Due date: November-07-2019 (In Class)
CHEN 304-501
Homework #8
1) (20 Points) A centrifugal pump with pressure increase p2 – p1 = a – bQ2 atm, where a and b are known
constants, pumping a slurry into a plate-and-frame filter. The filter has a cross-sectional area A cm2,
cake permeability, κ (darcies), filtrate viscosity μ (cP), and cake-to-filtrate volumetric ratio ε. A total
volume V cm3 of filtrate has been passed. The pump inlet and filter exit pressures are equal. Assume
that the slight difference between slurry and filtrate volumes is negligible.
If a = 0.2, b = 10–5, A = 100, κ = 100, μ = 1, ε = 0.1, and V = 104, all in units consistent with the above
definitions, calculate the current volumetric flow rate Q cm3/s.
2) (20 Points) The following data were obtained for a plate-and-frame filter of total area A = 500 cm2
operating under a constant pressure drop of Δp = 0.1 atm:
The filtrate is essentially water. The volume of the cake is one-tenth the volume of the filtrate passed.
The resistance of the filter medium may be neglected.
Make an appropriate plot and estimate the permeability κ (darcies) of the cake.
3) (30 Points) Consider three spherical particles with a diameter of 1 cm(A), 2 cm(B), and 4 cm(C). The
densities of these particles are given to be 2,500 kg/m3. They were left to free-fall above a water stream
having a uniform velocity profile (lateral velocity um= 0.1 m/s). Assume that these particles reach their
terminal velocity at the top of the water stream. Determine distance travelled by each particle.
C
B
A
4) (30 Points) 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 d and void fraction ε. A
volumetric flow rate Q of a liquid of density ρ and viscosity μ flows through the packing. Obtain a
differential equation that will allow you to determine the pressure drop across the system (do not solve
it).