A falling head permeameter test was conducted using the setup shown in Fig. $1$ with the conditions

below.

mass of the dry soil sample Ms: $1600g$

mass of the water in the sample $M_w$:$380g$

soil particle density ${}_s$:$2\mathrm{.}65\frac{g}{c}{m}^3$

density of water ${}_w$:$1\mathrm{.}0\frac{g}{c}{m}^3$

The initial hydraulic head difference $h_0$ was

$40cm$ and $h$ was $30cm$ time $t=500$ secs$.$

Answer the following questions.

Fig. $1$

$(1)$ How much is the porosity of the soil sample?

$(2)$ How much is the degree of saturation of the

sand sample?

$(3)$ How much is the hydraulic conductivity $(K)$ of the sand sample?

$(4)$ How much is the head difference $(h)$ at $t=1000sec?$

$(5)$ If the degree of saturation of the sample can be made by $100\%,$ does the measured hydraulic

conductivity increase or decrease? Also explain the reason of the answer.

$(6)$ What is the soil type and how much is the approximate $10\%$ passing particle size $(D_{10}).$