Q5. A construction site has a soil sample with the following details: - Wet weight of the sample (Wwet): 6.2 kg - Dry weight (Wdry): 5.3 kg - Votal volume (V): $$ 0.004 \mathrm{~m}^{3} $$ Tasks: 1. Calculate the density of the wetids (Vs): $$ 0.003 \mathrm{~m}^{3} $$ 2. Calculate the unit weight of the wet sample. 3. Calculate the porosity (n).

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Let's address each task step-by-step using the provided data:

- **Wet Weight of the Sample (Wwet):** 6.2 kg
- **Dry Weight of the Sample (Wdry):** 5.3 kg
- **Total Volume (V):** 0.004 m³
- **Volume of Solids (Vs):** 0.003 m³

---

### **1. Density of the Wet Soil (ρ₍wet₎)**

**Formula:**
$$
\rho_{\text{wet}} = \frac{W_{\text{wet}}}{V}
$$

**Calculation:**
$$
\rho_{\text{wet}} = \frac{6.2 \, \text{kg}}{0.004 \, \text{m}^3} = 1550 \, \text{kg/m}^3
$$

**Result:**
$$
\rho_{\text{wet}} = 1550 \, \text{kg/m}^3
$$

---

### **2. Unit Weight of the Wet Sample (γ₍wet₎)**

**Definition:**
Unit weight is the weight per unit volume of the soil.

**Formula:**
$$
\gamma_{\text{wet}} = \frac{W_{\text{wet}} \times g}{V}
$$
Where $$ g = 9.81 \, \text{m/s}^2 $$ (acceleration due to gravity).

**Calculation:**
$$
\gamma_{\text{wet}} = \frac{6.2 \, \text{kg} \times 9.81 \, \text{m/s}^2}{0.004 \, \text{m}^3} = \frac{60.822 \, \text{N}}{0.004 \, \text{m}^3} = 15205.5 \, \text{N/m}^3
$$

**Result:**
$$
\gamma_{\text{wet}} \approx 1.52 \times 10^4 \, \text{N/m}^3
$$

---

### **3. Porosity (n)**

**Definition:**
Porosity is the ratio of the volume of voids to the total volume.

**Formula:**
$$
n = \frac{V_v}{V}
$$
Where $$ V_v $$ is the volume of voids.

**Calculation:**
$$
V_v = V - V_s = 0.004 \, \text{m}^3 - 0.003 \, \text{m}^3 = 0.001 \, \text{m}^3
$$
$$
n = \frac{0.001 \, \text{m}^3}{0.004 \, \text{m}^3} = 0.25 \, \text{or} \, 25\%
$$

**Result:**
$$
n = 25\%
$$

---

### **Summary of Results:**

1. **Density of the Wet Soil:** $$ 1550 \, \text{kg/m}^3 $$
2. **Unit Weight of the Wet Sample:** $$ \approx 1.52 \times 10^4 \, \text{N/m}^3 $$
3. **Porosity:** $$ 25\% $$
- **Density of Wet Soil:** 1550 kg/m³ - **Unit Weight of Wet Sample:** Approximately 15,200 N/m³ - **Porosity:** 25%

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