Introduction:
The theory of flow of fluids through a porous medium is an important concept in civil engineering and hydrogeology. It helps in understanding the movement of fluids such as water, oil, or gas through porous materials like soil, sand, or rock. One key characteristic of the saturated porous medium is its compressibility or the ability to change volume under the influence of external forces.

Explanation:
The correct answer to the question is option 'B': Incompressible. Here's why:

Definition of a saturated porous medium:
A saturated porous medium refers to a material (such as soil or rock) that is completely filled with a fluid (such as water). The pores within the medium are filled with the fluid, and the fluid pressure is equal throughout the medium. In this state, the medium is at its maximum capacity to hold the fluid.

Compressibility of fluids:
Fluids can be broadly classified into two categories based on their compressibility:
1. Incompressible fluids: These fluids have negligible changes in volume under the influence of external forces. Liquids, such as water, are considered incompressible because their volume does not change significantly with changes in pressure.
2. Compressible fluids: These fluids can undergo significant changes in volume under the influence of external forces. Gases, such as air, are compressible because their volume can change significantly with changes in pressure.

Compressibility of saturated porous medium:
When a fluid flows through a saturated porous medium, the medium itself does not significantly change its volume. The fluid fills the pores within the medium, and the overall volume of the medium remains constant. Therefore, the saturated porous medium is considered incompressible.

Significance of incompressibility:
The assumption of incompressibility is commonly used in the theory of flow through porous media. It simplifies the mathematical equations and allows for the accurate prediction of fluid behavior within the medium. This assumption is valid for most practical engineering applications involving fluid flow through saturated porous media.

Conclusion:
In conclusion, according to the theory of flow of fluids through porous media, the saturated porous medium is considered incompressible. This means that the volume of the medium does not significantly change when fluid flows through it. This assumption of incompressibility simplifies the mathematical modeling and analysis of fluid flow in porous media.