P, as a function of elevation, z, from the planet surface to 12,000m. (Draw a schematic, set up the integral, no need to integrate. Clearly define your variables.) au ( tu , o u , o u " 81 82 + ar Oray0 au De du v g 2. + + + ar r 8z r? Oyamaza au au au Www + + + ay +9.. Oy 822 Bu + Du + Or + + + + + + psy P + + OR ar az 3