Drainage Systems

• Equilibrium Moisture Content (EMC) Isotherm Models:
• The equilibrium moisture content of agricultural grains is predicted by empirical and theoretical sorption isotherm equations:
• Kelvin equation: Based on capillary condensation in pores.
• Harkins-Jura equation: Based on multimolecular adsorption potential.
• Henderson equation (Modified Henderson equation): Most widely used empirical model for grain sorption isotherms.
• (D) Janssen equation: Calculates grain pressure in deep storage bins, not EMC.
• Conclusion: (A), (B) and (C) only (Option 3).

Correct option: (3) (A), (B) and (C) only,

• Hydraulic Jump Sequent Depth Calculation:
• Bélanger's Momentum Equation:

$$y_2 = \frac{y_1}{2} \left(\sqrt{1 + 8 Fr_1^2} - 1\right)$$

• Parameters:
• Channel width $B = 1\text{ m}$, Discharge $Q = 3.132\text{ m}^3\text{/s} \implies q = Q/B = 3.132\text{ m}^2\text{/s}$.
• Initial depth $y_1 = 0.8\text{ m}$.
• Initial velocity $v_1 = \frac{q}{y_1} = \frac{3.132}{0.8} = 3.915\text{ m/s}$.
• Initial Froude number:

$$Fr_1 = \frac{v_1}{\sqrt{g y_1}} = \frac{3.915}{\sqrt{9.81 \times 0.8}} = \frac{3.915}{\sqrt{7.848}} = \frac{3.915}{2.8014} = 1.3975$$ $$Fr_1^2 = (1.3975)^2 \approx 1.953$$

• Post-Jump Depth ($y_2$):

$$y_2 = \frac{0.8}{2}\left(\sqrt{1 + 8(1.953)} - 1\right) = 0.4 \times (\sqrt{16.624} - 1) = 0.4 \times (4.077 - 1) = 0.4 \times 3.077 \approx 1.23\text{ m}$$

• Conclusion: Depth of water after jump is 1.23 m (Option 1).

Correct option: (1) 23m

• Rheological Models of Deformable Materials:
• Hookean Body: An ideal linear elastic solid obeying Hooke's law, where stress is directly proportional to strain ($\sigma = E \cdot \epsilon$), recovering immediately upon release of stress.
• Newtonian Liquid: Ideal viscous fluid where shear stress is proportional to shear rate.
• St. Venant Body: Ideal plastic material that yields once a critical threshold stress is reached.
• Conclusion: Ideal elastic behaviour is explained by Hookean body (Option 3).

Correct option: (3) Hookean body

Evaluating the Assertion and Reason concerning Flow characteristics:

The correct answer is Option 1: Both (A) and (R) are true and (R) is the correct explanation of (A).