College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
A dimensionless quantity is a pure number without any physical units. It results from the ratio of two quantities with the same dimensions, cancelling out their units.
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Dimensionless quantities are crucial in simplifying equations and comparing physical phenomena.
Common examples include the Reynolds number, Mach number, and coefficients like friction or drag.
They often emerge in dimensional analysis to check the consistency of equations.
The value of a dimensionless quantity remains the same regardless of the unit system used, making them universal.
Dimensionless quantities can be derived using Buckingham's Pi theorem.
Review Questions
What is a dimensionless quantity and how is it derived?
Give two examples of dimensionless numbers commonly used in physics.
Why are dimensionless quantities important in dimensional analysis?
Related terms
Dimensional Analysis: A method to understand the relationships between different physical quantities by identifying their base dimensions such as length, mass, time, etc.
Buckingham's Pi Theorem: A key theorem in dimensional analysis that provides a method for computing sets of dimensionless parameters from given variables.
Reynolds Number: A dimensionless quantity that predicts flow patterns in different fluid flow situations.