Template:Model theory (Text, Slurry Flow, Morrell and Stephenson)

${\begin{array}{ll}Q_{m}=k_{m}J_{pm}^{2}\gamma ^{2.5}A\phi ^{-1.38}D^{0.5}&J_{pm}\leq J_{max}\\Q_{t}=k_{t}J_{pt}\gamma ^{2}AD^{0.5}&J_{p}>J_{max}\\&J_{pt}=J_{p}-J_{max}\\&J_{max}=0.5J_{t}-J_{po}\\&J_{po}=0.33(1-r_{n})\\&J_{p}=J_{pg}+J_{po}\\\end{array}}$

where

• $Q_{m}$ and $Q_{t}$ are the volumetric discharge rates of slurry through the grinding media zone and slurry pool, respectively (m³/h)
• $k_{m}$ and $k_{t}$ are the slurry discharge coefficients for the grinding media zone and slurry pool, respectively
• $J_{pm}$ is the net fractional slurry hold-up in the grinding media interstices (v/v)
• $J_{pt}$ is the net fractional slurry hold-up in the slurry pool (v/v)
• $\gamma$ is the open area weighted mean radial position of the grate apertures (m/m)
• $A$ is the total open area of grate apertures (m²)
• $D$ is the mill diameter (m)
• $\phi$ is the fraction critical speed of the mill (frac)
• $J_{p}$ is the net fraction of mill volume occupied by slurry (v/v)
• $J_{max}$ is the maximum net fractional slurry hold-up in the grinding media zone (v/v)
• $J_{t}$ is the fraction of mill volume occupied by grinding media, including associated interstices (v/v)
• $J_{po}$ is the dead fraction of mill volume which is occupied by slurry before discharge commences (v/v)
• $r_{n}$ is the relative radial position of the outermost grate apertures (m/m)