PROBLEMS

$29\mathrm{.}1.$ Trap rock is crushed in a gyratory crusher. The feed is nearly uniform $2-$in$.$ spheres. The differential screen analysis of the product is given in column $(1)$ of Table $29\mathrm{.}5.$ The power required to crush this material is $400k\frac{W}{?}$ ton. Of this $10kW$ is needed to operate the empty mill. By reducing the clearance between the crushing head and the cone, the differential screen analysis of the product becomes that given in column $(2)$ in Table $29\mathrm{.}5.$ From $($a$)$ Rittinger's law and $($b$)$ Kick's law, calculate the power required for the second operation. The feed rate is $110to\frac{n}{h}.$

TABLE $29\mathrm{.}5$

Data for Prob. $29\mathrm{.}1$

$\backslash$table$[[,$Product$],[$Mesh$,\backslash$table$[[$First grind$],[(1)]],\backslash$table$[[$Second grind$],[(2)]]],[\frac{4}{6},3\mathrm{.}1,],[\frac{6}{8},10\mathrm{.}3,3\mathrm{.}3],[\frac{8}{10},20\mathrm{.}0,8\mathrm{.}2],[\frac{10}{14},18\mathrm{.}6,11\mathrm{.}2],[\frac{14}{20},15\mathrm{.}2,12\mathrm{.}3],[\frac{20}{28},12\mathrm{.}0,13\mathrm{.}0],[\frac{28}{35},9\mathrm{.}5,19\mathrm{.}5],[\frac{35}{48},6\mathrm{.}5,13\mathrm{.}5],[\frac{48}{65},4\mathrm{.}3,8\mathrm{.}5],[-65,0\mathrm{.}5,],[\frac{65}{100},,6\mathrm{.}2],[\frac{100}{150},,4\mathrm{.}0],[-150,,0\mathrm{.}3]]$

$29\mathrm{.}2.$ Using the Bond method, estimate the power necessary per ton of rock in each of the operations in Prob. $29\mathrm{.}1.$

$29\mathrm{.}3.$ Solve Example $29\mathrm{.}2$ for a mill charge consisting entirely of $\frac{4}{6}-$mesh material. Plot the results and compare them with Fig. $29\mathrm{.}1.$

$29\mathrm{.}4.$ Solve Prob. $29\mathrm{.}3$ with $(a)=1\mathrm{.}1$ and $(b)=1\mathrm{.}6.$ Plot the results. Do they vary as you expected?

$29\mathrm{.}5.$ Solve Prob. $29\mathrm{.}3$ with $=1\mathrm{.}3$ and with $S$ varying with $D_p^3$ for material coarser than $10-$mesh and with $D_p^2$ for the finer sizes. Are the results as you predicted?

$29\mathrm{.}6.$ What rotational speed, in revolutions per minute, would you recommend for a ball mill $1200mm$ in diameter charged with $75-mm$ balls?