Question

In a porous media, the velocity of the percolating fluid is directly proportional to the hydraulic gradient. This statement was proposed by

• A. Henry Darcy
• B. Coulomb
• C. Stoke
• D. Allen Hazen

Hint:

When water flows through a porous medium like soil, the rate of flow depends on the slope of the energy (head) line, called the hydraulic gradient.

Answer 1

The Correct Option is A

Step 1: Flow through soil.
When water seeps through a porous medium like soil, the speed of flow depends on the slope of the energy line, called the hydraulic gradient \(i\).

Step 2: State the relation.
The discharge velocity \(v\) is found to be directly proportional to this hydraulic gradient, written as \[ v = k\,i, \] where \(k\) is the coefficient of permeability.

Step 3: Who proposed it.
This simple law of flow through porous media was found by experiment by the French engineer Henry Darcy in 1856, and it is called Darcy's law.

Step 4: Rule out Stoke.
Stokes gave the law of fall of a small sphere through a fluid, not the flow through soil, so he does not fit.

Step 5: Rule out Coulomb and Hazen.
Coulomb is linked with shear strength of soils, and Allen Hazen with the grain size relation for permeability, not with the velocity gradient law.

Step 6: Answer.
So the statement that velocity is proportional to the hydraulic gradient was proposed by Henry Darcy.

\[ \boxed{\text{Henry Darcy}} \]