$($b$)$ After a few days operation the filter head loss has increased significantly

more than would be expected. You test the trapped material and

determine that there is a high percentage of algae $($which the original

designers should have designed for but missed$).$ You decide to add a

DAF system in addition to the existing clarification systems.

The DAF system you choose produces air bubbles with diameter $15m.$

Analysis of the algae shows that it has a specific density of $1\mathrm{.}15$ and the

mean diameter of the particles is $45m.$ The works is treating

$1600m^3*$ day ${?}^{-1}$ and it is estimated that there is $1kg$ of algae per $m^3$ of

treated water.

You are reminded that:

$D_{pb}=(D_p^3+B_n(D_b^3){)}^{\frac{1}{3}}$

${}_{pb}=\frac{({}_p{D}_p^3+B_n{}_b{D}_b^3)}{(D_p^3+B_n{D}_b^3)}$

$u_{pb}=\frac{g({}_{\text{w}\text{a}\text{t}\text{e}\text{r}}-{}_{pb})D_{pb}^2}{18}$