Solution Exercise 9
Variables:
[latex]T\ = (k)(b) = (75\ m)\left( 7.06\ x\ 10^{- 6}\frac{m}{s} \right) = \ 0.00053\ m^{2}/s[/latex]
[latex]S\ = \ 0.0004[/latex]
[latex]Q\ = \frac{545\frac{\ \ m^{3}}{d}}{86400\ \frac{s}{d}} = 0.00631\ \frac{m^{3}}{s}[/latex]
[latex]r\ = \ 75\ m[/latex]
[latex]t = (36\ hrs)\left( 3600\ \frac{s}{hr} \right) = 129,600\ seconds[/latex]
Calculations:
[latex]u\ = \frac{r^{2}S}{4Tt} = \frac{\left\lbrack \left( 5625{\ \ m}^{2} \right)0.0004 \right\rbrack}{\left\lbrack 4\left( 0.00053\frac{{\ \ m}^{2}}{s} \right)129,600\ s \right\rbrack} = \ 0.0082[/latex]
reading from Table 4, [latex]W(u)\ = \ 4.26[/latex]
Drawdown at 36 hours [latex]s = \frac{Q}{4\pi T}W(u) = \frac{\left( 0.00631\frac{{\ \ m}^{3}}{s} \right)\ 4.23}{4\ \pi\ 0.00053\frac{{\ \ m}^{2}}{s}}\ \ = \ 4.02\ m[/latex]
Final head at 36 hours[latex]\ = \ 175\ - \ 4.02\ = \ 171\ m[/latex]