Page 150 - Separation process principles 2

Exercises 115

maintained at 2 wt%. After 5 h, the average moisture content is Section 3.5
8 wt%. Estimate:
3.32 Water at 25°C flows at 5 ft/s through a straight, cylindrical
(a) The diffusivity of water in the clay in cm2/s. tube cast from benzoic acid, of 2-in. inside diameter. If the tube is
(b) The additional time for the average moisture content to reach 10 ft long, and fully developed, turbulent flow is assumed, estimate
4 wt%. All moisture contents are on a dry basis. the average concentration of benzoic acid in the water leaving the
tube. Physical properties are given in Example 3.15.
3.25 A spherical ball of clay, 2 in. in diameter, has an initial mois-
ture content of 10 wt%. The diffusivity of water in the clay is 3.33 Air at 1 atm flows at a Reynolds number of 50,000 normal to
5 x lop6 cm2/s. At time t = 0, the surface of the clay is brought into a long, circular, 1-in.-diameter cylinder made of naphthalene.
contact with air such that the moisture content at the surface is main- Using the physical properties of Example 3.14 for a temperature of
tained at 3 wt%. Estimate the time for the average moisture content in 100°C, calculate the average sublimation flux in kmovs-m2.
the sphere to drop to 5 wt%. All moisture contents are on a dry basis. 3.34 For the conditions of Exercise 3.33, calculate the initial
average rate of sublimation in kmol/s-m2 for a spherical particle of
Section 3.4 1-in. initial diameter. Compare this result to that for a bed packed
3.26 Estimate the rate of absorption of pure oxygen at 10 atm and with naphthalene spheres with a void fraction of 0.5.
25°C into water flowing as a film down a vertical wall 1 m high and
Section 3.6
6 cm in width at a Reynolds number of 50 without surface ripples.
Assume the diffusivity of oxygen in water is 2.5 x cm2/s and 3.35 Carbon dioxide is stripped from water by air in a wetted-
that the mole fraction of oxygen in water at saturation for the above wall tube. At a certain location, where the pressure is 10 atrn
temperature and pressure is 2.3 x and the temperature is 25"C, the mass-transfer flux of C02 is
1.62 lbmolth-ft2. The partial pressures of C02 are 8.2 atrn at the in-
3.27 For the conditions of Example 3.13, determine at what
terface and 0.1 atrn in the bulk gas. The diffusivity of C02 in air at
height from the top the average concentration of C02 would corre-
these conditions is 1.6 x cm2/s. Assuming turbulent flow of
spond to 50% of saturation.
the gas, calculate by the film theory, the mass-transfer coefficient kc
3.28 Air at 1 atrn flows at 2 m/s across the surface of a 2-in.-long for the gas phase and the film thickness.
surface that is covered with a thin film of water. If the air and water
3.36 Water is used to remove C02 from air by absorption in a col-
are maintained at 25"C, and the diffusivity of water in air at these
umn packed with Pall rings. At a certain region of the column
conditions is 0.25 cm2/s, estimate the mass flux for the evaporation
where the partial pressure of C02 at the interface is 150 psia and
of water at the middle of the surface assuming laminar boundary-
the concentration in the bulk liquid is negligible, the absorption rate
layer flow. Is this assun~ption reasonable?
is 0.017 Ibmovh-ft2. The diffusivity of C02 in water is
3.29 Air at 1 atm and 100°C flows across a thin, flat plate of 2.0 x lop5 cm2/s. Henry's law for C02 isp = Hx, where H = 9,000
naphthalene that is 1 m long, causing the plate to sublime. The psia. Calculate:
Reynolds number at the trailing edge of the plate is at the upper
(a) The liquid-phase mass-transfer coefficient and the film
limit for a laminar boundary layer. Estimate:
thickness
(a) The average rate of sublimation in kmolls-m2
(b) Contact time for the penetration theory
(b) The local rate of sublimation at a distance of 0.5 m from the
(c) Average eddy residence time and the probability distribution
leading edge of the plate
for the surface-renewal theory
Physical properties are given in Example 3.14.
3.37 Determine the diffusivity of H2S in water, using the penetra-
3.30 Air at 1 atrn and 100°C flows through a straight, 5-cm- tion theory, from the following data for the absorption of H2S into
diameter circular tube, cast from naphthalene, at a Reynolds number a laminar jet of water at 20°C.
of 1,500. Air entering the tube has an established laminar-flow velocity
Jet diameter = 1 cm, Jet length = 7 cm, and Solubility of H2S in
profile. Properties are given in Example 3.14. If pressure drop through
water = 100 mol/m3
the tube is negligible, calculate the length of tube needed for the aver-
age mole fraction of naphthalene in the exiting air to be 0.005. The average rate of absorption varies with the flow rate of the jet as
follows:
3.31 A spherical water drop is suspended from a fine thread in
still, dry air. Show: Jet Flow Rate, Rate of Absorption,
(a) That the Sherwood number for mass transfer from the surface cm3/s moys x lo6
of the drop into the surroundings has a value of 2 if the characteris-
tic length is the diameter of the drop.
If the initial drop diameter is 1 mm, the air temperature is 38"C, the
drop temperature is 14.4"C, and the pressure is 1 atrn, calculate:
(b) The initial mass of the drop in grams.
(c) The initial rate of evaporation in grams per second.
(d) The time in seconds for the drop diameter to be reduced to
Section 3.7
0.2 mm.
3.38 In a test on the vaporization of H20 into air in a wetted-wall
(el The initial rate of heat transfer to the drop. If the Nusselt num-
column, the following data were obtained:
ber is also 2, is the rate of heat transfer sufficient to supply the heat
of vaporization and sensible heat of the evaporated water? If not, Tube diameter, 1.46 cm, Wetted-tube length, 82.7 cm
what will happen? Air rate to tube at 24°C and 1 atm, 720 cm3/s