# Soil Mechanics Questions and Answers – Permeability – Validity of Darcy’s Law

This set of Soil Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Validity of Darcy’s Law”.

1. The coefficient of permeability is equal to velocity of flow when _________
a) hydraulic gradient is equal to one
b) hydraulic gradient is less than one
c) hydraulic gradient is greater than one
d) hydraulic gradient is equal to zero

Explanation: According to Darcy’s law, we have,
V=ki
When i=1
V=k.

2. Darcy’s law of linear dependency is valid for only _______ flow conditions in soil.
a) laminar and turbulent
b) laminar
c) turbulent
d) intermediate

Explanation: The linear dependency between velocity of flow and hydraulic gradient is valid only for laminar conditions in the soil.

3. For Darcy’s law to be valid, the Reynolds number should be ________
a) greater than one
b) less than one
c) equal to one
d) greater than five

Explanation: The Darcy’s law is valid if flow through soils is laminar. The flow will be laminar only if the Reynolds number is less than one.

4. For flow through soils, the characteristic length in Reynolds number is taken as ________
a) uniformity coefficient
b) coefficient of curvature
c) coefficient of percolation
d) average diameter of the particles

Explanation: The validity if the Darcy’s law is expressed by the Reynolds number in the form,
$$\frac{vDaρw}{ηg} ≤ 1$$
Where, Da is the average diameter of the particles.

5. Darcy’s law in some cases is not valid in ______
a) clay
b) silt
c) fine sand
d) coarse-gravel

Explanation: The flow conditions in clay, sit and fine sand will be laminar, but whereas in the voids of the coarse gravel it will be a turbulent flow.
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6. The critical Reynolds number varies from ________ for validity of Darcy’s law.
a) 0.1-75
b) 75-100
c) 100-175
d) 175-200

Explanation: The Reynolds number is the ratio of inertia to viscous forces. For the validity of Darcy’s law, the critical Reynolds number varies from 0.1-75. The critical Reynolds number is the condition when the flow changes from laminar to turbulent flow.

7. The linear dependency between velocity of flow and hydraulic gradient exists if effective size of soil _______
a) does not exceed 3mm
b) exceeds 3mm
c) equal to 3mm
d) equal to 5mm

Explanation: In 1892, Allen Hazen concluded that the linear dependency between velocity of flow and hydraulic gradient exists if effective size of soil did not exceed 3mm.

8. The drainage property of silty clay is ________
a) very good
b) good
c) fair
d) very poor

Explanation: The drainage properties of clean sand, coarse and medium sands, and that of fine sand and loose silt are very good, good, and fair respectively. While the drainage property of silty clay is is very poor.

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