Alumina solids are being washed to remove \(\mathrm{NaOH}\) from liquid entrained with solids. The wet feed is a mixture of \(5.0 \mathrm{vol} \%\) solids (dry basis) and \(95.0 \mathrm{vol} \%\) liquid. Underflow streams from settlers maintain \(20.0 \mathrm{vol} \%\) of solids and \(80.0 \mathrm{vol} \%\) liquid. The feed flow rate (dry basis) is \(3000.0 \mathrm{~kg} / \mathrm{h}\) of solids, and \(\mathrm{NaOH}\) concentration in the entrained liquid is \(4.5 \mathrm{wt} \%\). We want to remove \(85.0 \%\) of \(\mathrm{NaOH}\). Find the flow rate of the required pure wash water. Data: \(ho_{\text {water }}=1.0 \mathrm{~kg} / \mathrm{L}, ho_{\text {solids }}=2.5 \mathrm{~kg} / \mathrm{L}\) (dry, crushed).

a. One equilibrium stage

b. Three-stage crossflow system with equal amounts of wash water in each stage

c. Eight-stage crossflow system with equal amounts of wash water in each stage