Question

For flows through porous media, Darcy’s law is applicable when Reynold’s Number is:-
1. < 2
2. = 0.1
3. > 1
4. < 1

Answer 1

Correct Answer - Option 4 : < 1

Darcy’s Law is valid when flow is laminar through soils and this can be ensured only when Reynolds’s Number, Re for soil is less than 1.

Note:

1. Darcy’s Law states that velocity of flow through porous media is directly proportional to hydraulic gradient for any given saturated soil under steady laminar flow conditions.

 If the rate of flow is Q through cross-sectional area (A) of the soil mass, Darcy's Law can be expressed as
V = Q/A = k × i
Where,

 k = permeability of the soil
i = dh/dl

dh = difference in total heads
dl = length of small soil element

2. The flow of water through different conduits is said to laminar if their respective Re satisfies the following criteria:

If Re < 500; then Open channel flow is laminar.

If Re < 2000: then flow in the pipe is laminar.

If Re < 10000; the flow in parallel plates is laminar.