**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Buckingham π theorem

Summary

In engineering, applied mathematics, and physics, the Buckingham pi theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n of physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters pi1, pi2, ..., pip constructed from the original variables, where k is the number of physical dimensions involved; it is obtained as the rank of a particular matrix.
The theorem provides a method for computing sets of dimensionless parameters from the given variables, or nondimensionalization, even if the form of the equation is still unknown.
The Buckingham pi theorem indicates that validity of the laws of physics does not depend on a specific unit system. A statement of this theorem is that any physical law can be expressed as an identity involving only dimensionless combinations (ratios or products) of the variables linked by the law (for example, pressure and volume are linked by Boyle's law – they are inversely proportional). If the dimensionless combinations' values changed with the systems of units, then the equation would not be an identity, and the theorem would not hold.
Although named for Edgar Buckingham, the pi theorem was first proved by the French mathematician Joseph Bertrand in 1878. Bertrand considered only special cases of problems from electrodynamics and heat conduction, but his article contains, in distinct terms, all the basic ideas of the modern proof of the theorem and clearly indicates the theorem's utility for modelling physical phenomena. The technique of using the theorem ("the method of dimensions") became widely known due to the works of Rayleigh. The first application of the pi theorem in the general case to the dependence of pressure drop in a pipe upon governing parameters probably dates back to 1892, a heuristic proof with the use of series expansions, to 1894.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related courses (3)

Related concepts (4)

Related publications (32)

Related people (1)

Related lectures (19)

CIVIL-210: Fluids mechanics (For GC)

Ce cours est une première introduction à la mécanique des fluides. On aborde tout d'abord les propriétés physiques des fluides et quelques principes fondamentaux de la physique, dont ceux de conservat

ChE-403: Heterogeneous reaction engineering

The theoretical background and practical aspects of heterogeneous reactions including the basic knowledge of heterogeneous catalysis are introduced. The fundamentals are given to allow the design of m

ME-271: Fluid flow

Dans ce cours introductif à la physique des fluides, l'étudiant commence par apprendre, au moyen de bilans de masse et de contraintes, à décrire et à prédire les écoulements types. Ces méthodes sont a

Similitude

Similitude is a concept applicable to the testing of engineering models. A model is said to have similitude with the real application if the two share geometric similarity, kinematic similarity and dynamic similarity. Similarity and similitude are interchangeable in this context. The term dynamic similitude is often used as a catch-all because it implies that geometric and kinematic similitude have already been met. Similitude's main application is in hydraulic and aerospace engineering to test fluid flow conditions with scaled models.

Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents).

Dimensionless quantity

A dimensionless quantity (also known as a bare quantity, pure quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). The corresponding unit of measurement is one (symbol 1), which is not explicitly shown.

Dimensional Analysis and Scalings

Covers fundamental concepts of dimensional analysis, physical similarity, and scalings, exploring the importance of expressing physical laws independently of units and the process of parameterizing problems.

Buckingham's Theorem II: Soap Bubble Pressure

Explores Buckingham's Theorem II with examples on soap bubble pressure and dimensional analysis.

Buckingham's Theorem II

Covers Buckingham's Theorem II and adimensional parameters in fluid mechanics.

The log law of the wall, joining the inner, near-wall mean velocity profile (MVP) in wall-bounded turbulent flows to the outer region, has been a permanent fixture of turbulence research for over hundred years, but there is still no general agreement on th ...

Brice Tanguy Alphonse Lecampion, Andreas Möri

Hydraulic fracturing treatments are often used in petroleum and other industries to increase the permeability of rock formations and occur naturally as magmatic intrusions. The resulting fractures, propagating perpendicularly to the minimum in-situ stress ...

2023Karen Ann J Mulleners, Fatma Ayancik Cinoglu

Dynamic stall on airfoils negatively impacts their aerodynamic performance and can lead to structural damage. Accurate prediction and modelling of the dynamic stall loads are crucial for a more robust design of wings and blades that operate under unsteady ...