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

:<math>
\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} A D^{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}
</math>

where
* <math>Q_{\rm m}</math> and <math>Q_{\rm t}</math> are the volumetric discharge rates of slurry through the grinding media zone and slurry pool, respectively (m<sup>3</sup>/h)
* <math>k_{\rm m}</math> and <math>k_{\rm t}</math> are the slurry discharge coefficients for the grinding media zone and slurry pool, respectively
* <math>J_{\rm pm}</math> is the net fractional slurry hold-up in the grinding media interstices (v/v)
* <math>J_{\rm pt}</math> is the net fractional slurry hold-up in the slurry pool (v/v)
* <math>\gamma</math> is the open area weighted mean radial position of the grate apertures (m/m)
* <math>A</math> is the total open area of grate apertures (m<sup>2</sup>)
* <math>D</math> is the mill diameter (m)
* <math>\phi</math> is the fraction critical speed of the mill (frac)
* <math>J_{\rm p}</math> is the net fraction of mill volume occupied by slurry (v/v)
* <math>J_{\rm max}</math> is the maximum net fractional slurry hold-up in the grinding media zone (v/v)
* <math>J_{\rm t}</math> is the fraction of mill volume occupied by grinding media, including associated interstices (v/v)
* <math>J_{\rm po}</math> is the dead fraction of mill volume which is occupied by slurry before discharge commences (v/v)
* <math>J_{\rm pg}</math> is gross fraction of mill volume occupied by slurry (v/v)
* <math>r_{\rm n}</math> is the relative radial position of the outermost grate apertures (m/m)