Dimensional Analysis and Similarity in Fluid Mechanics

Nord-Eddine Sad Chemloul

• Publisher: Wiley-ISTE
• Year: 2020
• ISBN:
  9781119788034
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Fluid Mechanics

Dimensional analysis is the basis for the determination of laws that allow the experimental results obtained on a model to be transposed to the fluid system at full scale (a prototype). The similarity in fluid mechanics then allows for better redefinition of the analysis by removing dimensionless elements.

This book deals with these two tools, with a focus on the Rayleigh method and the Vaschy-Buckingham method. It deals with the homogeneity of the equations and the conversion between the systems of units SI and CGS, and presents the dimensional analysis approach, before addressing the similarity of flows.

Dimensional Analysis and Similarity in Fluid Mechanics proposes a scale model and presents numerous exercises combining these two methods. It is accessible to students from their first year of a bachelors degree.

1
Homogeneity of Relationships and Conversion of Units

1.1 Introduction

The creation of a system of units requires the definition of basic units, their values, and the units derived from them. In mechanics, the units used are length, mass and time, but other options are possible as well, such as length and time, force and time, or mass, speed and time.

The first general conference on weights and measures was held in 1889 at the headquarters of the BPIM (Bureau international des poids et mesures or International Office of Weights and Measures), at the Breteuil pavilion in Sevres (in the suburbs of Paris). In this conference, new international prototypes of the meter and kilogram were officially adopted and filed with the Office.

In 1960, the 11th General Conference of Weights and Measures established the International System (SI), in which the rules for prefixes, derived units and other indications were established. The SI is based on a choice of seven well-defined base units that the convention considered dimensionally independent: the meter, the kilogram, the second, the ampere, the kelvin, the mole and the candela. Derived units are formed by combining the base units according to the algebraic relationships connecting the corresponding quantities. The names and symbols of some of these units may be replaced by special names and symbols, which may be used to express the names and symbols of other derived units.

In November 2018, the International System of units later underwent a significant revision at the 26th General Conference of weights and measures, the culmination of nearly 250 years of consideration given to finding the best way to define a system of units of measurement that would best reflect the natural world.

The General Conference of weights and measures, established at the end of the 19th Century, meets every four to six years to discuss, and possibly modify, the SI, ...