CL 351                                   Homework # 3

 

Due date: 25 August, 2005

 

1.       The dissolution of lead from lead-soldered joints in household piping is a possible health problem.  If the water flowing through the pipe is mildly acidic, then some of the lead will dissolve from the inner surface of the lead-soldered pipe section into the water.  New drinking water requirements stipulate that soluble lead concentration levels should not exceed 0.015 g/m3.  At present, water flows through a 0.025 m I. D. pipe at a bulk velocity of 0.2 m/sec.  The water chemistry results in a soluble lead concentration of 10 g/m3 at the surface of the soldered pipe section.  Determine the soluble lead concentration in the water after it passes three leas-soldered joints that are each 0.05 m in length.  The diffusivity of soluble lead in water is 1 x 10-9 m2/sec, and the kinematic viscosity of water is 1 x 10-6 m2/sec.  Use the following correlation to predict mass transfer coefficient:    Sh = 0.023 Re0.83Sc0.33.

 

2.       A stirred tank fermenter is used to cultivate aerobic micro-organisms in aqueous suspension.  The aerobic cells require dissolved oxygen for respiration, which is supplied by aerating the liquid medium.  An important design parameter for specifying the oxygen mass transfer rate in the fermenter is the volumetric mass transfer coefficient, kLa.  Based on power per unit volume of 1572 W/m3, aeration rate of 1m3 per minute, tank diameter of 1.5 m and liquid volume of 2 m3, determine the volumetric mass transfer coefficient and the oxygen mass transfer rate in .  Assume that the cells immediately consume the dissolved oxygen, so that the oxygen concentration in the liquid medium is essentially zero.  The Henry’s law constant for oxygen in water is 52, 500 bars.  Use correlation developed in the class.

 

3.       A disk of radioactively tagged benzoic acid 1 centimeter in diameter is spinning at 20 revolutions per minute in 94 cc of initially pure water.  We find that the solution contains benzoic acid at 7.3 x 10-4 g/cc after 10 hours 4 minutes and 3.43 x 10-3 g/cc after a long time.  What is the mass transfer coefficient?  How long will it take to reach fourteen percent saturation?  How closely does this mass transfer coefficient agree with that expected from correlation?  For correlation of mass transfer coefficient from a spinning disk, see handouts available in Hostel 10 photocopy room.

 

4.       Trichloroethylene (TCE), a common industrial solvent, is often found at low concentrations in industrial waste waters.  Stripping is a common process for removing sparingly soluble, volatile organic solutes such as TCE from aqueous solution.  A wetted wall column is used to study the stripping of TCE from water to air at a constant temperature of 293 K and a total system pressure of 1 atm.  The column inner diameter is 4 cm and height is 2 m.  In the present process, the volumetric air flow rate into the column is 2000 cm3/sec and water is falling at a velocity of 0.5 m/sec.  Estimate, the overall liquid side mass transfer coefficient for TCE across the liquid and gas film.  To predict mass transfer coefficient on gas side use the correlation given in Problem 1.  For mass transfer coefficient from a falling film (liquid side), see handouts available in Hostel 10 photocopy room. 

The process is dilute so that the bulk gas has properties of air and bulk liquid has properties of water.  The Henry’s law constant for TCE is 550 atm at 293 K.  Diffusivity of TCE in air is 8.08 x 10-6 m2/sec and that in water is 2 x 10-9 m2/sec.