2.16c. Mass transfer inside a circular pipe.
Water flows through a thin tube, the walls of which are lightly coated with benzoic acid (C7H6O2). The water flows slowly, at 298 K and 0.1 cm/s. The pipe is 1-cm in diameter. Under these conditions, equation (2-63) applies.
a) Show that a material balance on a length of pipe L leads to
where v is the average fluid velocity, and cA* is the equilibrium solubility concentration.
b) What is the average concentration of benzoic acid in the water after 2 m of pipe. The solubility of benzoic acid in water at 298 K is 0.003 g/cm3, and the mass diffusivity is 1.0 ´ 10Ð5 cm2/s (Cussler, 1997).
Solution
2.17b. Mass transfer in a wetted-wall tower.
Water flows down the inside wall of a 25-mm ID wetted-wall tower of the design of Figure 2.2, while air flows upward through the core. Dry air enters at the rate of 7 kg/m2-s. Assume the air is everywhere at its average conditions of 309 K and 1 atm, the water at 294 K, and the mass-transfer coefficient constant. Compute the average partial pressure of water in the air leaving if the tower is 1 m long.
Solution
For water at 294 K
2.18c. Mass transfer in an annular space.
In studying the sublimation of naphthalene into an airstream, an investigator constructed a 3-m-long annular duct. The inner pipe was made from a 25-mm-OD, solid naphthalene rod; this was surrounded by a 50-mm-ID naphthalene pipe.
Air at 289 K and 1 atm flowed through the annular space at an average velocity of 15 m/s. Estimate the partial pressure of naphthalene in the airstream exiting from the tube. At 289 K, naphthalene has a vapor pressure of 5.2 Pa, and a diffusivity in air of 0.06 cm2/s. Use the results of Problem 2.7 to estimate the mass-transfer coefficient for the inner surface; and equation (2-47), using the equivalent diameter defined in Problem 2.7, to estimate the coefficient from the outer surface.
Solution
In this situation, there will be a molar flux from the inner wall, NA1, with specific interfacial area, a1, and a flux from the outer wall, NA2, with area a2. A material balance on a differential volume element yields:
Define:
Then:
For the interior wall:
For the outer wall: