Final answer:
The common dimensionless parameter in fluid mechanics from the provided options is e. specific gravity, which is the ratio of a material's density to that of water, making it a valuable tool for comparing material densities without the concern for units.
Step-by-step explanation:
The common dimensionless parameter in fluid mechanics from the given options is specific gravity. Specific gravity is the ratio of the density of a material to the density of water at a specified temperature and pressure, typically 4.0 °C and one atmosphere, where the density of water is defined as 1000 kg/m³. It is a dimensionless quantity that facilitates easy comparison between different materials without concern for the units of density. An example is the specific gravity of aluminum, which is 2.7, indicating it is 2.7 times denser than water, regardless of the unit system.
Dimensionless parameters are vital in fluid mechanics as they allow for the comparison and analysis of different fluid flow scenarios without the need for unit conversions. Specific gravity is particularly useful in applications involving buoyancy and sedimentation processes, such as when using Stokes' law to calculate the terminal velocity of particles in a fluid or to determine the viscosity of a liquid based on the time it takes for an object to fall a certain distance.