# Source of Water Supply, Distribution System and Well Hydraulics

 Question 1
The concentration $s(x,t)$ of pollutants in a one-dimensional reservoir at position $x$ and time $t$ satisfies the diffusion equation
$\frac{\partial s(x,t)}{\partial t}=D\frac{\partial^2 s(x,t)}{\partial x^2}$
on the domain $0 \leq x \leq L$, where $D$ is the diffusion coefficient of the pollutants. The initial condition $s(x, 0)$ is defined by the step-function shown in the figure.

The boundary conditions of the problem are given by $\frac{\partial s(x,t)}{\partial x}=0$ at the boundary points $x = 0$ and $x = L$ at all times. Consider $D = 0. 1 m^2/s, s_0 = 5 \mu mol/m$, and $L = 10 m$.
The steady-state concentration $\tilde{S}\left ( \frac{L}{2} \right )=S\left ( \frac{L}{2},\infty \right )$, at the center $x=\frac{L}{2}$ of the reservoir (in $\mu$mol/m) is ___________. (in integer)
 A 1 B 2 C 3 D 4
GATE CE 2022 SET-2   Environmental Engineering
Question 1 Explanation:
From figure s(x,t)
at $x=0\Rightarrow s(0,t)=s_0=5$
at $x=0.4L\Rightarrow s(0.4L,t)=s_0=5$
at $x=L\Rightarrow s(L,t)=0$
From $x = 0\; to \;x = 0.4 L$
Concentration of pollutant $5\mu \; mol/m \times (0.4 \times 10m) =20 \mu \; mol$
$x = 0.4L\; to \;x = L$
Concentration of pollutant = 0
Total concentration of pollutant in 10 m $=20 \mu \; mol$
In infinite time this concentration will be diluted so concentration of pollutant per m
$=\frac{20}{10} \mu \; mol/m=2 \mu \; mol/m$
Under steady state condition, concentration of pollutant will be uniformly distributed.
Steady state concentration at $x=\frac{L}{2} =2\mu \; mol/m$
 Question 2
A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and the unit weight of the lake water is $9790 \mathrm{~N} / \mathrm{m}^{3}$, the absolute pressure (in kPa,round off to two decimal places) at the maximum depth of the lake is ___________
 A 678.4 B 258.6 C 458.2 D 125.9
GATE CE 2021 SET-2   Environmental Engineering
Question 2 Explanation:
Absolute pressure at maximum depth of the lake $=P_{\text {atm }}+\rho g h$
$=91+\frac{9790(60)}{1000}=678.4 \mathrm{kPa}$

 Question 3
Dupuit's assumptions are valid for
 A artesian aquifer B confined aquifer C leaky aquifer D unconfined aquifer
GATE CE 2018 SET-2   Environmental Engineering
Question 3 Explanation:
Dupuit's theory assumptions hold that groundwater flows horizontally in an unconfined aquifer and that ground water discharge is propotional to saturated aquifer thickness.
 Question 4
A tracer takes 100 days to travel from Well-1 to Well-2 which are 100 m apart. The elevation of water surface in Well-2 is 3m below that in Well-1. Assuming porosity equal to 15%, the coefficient of permeability (expressed in m/day) is
 A 0.3 B 0.45 C 1 D 5
GATE CE 2016 SET-2   Environmental Engineering
Question 4 Explanation:
Seepage velocity,
\begin{aligned} V_{s}&=\frac{v}{n}=\frac{\text { distance }}{\text { time }}\\ \text{as per Darcy},\\ v &=k i \\ \frac{k i}{n} &=\frac{100 \mathrm{m}}{100 \mathrm{days}} \\ i &=\frac{\text { head difference }}{\text { length }}=\frac{3}{100} \\ \frac{k \times 3}{0.15 \times 100} &=\frac{100}{100} \mathrm{m} / \mathrm{day} \\ k &=5 \mathrm{m} / \mathrm{day} \end{aligned}
 Question 5
Water table of an aquifer drops by 100 cm over an area of 1000$km^{2}$. The porosity and specific retention of the aquifer material are 25% and 5%, respectively. The amount of water (expressed in $km^{3}$ ) drained out from the area is ______ .
 A 0.2 B 0.3 C 0.5 D 0.7
GATE CE 2016 SET-2   Environmental Engineering
Question 5 Explanation:
\begin{aligned} S_{\mathrm{r}}+S_{\mathrm{y}} &=n \\ \frac{5}{100}+\frac{V_{\mathrm{w}}}{10^{3} \times 10^{6} \times 1} &=\frac{25}{100} \\ V_{\mathrm{w}} &=0.2 \times 10^{9} \mathrm{m}^{3}=0.2 \mathrm{km}^{3} \end{aligned}

There are 5 questions to complete.