Question

Derivation of Hooghoudt's equation assumes

• A. Steady state conditions
• B. Unsteady state conditions
• C. Fluctuating water table conditions
• D. Trafficability conditions to ease early tillage operations

Hint:

Hooghoudt's Equation $\implies$ Steady-state drainage ($q = \text{constant}$). Glover-Dumm $\implies$ Unsteady/transient falling water table.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Hooghoudt's equation (1940) is the benchmark analytical solution for calculating subsurface drain spacing under steady-state rainfall recharge.
Key Formula or Approach:
\[ L^2 = \frac{4 K_1 m^2 + 8 K_2 d m}{q} \quad \text{(Hooghoudt's Steady-State Drain Spacing Equation)} \]

Step 2: Detailed Explanation:
Hooghoudt's classic drain spacing derivation is based on the following key hydraulic assumptions:
1. Steady-State Flow: The rate of recharge to the water table (\(q\)) equals the steady discharge rate into drains, maintaining a steady, constant water table shape.
2. Dupuit-Forchheimer Assumptions: Flow streamlines are horizontal and uniform with depth.
3. Equivalent Depth ($d$): Uses an equivalent depth to account for radial flow convergence near drain boundaries.
(Unsteady transient drainage is modeled by Glover-Dumm Kraijenhoff van de Leur equations).

Step 3: Final Answer:
Thus, Hooghoudt's equation assumes Steady state conditions, corresponding to option (A).