Solution Exercise 11
Curve match:
Variables:
[latex]Q:\ 100\mathbf{\ }\frac{m^{3}}{d};0.00116\ \frac{m^{3}}{s}[/latex]
[latex]r:\ 20\mathbf{\ }m[/latex]
[latex]b:20\ m[/latex]
[latex]t:\ 1\mathbf{\ }\min\ (60\ seconds)[/latex]
[latex]s:\ \ 1\mathbf{\ }m[/latex]
[latex]\frac{1}{u}:\ 18;\ \ \ \ \ u = \ 0.056[/latex]
[latex]W(u):\ 2.9[/latex]
[latex]T\ = \ \ \frac{Q\ \ W(u)}{4\ \ \pi\ \ s} = \frac{0.00116\ \frac{{\ \ m}^{3}}{s}\ (2.9)}{4\ \ \pi\ \ 1\ m} = \ 0.000267\frac{{\ \ m}^{2}\ }{s}[/latex]
[latex]S\ = \ \frac{4\ \ T\ \ u\ \ t}{r^{2}} = \ \frac{(4)\ 0.000267\ \frac{{\ mt}^{2}\ }{s}\ \ (0.056)\ 60s}{{(20\ m)}^{2}}[/latex] = [latex]\ {\ 9.0x10}^{- 6}[/latex]
[latex]K\ = \frac{T}{b} = \frac{0.000267\ \frac{{\ \ m}^{2}\ }{s}}{20\ m}\ = \ 1.34\ x\ 10^{- 5}\ \frac{m\ }{s}[/latex]