Part $2$: Date seeds size reduction unit operation

At lab scale, a certain crusher takes date kernels whose average particles diameter is $20mm$ and crushes it to a product whose average particle diameter is $10mm,$ at a rate of $100k\frac{g}{?}$ hour. At this rate, the mill takes $0\mathrm{.}12kW$ of power.

Tasks: What would be the power consumption for same capacity if the average particle diameter in the product is $75m?($use first run data to estimate the coefficients $K_K,K_R,$ and $K_B)$

Compute the energy consumed by Kick's Law, and Bond's Equation.

Which law$($s$)$ is most consistent with data of figure $29\mathrm{.}16?$

FIGURE $29\mathrm{.}16$

Energy consumption vs$.$ product size in size$-$reduction equipment. $($By permisslon, fram Commintion and Energy Consumption, NMAB$-261,$ Natlonal Acadany Preis, $1981.)$

Size reduction: Power consumption $($in $kW\frac{h}{?}$ ton$)$

$\frac{p}{m}=K_R(\frac{1}{D_{VP}}-\frac{1}{D_{VF}}),$ Rittenger's Law

$\frac{p}{m}=K_{K}ln(\frac{D_{VF}}{D_{Vp}}),$ Kick's LaW

$\frac{p}{m}=K_B(\frac{1}{\sqrt[\phantom{2}]{D_{PP}}}-\frac{1}{\sqrt[\phantom{2}]{D_{PF}}}),$ Bond's Law