Q$2-$ A sanitary sewer system will be designed for the village of Gemikona$$ for the year $2040.$ The

projected layout of the system, which corresponds to the end of the lifetime of the system, is shown in

the following figure and the topographic elevations of the top surfaces of manholes are given in the

table below.

Considering the following data:

Variable $\frac{N}{n}$ with $N=0\mathrm{.}016,$

Groundwater infiltration is $0\mathrm{.}3l\frac{t}{s}\frac{?}{ha},$

Rainfall contribution is $0\mathrm{.}5l\frac{t}{s}\frac{?}{ha},$

Min. depth of cover is $2m.$

Commercial pipes are available for every $50mm$ increment of pipe diameter.

The minimum full flow velocity for self$-$cleansing is $0\mathrm{.}6\frac{m}{s}$

The maximum full flow velocity is $4\frac{m}{s}$

$P$ is the percent population in the area concerned,

The percent return of municipal water use to the sewer system in each area is $80\%,$

The length of all sewers is $120m$

The population data in the city are $P_{2000}=3000$ and $P_{2010}=3800$

a$)$ Estimate the population in $2040,P_{2040},$ using geometric extrapolation.

b$)$ Design sanitary sewer between manholes M$7$ and M$8(D_{\text{p}\text{i}\text{p}\text{e}}=?,$ Elevbottom $=?$ for M$7$ and M$8).$