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

${\begin{array}{ll}Q_{\rm {m}}=k_{\rm {m}}{J_{\rm {pm}}}^{2}\gamma ^{2.5}A\phi ^{-1.34}D^{0.5}&J_{\rm {pm}}\leq J_{\rm {max}}\\Q_{\rm {t}}=k_{\rm {t}}J_{\rm {pt}}\gamma ^{2}AD^{0.5}&J_{\rm {p}}>J_{\rm {max}}\\&J_{\rm {pt}}=J_{\rm {p}}-J_{\rm {max}}\\&J_{\rm {max}}=0.5J_{\rm {t}}-J_{\rm {po}}\\&J_{\rm {po}}=0.33(1-r_{\rm {n}})\\&J_{\rm {p}}=J_{\rm {pg}}-J_{\rm {po}}\\\end{array}}$

where

• $Q_{\rm {m}}$ and $Q_{\rm {t}}$ are the volumetric discharge rates of slurry through the grinding media zone and slurry pool, respectively (m³/h)
• $k_{\rm {m}}$ and $k_{\rm {t}}$ are the slurry discharge coefficients for the grinding media zone and slurry pool, respectively
• $J_{\rm {pm}}$ is the net fractional slurry hold-up in the grinding media interstices (v/v)
• $J_{\rm {pt}}$ 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)
• $J_{\rm {p}}$ is the net fraction of mill volume occupied by slurry (v/v)
• $J_{\rm {max}}$ is the maximum net fractional slurry hold-up in the grinding media zone (v/v)
• $J_{\rm {t}}$ is the fraction of mill volume occupied by grinding media, including associated interstices (v/v)
• $J_{\rm {po}}$ is the dead fraction of mill volume which is occupied by slurry before discharge commences (v/v)
• $J_{\rm {pg}}$ is gross fraction of mill volume occupied by slurry (v/v)
• $r_{\rm {n}}$ is the relative radial position of the outermost grate apertures (m/m)