Concept# Dimensional analysis

Summary

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed. The term dimensional analysis is also used to refer to conversion of units from one dimensional unit to another, which can be used to evaluate scientific formulae.
Commensurable physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measurement; e.g., metres and feet, grams and pounds, seconds and years. Incommensurable physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres and grams, seconds and grams, metres and second

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 publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people (10)

Related concepts (116)

International System of Units

The International System of Units, internationally known by the abbreviation SI (for Système International), is the modern form of the metric sys

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 wid

Momentum

In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, p

Related publications (100)

Loading

Loading

Loading

Related units (8)

Related lectures (311)

Related courses (146)

ME-201: Continuum mechanics

Continuum conservation laws (e.g. mass, momentum and energy) will be introduced. Mathematical tools, including basic algebra and calculus of vectors and Cartesian tensors will be taught. Stress and deformation tensors will be applied to examples drawn from linear elastic solid mechanics.

ME-444: Hydrodynamics

Nondimensionalized Navier-Stokes equations result in a great variety of models (Stokes, Lubrification, Euler, Potential) depending on the Reynolds number. The concept of boundary layer enables us then to identify the different components of the hydrodynamic drag.

PHYS-739: Conformal Field theory and Gravity

This course is an introduction to the non-perturbative bootstrap approach to Conformal Field Theory and to the Gauge/Gravity duality, emphasizing the fruitful interplay between these two ideas.

The effects miniaturization has on microsystems and related fields are the central subject of this work. Physical phenomena we are used to in our conventionally sized world seldom work at smaller scales. Before attempting to design a microsystem or try to perform any operation on or with it, the outcome of size reduction has to be considered. When well-known phenomena are involved it remains relatively simple to predict the outcome as a function of size. Unfortunately the behavior of microsystems is, in many cases, governed by phenomena that have been systematically and correctly neglected. In consequence our knowledge about them is limited to the point that we can't establish a relation between them and the size of the system. Dimensional analysis and theory of similitude are two engineering tools that have been long used to solve problems where analytical solutions were not available. While the first one gives us the possibility of obtaining prediction equations for our phenomena based on our initial hypothesis, the second allows us to test the validity of our findings through the use of models of convenient size. Combined they allow information and data obtained from the study of different cases where similar phenomena are involved to be extrapolated to the case under consideration. Ship engineering has benefited from those tools: the flow around a ship's hull is difficult to describe analytically and full-sized models are uneconomical to build for testing purposes alone. Since microsystems find themselves in a similar situation (some effects can't be described analytically and full-size models are difficult to work with) the use of dimensional analysis and similitude to solve different problems encountered in this domain is proposed. The subject of forces at the microsystem level is treated in detail to show how dimensional analysis can be used both qualitatively and quantitatively to help understand how forces behave at this scale.

Energy storage is a central issue in the green economy with half the global end energy usage being heat. Latent heat thermal energy storage (LHTES) provides an energy dense heat storage solution with a well-defined discharge temperature. Utilizing low-cost, high-temperature, high-conducting metal alloys as phase change materials (PCMs) enables high energy and power density LHTES systems. Detailed characterization, reliable design tools and guidelines for modelling and building such systems are missing. This thesis presents design-related and operation-oriented innovations for such systems at different scales: (a) application-scale experimental-numerical demonstration of a LHTES test-bed, (b) non-dimensional numerical study of low and high-conducting PCMs at storage-unit scale, (c) novel power dense macro-porous PCM structures at encapsulation scale, and (d) interface scale experimental melt interface tracking by advanced tomography techniques for high-temperature PCMs.A megajoule scale high-temperature LHTES modular LHTES test-bed was built and tested, for charging-discharging at temperatures up to 950 K with aluminium alloy PCM encapsulated in stainless steel and air as the heat transfer fluid (HTF). Engineered open-cell cellular ceramic lattice were used as porous fins for enhancing the HTF-PCM heat transfer. Successful first operation was demonstrated with near-isothermal discharge for 2.7 hours in a 1.31 MJ storage. A quasi-1D lumped parameter model was developed and validated to quantify its thermal stratification, heat losses, and phase change characteristics. Heat storage characteristics of scaled configurations of the test-bed were predicted using the model.A 2D transient phase change model was used to compare a high-conducting, high melting point aluminium alloy PCM with a commercially available low-conducting, low melting point paraffin wax to quantify the effect of PCM properties, encapsulation shape, load conditions, and buoyancy driven internal convection on the power density. Parametric study and non-dimensional analysis quantified the influence of thermal and geometrical parameters on phase change and contribution of natural convection inside the encapsulations linking the melt fraction and heat transfer rates to combination of Fourier, Stefan, Rayleigh and Nusselt numbers.With high-conducting PCMs, the LHTES power density is limited by HTF-PCM convective heat transfer which can be enhanced by using novel macro-porous encapsulation designs. A comparison of several random and ordered macro-porous cells was performed with a 3D coupled CFD-phase change model. A mesh-based convolutional neural network was trained to emulate the 3D model and predict phase change time and pressure drop characteristics. Finally, a synchrotron source X-ray tomography experimental campaign to create a validation case for phase change models of high-temperature PCMs is detailed. Transient 3D melt interface tracking was conducted for aluminium alloy in cylindrical encapsulations heated using lasers. As the beamline was limited to small samples, a furnace heating setup was also built for radiography experiments of larger cubic samples at a tabletop CT facility.This thesis presents a combination of modelling frameworks and experimental setups to provide general understanding of transient heat transfer in PCMs at different scales, provide novel approaches for heat transfer enhancement, and tools for designing high-temperature LHTES systems.