What is the name for the measure of the interconnectedness of spaces in a material and how it controls how readily a rock or sediment will transmit fluids?

Permeability

permeability of any medium or substance is directly proportional to its fluid transmission ability

Explanation:

Permeability measures the ability of any medium or substance to allow transmission of any substance through it

The higher is the amount of free space with in any substance and medium, the higher is its ability to transmit other substances through it and hence higher is the permeability.

Thus, permeability of any medium or substance is directly proportional to its fluid transmission ability

Permeability

Explanation:

Permeability is usually defined as the property of rock in which the water (liquid or fluid) can easily percolate down into the deeper zone, through the interconnected pore spaces.

There are some factors that control the permeability, such as the shape and size of the voids, void ratio and the degree of saturation.

A highly permeable rock will allow more water to percolate through the voids in comparison to a low permeable rock. This percolated water eventually mixes with the groundwater.

For example, Gravels have high permeability, and Granite has low permeability.