Soil Chemistry

• Theoretical Assumptions of Darcy's Law:
• Kinetic energy of the flowing fluid is negligible (flow velocity is very low).
• Fluid is incompressible with constant mass density ($\rho = \text{constant}$).
• Fluid dynamic viscosity ($\eta$) remains uniform and constant.
• Fluid flow is strictly laminar ($Reynolds\ number \lt 1 - 10$).
• Conclusion: Statements (A), (B), (C), and (D) are all valid assumptions. (Correct answer: Option 3)

• Step 1: Calculate Total Hills per Hectare:

$$\text{Area} = 10,000\text{ m}^2, \quad \text{Spacing} = 0.20\text{ m} \times 0.20\text{ m} = 0.04\text{ m}^2$$ $$\text{Total Hills} = \frac{10,000}{0.04} = 250,000\text{ hills/ha}$$

• Step 2: Seedlings Required for Planting:

$$\text{Seedlings needed in main field} = 250,000 \times 2 = 500,000\text{ seedlings}$$

• Step 3: Account for 20% Uprooting Damage:

$$\text{Total seedlings required in nursery} = \frac{500,000}{1 - 0.20} = \frac{500,000}{0.80} = 625,000\text{ seedlings}$$

• Step 4: Account for Germination (90%) and Purity (90%):

$$\text{Real Value of Seed} = 0.90 \times 0.90 = 0.81$$ $$\text{Total seeds to be sown} = \frac{625,000}{0.81} \approx 771,605\text{ seeds}$$

• Step 5: Calculate Seed Rate using Test Weight (25 g per 1000 seeds):

$$\text{Seed Rate (kg/ha)} = \frac{771,605 \times 25\text{ g}}{1000 \times 1000} = 19.29\text{ kg/ha} \approx 19.3\text{ kg/ha}$$

• Conclusion: The required seed rate is 19.3 kg/ha. (Correct answer: Option 4)

• Definitions:
• Volume of soil solids = $V_s$
• Volume of soil pores = $V_f$
• Total soil volume = $V_t = V_s + V_f$
• Porosity ($f$) = $\frac{V_f}{V_t} = \frac{V_f}{V_s + V_f}$
• Void ratio ($e$) = $\frac{V_f}{V_s}$
• Derivation:
• Dividing the numerator and denominator of $f$ by $V_s$:

$$f = \frac{\frac{V_f}{V_s}}{1 + \frac{V_f}{V_s}} = \frac{e}{1 + e}$$

• Conversely, $e = \frac{f}{1 - f}$.
• Conclusion: The relationship $f = \frac{e}{1 + e}$ is correct. (Correct answer: Option 4)

• Assertion (A) is True: Medium-textured soils (silt loam, loam, and very fine sandy loam) exhibit the highest susceptibility to water erosion (highest soil erodibility factor $K$ in USLE).
• Reason (R) is True: Silt and very fine sand particles lack strong physicochemical cohesion (unlike clay particles) and are too small to resist detached transport (unlike coarse sand), which significantly increases detachment and wash-off.
• Relationship: Because high silt and very fine sand fractions reduce aggregate stability while remaining readily transportable by surface runoff, Reason (R) directly explains Assertion (A).
• Conclusion: Both (A) and (R) are true and (R) is the correct explanation of (A) (Option 1).

Correct option: (1) Both (A) and (R) are true and (R) is the correct explanation of (A)