# User:Egm3520.s13.Jeandona

${\displaystyle M_{s}=M_{sm}-M_{m}}$

${\displaystyle e={\frac {V-{\frac {M_{s}}{G_{s}\cdot \rho _{w}}}}{frac{Ms}{G_{s}\cdot \rho _{w}}}}}$

${\displaystyle Ex:e={\frac {{\frac {0.1ft^{3}\cdot 0.0283168m^{3}}{1ft^{3}}}-{\frac {8.0758}{2.65\cdot 1000}}}{\frac {8.0758}{2.65\cdot 1000}}}}$

${\displaystyle D_{r}={\frac {e_{max}-e}{e_{max}-e_{min}}}\cdot 100\%}$

${\displaystyle Ex:D_{r}={\frac {0.679-0.65}{0.679-0.429}}\cdot 100\%{\mbox{ }}={\mbox{ }}11.6\%}$

${\displaystyle V:}$ Volume of mold

${\displaystyle M_{s}:}$ Dry mass of soil in mold

${\displaystyle G_{s}:}$ Specific gravity of the solids

${\displaystyle \mathrm {P} _{w}:}$ Density of water

${\displaystyle e_{max}:}$ Void ratio of the soil in its loosest state

${\displaystyle e_{min}:}$ Void ratio of the soil in its densest state

${\displaystyle e_{insitu}:}$ in situ void ratio

# To be Deleted:

${\displaystyle {\mbox{ }}\delta ={\frac {M_{s}}{(1+w)A_{o}\cdot L_{o}}}}$

${\displaystyle Ex:{\mbox{ }}\delta ={\frac {124.94g}{1+0.148}}\cdot {\frac {1Ib}{453.593g}}\cdot {\frac {1}{1.34in^{2}\cdot 2.857in}}\cdot {\frac {1728in^{3}}{1ft^{3}}}=108.30pcf}$

${\displaystyle M_{s}=Mass{\mbox{ }}of{\mbox{ }}soil=124.94g}$

${\displaystyle Gain_{Non-inverter}|_{R_{f}=R_{i}=10\kappa \omega }=1+{\frac {R_{f}}{R_{i}}}=2}$

${\displaystyle {\text{Percent Difference}}={\frac {10-9.406}{10}}\cdot 100=5.94\%}$

${\displaystyle Gain{\mbox{ }}\alpha {\mbox{ }}{\frac {V_{i}n}{V_{o}ut}}}$

# Permeability

${\displaystyle k_{CHT}={\frac {QL}{t\cdot \Delta hA}}}$

${\displaystyle Ex:k_{CHT}={\frac {797.75\cdot 12}{34\cdot 70\cdot 46.06}}{\mbox{ }}={\mbox{ }}0.08733}$

${\displaystyle k_{FHT}=2.3{\frac {aL}{At}}log_{10}{\frac {h_{i}}{h_{f}}}}$

${\displaystyle Ex:k_{FHT}=2.3{\frac {2.35\cdot 12}{46.06\cdot 4.89}}log_{1}0{\frac {100}{58}}}$

${\displaystyle k_{20^{\circ }C}={\frac {\mu _{T}}{\mu _{20^{\circ }}}}}$

${\displaystyle Ex:k_{20^{\circ }C}={\frac {9.81}{10.09}}0.0873{\mbox{ }}={\mbox{ }}0.0849}$

Legend of Variables:

${\displaystyle k_{CHT}:}$ coefficient of permeability for constant head test(cm/s)

${\displaystyle k_{FHT}:}$ coefficient of permeability for falling head test(cm/s)

${\displaystyle Q:}$ total quantity of water (cm${\displaystyle _{3}}$)which flowed through the sample in elapsed time t (s)

${\displaystyle \Delta h:}$ total head loss (cm)

${\displaystyle A:}$ cross-sectional area of permeameter (cm${\displaystyle _{2}}$)

${\displaystyle L:}$ length of sample in permeameter (cm)

${\displaystyle a:}$ cross

${\displaystyle h_{i}:}$ initial height of water above outflow (cm)

${\displaystyle h_{f}:}$ final height of water above outflow (cm)

${\displaystyle k_{20^{\circ }C}:}$ coefficient of permeability at 20${\displaystyle ^{\circ }}$C

${\displaystyle \mu _{T}:}$ viscosity of water at a specific temperature

${\displaystyle \mu _{20^{\circ }C}:}$ viscosity of water at 20${\displaystyle ^{\circ }}$C