Cpl300s - Exam - Data Page - 5 June 2014

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DATA PAGE Linear regression derivation Y = a1 + a2X

  Y   X     X   XY   N  X   X  2

a1

2

2

a2 

N   XY     X   Y  N  X 2   X 

Mean diameter of a particulate system based on length x d d length where x  mass fraction x  d2 Mean diameter of a particulate system based on surface area 1 d surface where x  mass fraction x d Comminution

Von Rittinger’s law of crushing Kick’s law of crushing L E  K K f c ln 1 L2 Bond’s law of crushing 10W i 10W i W   P F Particle Technology

General expression for free settling ratio dA  B   f  dB  A   f

n







 1 1    L2 L1 

E  fRKR 

2

Where

2

Stokes’ law 50 m  Intermediate 50 m – 5000 m Newton’s law 5000m 

n = 0.5 0.5 < n < 1 n=1

Hydrocyclone Partition curve model 1 (standard model)     d      1 exp       d 50     %  100   d    exp     d    exp   2     50     Partition curve model 2 %  100 1  exp(d / d 50  0.115 )3



I

d 50



d 75  d 25 2d 50

13.7( Do Di ) 0.68  0.53 Q (  s   l ) 0 .5

Where

d 50

Imperfection relationship

D0 DI Q s l d50

= = = = = =

Cut point relationship 1 is the overflow diameter (cm) is the inlet diameter (cm) is the total flow rate (m3h-1) RD of the solids RD of the liquid the cut point (m)

 Dc3   4.5  1.2   L (  s  l ) 

Where



DC  L D50

Cut point relationship 2

is the diameter of the cyclone changer (cm) is the viscosity of the liquid (Pa.s, mNs/m 2) is the feed flow rate (l/min) is the cut point in (m)

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Leaching

dM kA(C s  C )  dt X The dynamic leach equation (assuming that the stagnant layer is mechanism controlling) WhereM t A X Cs C k

is the mass of diffusing component (mass) is time is the interfacial area through which mass transfer occurs is the thickness of the laminar layer is the concentration on the surface of the leach particle (mass.vol -3) is the concentration in the bulk solution surrounding the leach particle (mass.vol 3 ) is the mass transfer coefficient (area.time-1)

An algebraic equation giving the change of concentration in a batch leach vessel

 kA  C  C s  1  exp   VX  WhereV

  t   

is the volume of the liquid in the batch leach vessel (m 3)

Filtration dV P . A  dt  ( RC  RM ) Darcy’s law

Where  P A  V t Rc Rm

is the pressure drop across filter bed (Pa) is the area of the filter bed (m2) is the dynamic viscosity of the filtrated liquid (Pa.s) is the volume of fitrate passed at time (m 3) is time (s) is the filter cake resistance to the flow of filtrate, it is a variable, (m -1) medium resistance to the flow of the filtrate, it is a constant, (m -1)

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Dynamic and algebraic equations associated with filtration

Rm . r.C. 2 V  V t 2. s .P. A 2 P. A

Functions used to solve quadratic systems

 b  b 2  4ac x 2a

Thickness 

where 0  ax 2  bx  c

C V s  A

Filter cake thickness can be determined from the following

equation Where

C V A s

is mass of solid associated with unit volume of filtrate (kg.m -3) is the volume of filtrate developed to date (m 3) is the area through which filtration occurs (m 2) is the density of the of the solid (kg.m -3)

Sedimentation An algebraic equation derived for the calculation of thickener cross sectional area A

Q (Y  U )C s uc 

A

Q uc

 

 1

C  Cu 

Where Q is volumetric feed rate to thickener (m3.s-1) A is horizontal cross-section of thickener required (m 2) C is fractional volumetric concentration uc is sedimentation velocity at concentration C (m.s -1) Cu is fractional volumetric concentration in the under flow

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General information Avagardo’s number 6.023  1023 atoms per mole Charge per electron 1.602  10-19 coulombs per electron Volume of a sphere 4/3 x pi x radius3 External surface area of a sphere 4 x pi x radius2