A model sphere with diameter d, soaked with ethanol, is kept still in a stream of air. Dimensional analysis shows that the expression which relates the mass transfer coefficient of the ethanol evaporation, k, to the sphere diameter d, the mean air velocity, u, the diffusion coefficient of the ethanol in the air, D, and the air properties, density p and viscosity , is of the form: Sh = f(Re, Sc) where Sh = and Sc= pD kd D dup is the Sherwood number, Re = - is the Schmidt number. is the Reynolds number a) What is the significance of each of the dimensionless groups? A sphere, 5 cm in diameter, soaked in ethanol, is within a stream of air. Experiments have given the values reported in Table Q1 of the mass transfer coefficient of the ethanol in the air: Table Air velocity and mass transfer coefficient for the 5 cm sphere 30 40 10.8 13.4 air velocity (m s-) mass transfer coefficient (m s-) 10 4.5 20 7.6 b) Show for what range of air velocities can the above results be used for a sphere of 2 cm in diameter in the same air stream. c) What would be the mass transfer coefficients in the case of the 2 cm sphere? Air properties: density = 1.21 kg m-, viscosity = 1.78 x 10-5 kg m-1 s-1. Diffusion coefficient of ethanol in air = 1.26 x 10-5 m s-1.