Dimensionless Numbers Reference Page
Where Does Sherwood Hide His Unit?
What the Schmidt?

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Intro to Dimensionless Numbers

Many important relationships in chemical and thermal engineering are expressed using dimensionless numbers. These quantities combine several physical variables into ratios that have no units, allowing engineers to compare systems that operate at very different physical scales.

Dimensionless numbers are widely used in fluid mechanics, heat transfer, and mass transfer. They often arise naturally when equations are nondimensionalized or when experimental data are correlated. Well-known examples include the Reynolds number, Prandtl number, Nusselt number, Sherwood number, and Schmidt number.

The two videos on this page introduce the concept of dimensionless numbers and then demonstrate how they are used in engineering analysis.

Where Does Sherwood Hide His Unit? Principles

This video introduces the idea of dimensionless numbers and explains why they are so useful in engineering analysis. It discusses how dimensionless parameters arise from dimensional analysis and shows how they allow engineers to compare physical systems with different sizes, fluids, or operating conditions.

Visuals

What the Schmidt? Examples

This video provides examples of commonly used dimensionless numbers and shows how they are applied in engineering calculations. It explains the physical meaning of several important dimensionless parameters and demonstrates how they help simplify complex transport phenomena.

Visuals

Examples and Definitions

Definitions

Dimensionless Number (Dimensionless Parameter)
A quantity with no physical units formed by combining dimensional variables into ratios or products. Dimensionless numbers often characterize the relative importance of different physical effects in a system. Examples include the Reynolds number, Prandtl number, Nusselt number, Sherwood number, and Schmidt number.
Dimensional Homogeneity
The requirement that every term in a physically meaningful equation must have the same dimensions. Dimensional homogeneity is often used as a check when deriving equations or performing algebraic manipulations.
Dimensional Analysis
A mathematical method that uses the dimensions of physical variables to derive relationships among them. Dimensional analysis is commonly used to identify important dimensionless groups that govern the behavior of physical systems.
Similarity (Dynamic Similarity)
A condition in which two systems behave in the same way because the relevant dimensionless parameters have the same values. Similarity is widely used when applying experimental results from laboratory-scale systems to full-scale engineering equipment.