What is Dimensional analysis: Definition and 259 Discussions

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 measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or SI system than in others, due to the regular 10-base in all units. Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra.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 originally expressed in differing units of measure, e.g. yards and metres, pounds (mass) and kilograms, 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 originally expressed in, e.g. meters and kilograms, seconds and kilograms, meters and seconds. For example, asking whether a kilogram is larger than an hour is meaningless.
Any physically meaningful equation, or inequality, must have the same dimensions on its left and right sides, a property known as dimensional homogeneity. Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on derived equations and computations. It also serves as a guide and constraint in deriving equations that may describe a physical system in the absence of a more rigorous derivation.
The concept of physical dimension, and of dimensional analysis, was introduced by Joseph Fourier in 1822.

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  1. A

    Fluid Mechanics dimensional analysis repeating parameters

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  2. H

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  3. A

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  4. M

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  5. P

    Is the API Hydrocarbon Emission Formula Dimensionally Consistent?

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  6. A

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  7. S

    I Rescaling the equation of motion of inflation

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  8. D

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  9. Shing Ernst

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  10. goonking

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  11. S

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  12. Biker

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  13. W

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  14. M

    I Dimensional Analysis: Torque, Moment of Inertia & Angular Acceleration

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  15. P

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  16. khaledS

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  17. N

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  18. N

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  19. E

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  20. T

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  21. B

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  22. B

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  23. B

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  24. DaTario

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  25. D

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  26. V

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  27. Yousufshad

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  28. B

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  29. 0

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  30. Blargian

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  31. D

    Dimensional Analysis? Involving Temperature

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  32. M

    Dimensional Analysis: Solving E = (1/2) mv Equation

    Homework Statement Is the following equation dimensionally correct? Homework Equations E = (1/2) mv where: E = energy m = mass v = speed The Attempt at a Solution 1. I understand that the 1/2 is irrelevant. 2. I broke everything down into length, time, and mass. 3. I got ML^2/T^2 = ML/T 4. My...
  33. N

    Dimensional Analysis of Planck Length

    Hello! So in looking at black hole thermodynamics, I came across the equation ## l_p = \sqrt{G\hbar} ## But in doing a dimensional analysis of ## \sqrt{G\hbar} ## I get ## [\sqrt{G \hbar}] = \sqrt{ \frac{Nm^2}{kg^2} \frac{m^3}{kgs} } ## This obviously doesn't amount to a length. What...
  34. K

    Dimensional analysis on equation including scattering length

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  35. S

    Dimensional analysis and minima of a potential

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  36. P

    How can dimensional analysis be carried out correctly?

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  37. 5

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  38. S

    Buckingham-Pi for "algorithmic" non-dimensionalization

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  39. 1

    Why do things far away seem smaller?

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  40. Xiaomin Chu

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  41. C

    How to Determine Pi Groups for Fluid Flow Through an Orifice

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  42. J

    How Can I Solve Part C Using Buckingham Pi Theorem and Newton's Method?

    Hi, this is my first post, so sorry if this is posted on wrong section etc. Do not worry about the initial part of dimensional analysis, that was fine - use Buckingham pi therem, but here's the prob... Below is the question, I am stuck on being part C, however to show you guys what needs to be...
  43. P

    Dimensional Analysis: Matrix Setup for M/(L^2T^2)

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  44. Mr Davis 97

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  45. davidbenari

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    Once an equation is well put and there is dimensional homogeneity like: ##mx''+\beta x' + kx=f(x)## ; ##Lq''+Rq'+q/c=E(t)## (mass-spring; Kirchoff's diff eq.) One proceeds with the math as if there were no actual units involved and just solved a problem dealing with only numbers. Is there...
  46. B

    Dimensional analysis of a physical pendulum

    Hi! Sorry if this is the wrong section to post this: I am doing a laboration on physical pendulums and I have a bit of trouble making sense of it all and I am in need of some guidance. When I do the analysis I get the standard mathematical pendulum. [T]=[m]^a*[l]^b*[g]^c, where a = 0, b = -c...
  47. G

    Power Calculation for Scaled Pump Model

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  48. G

    Dimensional Analysis problem - choosing variables

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  49. G

    Dimensional Analysis and buckingham pi

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  50. V

    Dimensional analysis - atomic bomb explosion radius

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