Questions tagged [dimensional-analysis]

The study of the relationships between physical quantities by identifying their units of measure and fundamental dimensions. It is used to convert from one set of units to others such as from miles per hour to meters per second, or from calories per slice of cake to kilocalories per whole cake.

What questions should have this tag? Questions which are related to the conversion between different units of measurement or fundamental dimensions (for example, converting speed from miles per hour to meters per second).

What are the basic methods? The factor-label method for converting units involves first creating a series of ratios equaling 1 from known identities and using those to multiply your input, cancelling dimensional units which appear both in the numerator and denominator until the result is in the desired dimensions.

For example, $10 \frac{\text{miles}}{\text{hour}} = 10\frac{\text{miles}}{\text{hour}}\times 5280\frac{\text{feet}}{\text{miles}}\times \frac{1}{3600}\frac{\text{hour}}{\text{second}} = 14.\overline{6}\frac{\text{feet}}{\text{second}}$

Important links:

Dimensional Analysis (chem.tamu.edu)

Wikipedia: Dimensional Analysis

326 questions
1
vote
1 answer

Dimensional analysis of a nonlinear system of differential equations

I am trying to do a dimensional analysis of a nonlinear system of differential equations. I have some problems with determine the dimensions of the different variables. The differential system is with inspiration from E.C. Zeeman's catastrophe…
lala_12
  • 89
1
vote
0 answers

Proving Buckinham-pi theorem - logarithm of a unit

Is there any such thing as the logarithm of a unit? E.g. $log(kg)$? I'm trying to prove the Buckingham-pi theorem through 3 lemmas. Lemma 1: Assume $R_1, ..., R_n$ are given physical quantities and $r = rank(A)$. Then there are precisely $n - r$…
harisf
  • 329
0
votes
1 answer

How to determine whether there is a relationship between multiple physical dimensions?

I want to show that acceleration, pressure and area are independent dimensions meaning that there is no relationship between either pair of values. One cannot be written in terms of the others. Here is my…
picaposo
  • 311
0
votes
1 answer

Question regarding units of an equation

For a university project, I need to use the following equations, but I am having difficulty with the units of the term of the left-hand side (ΔXh). As far as I understand it, the units of this term should be µgCOD/(litre*hour), but I cannot see how…
0
votes
2 answers

Dimensions (squared, cubed, and more!!)

I know that when you square something you can visualize it as a 2d square. When you cube it you can visualize it as a 3d cube. For example: 2^2 -- a 2 by 2 square 2^3 -- a 2 by 2 by 2 cube I've been puzzling over how something would look when you…
Zachooz
  • 169
  • 7
0
votes
1 answer

Unit Conversion

I'm working with the following equation: Rs [mg/(cm^2 . day)] = K [units not given] * X [mg/cm^2] * shearstress^0.58 [dyne/cm^2] As far as I can tell, 1 dyne = 10^-5 Newtons. The first issue I'm having is determining the units of K. The fact that…
0
votes
1 answer

Non-Dimensionalise This Equation

I'm first to find the units of all model parameters and subsequently non-dimensionalise the equation. We're given that $y$ and $t$ have units of time whilst $c$ has units of length (with $c$ taken to be a model parameter and $e^x=exp(x)$). The…
Jamie3213
  • 173
0
votes
0 answers

Can we calculate the dimensionality of some discrete space?

Is it possible to calculate the number of dimensions in some discrete space if we have only a complete scheme of all its points and possible transitions between them? There are no regularities, fractals and the like in its organization. We have…
0
votes
1 answer

Does dimensional analysis require a dependent variable with units?

In a dimensional analysis of a=f(b,c,d), is it possible for a to be unitless? I know that there are limitations on dimensionless parameters, such as the inability to represent a non-linear relationship. I want to know if any similar limitations are…
0
votes
0 answers

Stuck on problem about dimensional analysis

This is the first part of a long exercise: We consider heat conduction in a rod of length $l$. The rod is assumed to be thermally isolated everywhere. Starting with a given temperature distribution $u(x, 0)$ over the rod, we are interested in the…
Ruby
  • 311
0
votes
1 answer

Does This Concept for Defining a Nearest Neighbor in High Dimensions Make any Practical Sense?

I'm not particularly well-educated in mathematics. I've been reading about the, 'curse of dimensionality,' and how distance metrics become meaningless in high-dimensional spaces. I then thought: What if you treat each dimension in a high-dimensional…
0
votes
2 answers

Most basic equation: Heart rate is in units of bpm. What are the units of "b"?

This is the most simple question in the world, but it is surprisingly difficult to explain to a student. The heart rate is measured in bpm, beats per minute. Minutes are a true unit. Beats are not a true unit. However, we are using beats as if it…
Chris
  • 189
0
votes
1 answer

How to calculate the center of an n-cube (hypercube) given the minimum values and maximum values in each dimension?

I am working with a box-embedding-based method in machine learning, and for a particular problem, I have two objects that are represented as two $n$-cubes in $n$-dimension ($n$ might be $16, 32, 64, ...,$ so the method should be general for an…
0
votes
0 answers

How can one imagine the lattice packing of (hyper)spherical particles, in n-dimensional space? like we have the lattices in 3D?

We can put 4 unit circles inside a square of length 4 units, such that all the circles will touch the boundary and also adjacent circles, and there will be a hollow in between the 4 circles. So we can also consider a 3D cube of length 4 units, and…
0
votes
0 answers

Dimensional Analysis help

So a few people have tried explaining how to do dimensional analysis to me and I think I may understand how to but I am not 100% sure. Unsolved This is what I belive is correct My Answer Full Question Any help is appreciated
Harry
  • 3
  • 1