CHL 331

Problem Sheet # 2

  1. A 150- mm-thick demister pad for removing fine droplets of H2SO4 from a gas stream is made of 50-m fibers randomly oriented in the plane perpendicular to the gas flow. The average porosity is 0.90. Calculate the pressure drop for gas velocities of 0.3 and 0.9 m/s at 90oC and 1 atm using the drag coefficients for individual fibers.
  1. Urea pellets are made by spraying drops of molten urea into cold gas at the top of a tall tower and allowing the material to solidify as it falls. Pellets 6 mm in diameter are to be made in a tower 25 m high containing air at 20oC. The density of urea is 1.330kg/m3. Viscocity of air is 10-5 PaS. (a) What would be terminal velocity of the pellets, assuming free settling conditions? (b) Would the pellets attain 99 percent of this velocity before they reached the bottom of the tower?
  1. Spherical particles1 mm in diameter are to be fluidized with water at twice the minimum velocity. The particles have an internal porosity of 40 percent, an average pore diameter of 10 m, and a particle density of 105g/cm3. Prove that flow through the internal pores is very small compared to the flow between the particles, and that the internal porosity can be neglected in predicting the fluidization behavior.
  1. Catalyst pellets 5 mm in diameter are to fluidized with 45,000 kg/h of air at 1 atm and 80oC in a vertical cylindrical vessel. The density of the catalyst particles is 960 kg/m3: their sphericity is 0.86. If the given quantity of air is just sufficient to fluidize the solids, what is the vessel diameter?
  1. Figure given below outline briefly the justification for supposing that the energy-equation frictional dissipation term for flow with superficial velocity 0through a packed bed of length is of the form:

= (au0 +b),

in which and are constants that depend on the nature of the packing and the

properties of the fluid flowing through the bed.

Flow through a packed bed

As shown in figure a bed of ion-exchange resin particles of depth L = 2 cm is supported by a metal screen that offers negligible resistance to flow at the bottom of acylindrical container. Liquid (which is essentially water with  = 1 cP and  = 1g/cm3) flows steadily down through the bed. The pressure at both the free surface of the water and at the exit from the bed are both atmospheric.

The following results are obtained for the liquid height H as a function of superficial velocity u0:

H (cm):2.575.4

u0 (cm/s): 0.1 1.0

First, obtain the values of the constants a and b for the packed bed. (Hint: perform overall energy balances between the liquid entrance and the packing exit, ignoring any exit kinetic energy effects.) Second, what is the d’ Arcy law permeability, , (cm2) for the packed bed at very low flow rates?

Third, a prototype apparatus is to be constructed in which the same type of ion-exchange particles are contained between two metal screens in the form of a hollow cylinder of outer radius 5 cm and inner radius 0.5 cm. What pressure difference (bar) is needed to effect a steady flow rate of 10 cm3/s of water per cm length of the hollow cylinder? (If needed, assume the flow is from the outside to the inside.)

  1. Figure given below shows a particle of mass that is ejected vertically upwards from the surface of fluidized bed with an initial velocity . The velocity of the fluidizing gas above the bed is, and the resulting drag force on the particle is D = c (, where c is constant and is the current velocity of the particle.

Departure of particle from the top of a fluidized bed.

Prove that the maximum height h to which the particle can beentrained above

the bed is given by:

in which is the steady upwards velocity of the particle when the drag and gravitational forces are balanced.

  1. Figure given below shows an apparatus for studying flow in a porous medium.

Fluid of high viscosity  flows between two parallel plates PP under the

influence of a uniform pressure gradient dp / d. Midway between the plates is a

slab S of porous material of void fraction  and permeability The diagram

shows the velocity profile in the fluid, the velocity within the slab being the

interstitial velocity:

.2

Apparatus for studying flow in a porous medium.

Explain why the velocity profile is of the form indicated, with particular attention to

the boundary conditions at the slab surfaces. Show that the total flow rate per

unit width is:

  1. Figure given below shows a spherical reactor of internal diameter D that is packed to a height H (symmetrically disposed about the “equator”) with spherical catalyst

particles of diameter and void Fraction. A volumetric flow rate of a liquid of

density and viscosity flows through the packing.

Flow through a spherical reactor.

How would you determine the resulting pressure drop? Give sufficient detail so that

Somebody else could perform all necessary calculations based on your plan.