Summary of Lecture 15 CHEE2945 Particle Engineering

CHEE2945 – Lecture 15

Dewatering suspensions:
- To remove water from suspensions, it is often forced through a settled bed of
particles on a porous surface.
- It is important to know the relationships of the depth of the particle bed,
particle size, the pressure drop across the bed, the volumetric flow rate of
water out of the bed, bed voidage, fluid density, fluid viscosity, etc.



Darcy’s law:
- Darcy’s law is given by:
k ∆P
U=
μ L

where k =¿bed permeability.
- One problem with Darcy’s law is that k is not known, and it doesn’t work at
high flow rates.
- It works quite well for laminar flow.
- One possible solution to the limitations of Darcy’s law, we could replace the
bed by a series of interconnected pipes through a solid block.



Pipe flow:
- The pressure drop across a pipe can be predicted by:
L
∆ P=2 f ρU 2
D

where f =¿ pipe friction factor, which is a function of Reynold’s number.
DUρ
ℜ=
μ

- For laminar flow ( ℜ< 2100, for pipes):
16
f= ℜ

32 μLU
∆ P=
D2
- For turbulent flow ( ℜ> 4000, for pipes), we can use the Blasius equation (for
4000< ℜ<105 :