Appendix - Permeability of Soil, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering PDF Download

Appendix    

Head loss in each layer,  \[{h_1}={H_1}{i_1}\] ,  \[{h_2}={H_2}{i_2}\]...................\[{h_n}={H_n}{i_n}\]              (17.10)

The total head loss \[h={h_1} + {h_2} + .................. + {h_n}\]                   (17.11)

The velocity of flow is same in all the layers. Thus,

\[v={k_v}{h \over H}={k_1}{{{h_1}} \over {{H_1}}}={k_2}{{{h_2}} \over {{H_2}}}=\cdots={k_i}{{{h_i}}\over {{H_i}}}=\cdots={k_n}{{{h_n}} \over {{H_n}}}\]                                                         (17.12)

where k_v is the coefficient of vertical permeability. Rearranging,

\[h=v{H \over {{k_v}}}\quad {h_1}=v{{{H_1}}\over{{k_1}}}\quad {h_2}=v{{{H_2}}\over{{k_2}}}\quad\cdots{h_i}=v{{{H_i}}\over{{k_i}}}\quad\cdots{h_n}=v{{{H_n}}\over{{k_n}}}\]                      (17.13)

The total head loss

\[h=v{H \over{{k_v}}}=v{{{H_1}}\over {{k_1}}}+v{{{H_2}}\over{{k_2}}}+\cdots v{{{H_i}}\over{{k_i}}}+\quad\cdots v{{{H_n}}\over {{k_n}}}\]                         (17.14)

\[{H \over{{k_v}}}={{{H_1}}\over{{k_1}}}+{{{H_2}}\over {{k_2}}}+\cdots{{{H_i}} \over {{k_i}}}+\quad\cdots{{{H_n}}\over {{k_n}}}\]                                       (17.15)

\[{k_v} = \frac{H}{{\frac{{{H_1}}}{{{k_1}}}+\frac{{{H_2}}}{{{k_2}}}+\cdots\frac{{{H_i}}}{{{k_i}}}+\quad\cdots\frac{{{H_n}}}{{{k_n}}}}}\]                 (17.16)