$8\mathrm{.}4$ A flocculation basin is to be designed for a water coagulation plant, and the design flow is $\backslash (49,200\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$d$\}\backslash ).$ The basin is to be a cross$-$flow hori$-$zontal$-$shaft, paddle$-$wheel type with a mean velocity gradient of $\backslash (26\mathrm{.}7\backslash$mathrm$\{$~s$\}^\{-1\}\backslash )($at $\backslash (10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )),$ a detention time of $45$ min $,$ and a $\backslash ($ G T $\backslash )$ value from $50,000$ to $100,000.$ Tapered flocculation is to be provided, and three compartments of equal depth in series are to be used, as shown in Figure $8\mathrm{.}19($b$).$ The compartments are to be separated by slotted, redwood baffle fences, and the basin floor is level. The $\backslash ($ G $\backslash )$ values are to be $50,20,$ and $\backslash (10\backslash$mathrm$\{$~s$\}^\{-1\}\backslash ).$ The flocculation basin is to have a width of $27\mathrm{.}43$ m to adjoin the settling basin. The paddle wheels are to have blades with a $\backslash (150-\backslash$mathrm$\{$mm$\}\backslash )$ width and a length of $3\mathrm{.}05$ m $.$ The outside blades should clear the floor by $305$ mm and be $305$ mm below the water surface. There are to be six blades per paddle wheel, and the blades should have a clear spacing of $305$ mm $.$ Adjacent paddle wheels should have a clear spacing of $760$ to $915$ mm between blades. The wall clearance is $305$ to $460$ mm $.$ Determine:

a$.$ The basin dimensions.

b$.$ The paddle$-$wheel design.

c$.$ The power to be imparted to the water in each compartment and the total power required for the basin.

d$.$ The range in rotational speed for each compartment if $\backslash (1$: $4\backslash )$ variable$-$speed drives are employed.