(a) For what conditions is the Leveque approximation valid? (b) For the Leveque problem derived in class for a pipe with diameter d and length L, derive the flux at the surface of the pipe and the mass transfer coefficient. Find the local mass transfer coefficient kc and the average mass transfer coefficient kc. (c) Determine the Sherwood number Shd as a function of the Reynolds number, Schmidt number and the ratio (d/L). (d) Determine the ratio between the average mass transfer coefficient in the Leveque approximation theory to that of the average mass transfer coefficient in the Higbie penetration theory. (e) How does this ratio scales with the Peclet number and the length scales? Peclet number is Pe=VL/D Hint: The concentration for the Leveque problem in a pipe is given by: c1=(4/3)c1ie3d where the variable =s(9DRz4VM)1/3 where R is the radius of the pipe and D is the diffusion coefficient and VM is the maximum velocity of the Hagen Poiseuille profile in the pipe