dimensionless number
Quick Summary
In fluid mechanics, a dimensionless number is a pure number without dimensions, meaning it is independent of the units used. These numbers are crucial for understanding the behavior of fluids.
The Reynolds number is a key example. It helps determine whether fluid flow is smooth (laminar) or chaotic (turbulent). Generally, a Reynolds number below 2,000 indicates laminar flow, while values above 2,000 suggest turbulent flow. The transition range is typically between 1,000 and 5,000.1
Dimensionless numbers are constructed as ratios of quantities with the same dimension. For instance, pi ((\pi)) is the ratio of a circle's circumference to its diameter, both lengths. The pi theorem, introduced by Edgar Buckingham, shows how to group variables into dimensionless terms, simplifying complex physical relationships.23
Ask Britannica AI about this topic
Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.
