Question:medium

Which of the following statements regarding Hooghoudt's equation are correct?
(A). Gives the relation between the spacing of drains and the height of the water table.
(B). Darcy's law is valid for the flow.
(C). The soil is heterogenous.

Choose the correct answer from the options given below:

Show Hint

Hooghoudt's equation is the classic steady-state subsurface drainage model.
Key assumptions: steady-state flow, homogeneous soil, and validity of Darcy's Law.
  • (B) and (C) only.
  • (A) and (C) only.
  • (A) and (B) only.
  • (C) only.
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Recall what Hooghoudt's drainage equation is used for.
Hooghoudt's equation is a steady state formula used to design the spacing between parallel subsurface drain pipes needed to keep a water table at or below a target depth, given the soil's hydraulic conductivity, the drain depth, and the recharge rate from rainfall or irrigation. That is precisely what statement A describes, so A is true.
Step 2: Recall the flow law the equation is built on.
The equation is derived by applying Darcy's law to describe groundwater converging on the drains, along with the Dupuit-Forchheimer assumption for the shape of the water table, both resting on Darcy's law being valid for this flow, so statement B is true.
Step 3: Recall the key simplifying assumption about the soil itself.
To keep the mathematics tractable, Hooghoudt's derivation assumes the soil profile is homogeneous and isotropic in its hydraulic conductivity, and it introduces the equivalent depth concept specifically to approximate layered or non-uniform soils as an equivalent homogeneous layer. So the equation's basic assumption is homogeneity, not heterogeneity, making statement C false.
Step 4: Combine the findings.
A and B correctly describe the equation while C states the opposite of its core assumption, so only A and B are correct together.
\[ \boxed{(A) and (B) only.} \]
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