Darcy’s law is assumed to be valid for flow of water through soil when Reynold’s number is
- A< 1400
- B< 2000
- C> 2000
- D< 1Correct
Solution
Concept
Validity of Darcy's Law
Formula
Q = K × A × i Where: - Q = Volumetric flow rate or discharge - K = Coefficient of permeability (hydraulic conductivity) - A = Cross-sectional area of flow - i = Hydraulic gradient (i = Δh / L)For Reynolds number in soil: Re = (ρ \* v \* d) / μ Where: - ρ = Fluid density - v = Discharge velocity - d = Average particle/grain diameter - μ = Dynamic viscosity of fluid
Step-by-step solution
1. Recall that Darcy's law is valid only for laminar flow through porous soil media. 2. For flow through soil pores, the flow remains laminar when the Reynolds number (Re) is less than 1. 3. Select Option D (\< 1).
Explanation
Darcy's law applies only when water flows smoothly (laminar flow) through soil pores without turbulence. For flow in porous media like soil, the flow remains strictly laminar when the Reynolds number is less than 1.
Shortcut
Remember "Darcy = 1": Darcy's law for soil (laminar flow in microscopic pores) requires Re < 1, unlike pipe flow where the limit is much higher (Re < 2000). So, for soil/Darcy, think "1 and done" (Re < 1).
Common mistake
Students often confuse the Reynolds number criterion for laminar flow in pipe flow (Re < 2000) with that for flow through soil/porous media (Re < 1), leading them to incorrectly select Option B (< 2000) instead of Option D (< 1).
Correct answer: D) < 1