2) Falling Drops Imagine a solid sphere of d friction, Fd, balances the weight of the sphere, W. The weight of the sphere is simply its mass, m, ameter, d, falling through the air. After its release, the sphere accelerates ty is obtained when the drag force due to air times acceleration due to gravity (g 9.8 m/s), W mg and the drag force can be computed as 2 A where Ca is a dimensionless empirical drag coefficient, p is the density of the air, is the velocity of the sphere, and A d/4 is the frontal area of the falling sphere. 1 of 4 CHEN 3170- APPLIED MATH METHODS MAASE, SPRING 2019 HW #4 A common correlation for the drag aerodynamic drag of smoo NOTE-Write, test and yalidate the equations / model to calculate drag coefticients an independent fun ction program and then use the function in your longer program!) 24 Where Re is the Reynolds number pu vd Re - and u is the dynamic viscosity of the air. Because the properties of air (e.g., H and p) are temperature-dependent, the terminal velocity will vary with temperature. To investigate this dependence, we will assume that air is an ideal gas, giving (T) RT where R -287.0 J/kg-K is the gas constant for air, P is the absolute air pressure in Nim2 and Tis the temperature in Kelvin. Use the following correlation for viscosity NOTE- Write, test and validate this as an independent function program and then use the function in your longer program) where the viscosity is given in kg/m-s with respect to temperature given in Kelvin and bi -2.156954157 x 10"14, b2 -5.332634033 x 10-l1, b 7.477905983 x 108. and b4- 2.527878788 x 107 Assuming standard atmospheric pressure (P 101300 N/m), m 0.5 kg, and d- 15 cm, compute and plot the terminal velocity of the sphere over the temperature range from -60C to 60C Once you have the plots you can re-compute a number of intermediate variables to help you rationalize that your solution makes physical sense. In particular, you should also generate a series of curves for vs. T, vs. T Re vs. T, and Ca vs. T. Are all of these plots reasonable? Do they help justify the behavior observed for v vs. T? Explain