4. A fluid is flowing in a vertical pipe and mass transfer is occurring from the pipe wall to the fluid. Use dimensional analysis to prove the relationship of the mass-transfer coefficient k to the variables D, p, , v, DAB, 9, Ap, and L, where D is pipe diameter, L is pipe length, and Ap is the density difference as k',D DAB gLpAp Dvp 'PDAB 4 = fe