Consider the following statements regarding permeability: A) permeability is directly proportional to unit weight of water B) permeability is directly proportional to (1/2 viscosity) C) permeability is directly proportional to D^2 D) permeability is directly proportional to entrapped air in voids 1) A,B,C 2)A,B,D 3)A,C,D 4)A,BC,D?

Question

Answer

Permeability in relation to different factors:

A) Permeability is directly proportional to unit weight of water:
The unit weight of water refers to the weight of a unit volume of water. Permeability is a measure of how easily water can pass through a material. The unit weight of water affects the pressure and flow of water through a porous medium. Generally, the higher the unit weight of water, the higher the pressure and flow of water through the material. Therefore, permeability is directly proportional to the unit weight of water.

B) Permeability is directly proportional to (1/2 viscosity):
Viscosity refers to the resistance of a fluid to flow. The higher the viscosity of a fluid, the more difficult it is for the fluid to flow through a porous medium. In the equation for permeability, the viscosity term appears in the denominator. Therefore, as the viscosity decreases, the permeability increases. By taking the reciprocal of the viscosity and multiplying it by a constant (1/2), we can see that permeability is directly proportional to (1/2 viscosity).

C) Permeability is directly proportional to D^2:
D represents the characteristic particle size of the porous medium. Permeability is affected by the size and arrangement of the void spaces within the material. As the characteristic particle size increases, the void spaces also increase, allowing for easier flow of water through the material. The permeability is directly proportional to the square of the characteristic particle size (D^2), indicating that a larger particle size results in a higher permeability.

D) Permeability is directly proportional to entrapped air in voids:
When there is entrapped air in the voids of a porous medium, it can affect the flow of water through the material. The presence of air can decrease the effective porosity and increase the tortuosity of the flow paths, resulting in a lower permeability. Therefore, permeability is inversely proportional to the amount of entrapped air in the voids.

Summary:
Based on the given statements, the correct answer is 2) A, B, D. Permeability is directly proportional to the unit weight of water (A), permeability is directly proportional to (1/2 viscosity) (B), and permeability is directly proportional to entrapped air in voids (D). However, permeability is not directly proportional to D^2 (C), but rather inversely proportional to it.

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