Dimensional analysis means to obtain results by analyzing the units in question, etc. DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.

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Show that boundary layers diffuse out from the plate with speed $\sqrt{\frac{\nu}{t}}$ [on hold]

I was wondering if someone could help me with this problem. I think it's quite simple, but I'm not sure how to do it! An infinite horizontal plate moves with speed $U$ in its on plane relative to ...
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0answers
51 views

How to make two equations dimensionless? [closed]

I recently got set this problem and am having trouble scaling the resulting equations. Any help would be appreciated. An incompressible thermal conducting fluid is contained between two infinite ...
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4answers
1k views

What happens to the units when squaring a variable?

What happens to the units of a squared variable? For example, if I squared velocity, would the units, metres per second (${\rm m}/{\rm s}$), change as well?
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Dimensional analysis - When can you introduce constants that make dimensions compatible?

I have just read this question: What justifies dimensional analysis. One statement was: Maybe the speed of a comet is given by its period multiplied by its mass. Why not? As a formula this is ...
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3answers
116 views

Given the Newton constant $G$, the speed of light $c$ and the Planck constant $h$, construct an energy of the system [closed]

How do I use dimensional analysis to construct an energy for the system given the Newton constant $G$, the speed of light $c$ and the Planck constant $h$? I don't know of any energy formulas ...
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2answers
159 views

Can you express mass in other dimensional units?

I'm just started a Physics I course, and while I've paid attention, I'm stuck on one of the first problems: Express mass ($M$) in terms of acceleration($a$), density($D$), area($A$), and time($t$). ...
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3answers
82 views

Does the ratio of thermal energy to planck's constant have physical significance?

I realized that I had never noticed that $\left[ \frac{\hbar}{k_B T} \right]=$ Time. At $T \approx 300 K$, we have $\frac{\hbar}{k_B T} \approx 10$ fs. What, if anything, does this quantity mean? Does ...
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1answer
30 views

Scaling arguments and derivatives

I am trying to understand scaling arguments. Imagine one has a physical theory described by an equation whereby the first (spatial) derivative of a quantity, say $G$, equals the second (spatial) ...
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4answers
87 views

What forms can units take?

They have stated in my physics book that all units can be made by combining SI base units. I have got a few question about this. Can we raise one unit to the power of another unit? For instance: ...
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0answers
17 views

Dimensional Analysis of tunnelling current expression

I have been racking my head trying to get the units to work on an expression for 1D tunnel current through a potential barrier. This expression is straight from S. Sze's "Physics of Semiconductor ...
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3answers
48 views

Drag force - dimensional analysis

I have tried the following example from the link: MIT OCW 8.012 PS1 It is about dimensional analysis. Derive an expression for the drag force on a ball of radius $R$ and mass $M$ moving with ...
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0answers
89 views

When can two quantities be added together?

Whenever two things are to be added together, one typically needs to check whether this actually makes sense, and an addition is said to make sense, in principle, when the units match up. Yet, ...
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1answer
48 views

Expanding physical quantities in dimensionless parameters [closed]

I have a system with two dimensionful parameters, say, chemical potential ($ \mu $) and temperature ($ T $). Now I want to write down an ansatz for any physical quantity (e.g, Greens function) at ...
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1answer
55 views

Rayleigh dimensional analysis [closed]

Rayleigh dimensional analysis is often used by scientists to find formulas through their physical dimensions. How does it work and can you provide an example?
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1answer
53 views

physical meaning of dimensionless parameter

What does it mean when there is nor not a dimensionless parameter in my model? In quantum harmonic oscillator, we don't have dimensionless parameter while in hydrogen atom case we have one which is ...
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1answer
74 views

What is the difference between unit and dimensions?

If I say Height of a block = 2m, then would "Height" be called as a dimension
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11answers
4k views

Why are angles dimensionless and quantities such as length not?

So my friend asked me why angles are dimensionless, to which I replied that it's because they can be expressed as the ratio of two quantities -- lengths. Ok so far, so good. Then came the question: ...
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1answer
95 views

Relating period, volume, surface area and the velocity of sound by dimensional analysis

The question is:- There is a dimensional relation between period T, volume V, surface area A and the velocity of sound C. Assume that period increases with volume and decrease with increase in area. ...
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2answers
131 views

Do bras and kets have dimensions?

I'm trying to understand more intuitively what bras and kets are, but some aspects of them remain a mystery to me. We usually think of $\psi (x)$ as having dimension of $[1/\sqrt{L}]$ so that ...
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0answers
100 views

Exercises with solutions in dimensional analysis - reference request

I am currently trying to brush up on my skills in dimensional analysis, and computing with units. Is there a good source of worked examples, and exercises with solutions? I'd prefer to have solutions ...
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2answers
124 views

What does this equation mean? [closed]

So I have just entered 11th grade and started limits on my own but my Physics textbook has an equation which I don't understand, I suspect it uses integration which I haven't learned yet. So can ...
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0answers
19 views

Intuitive understanding of multiplied units [duplicate]

I intuitively grasp division of units as "per", or "the amount you get out compared to what you get in," but when units are multiplied together, as in Newton-meters or whatever, I'm not really capable ...
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2answers
121 views

Dimensional Analysis Question [closed]

First of, I would like to say that I have tried this question, and have my answer as well, just not sure such a method of obtaining the answer is valid or not, therefore trying to look for help here. ...
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1answer
89 views

Buckingham-$\Pi$ theorem application: the case of only 0 or 1 dimensionless groups?

In dimensional analysis, we might consider a problem like: $$ f(q_1, q_2, ..., q_{n-1}) = q_{n} $$ where $q_i$ are physical quantities of interest. In order to determine how many $\Pi$ groups can be ...
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1answer
107 views

Is the dimension “number of particles” a fundamental, or derived dimension (based on mass), or does it depend on the context, or is it dimensionless?

I consider "fundamental quantities" to be those that have dimensions that are are like length, mass, time, temperature, and so on. "Derived quantities" have dimensions that can be written in terms of ...
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0answers
51 views

What does mathematical equivalence means here?

On Motls blog, http://motls.blogspot.com/2012/06/on-importance-of-conformal-field.html, while I was trying to understand what dimensional transmutation means, he said: I said that by omitting the ...
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2answers
61 views

Natural unit conversion

I'm a bit confused about different notions of "natural units" that I encounter occasionally. I'm familiar with Planck units, and in particular I can understand the conversion between, say, metres and ...
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1answer
51 views

What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + ...
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4answers
715 views

Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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1answer
74 views

Does the path integral measure have dimension?

For example, in the field functional integral: $$\int D\phi \ e^{S[\phi]} $$ Does the $D\phi$ here have dimensions?
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2answers
82 views

What does a unit like $C^{1/5}$ or $kg^{1/2}$ physically mean?

I'm more of a math guy than a physics guy so bear with me.... In fractal geometry, fractals are considered to have fractional dimension. For instance an object such as the Koch curve has a fractal ...
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1answer
62 views

Dimensionless numbers in relativistic theory

Dimensionless numbers allow physicists and engineers to extend the physical modeling landscape by reducing otherwise complex mathematics to a simple proportional relationship. For example by assuming ...
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2answers
597 views

Is $0\,\mathrm{m}$ dimensionless?

Is $0 \, \mathrm m = 0 \, \mathrm s = 0 \,\mathrm {kg} = 0$? How do we define $[0 \, \mathrm m]$? I once was given an assignment where I was asked to deduce and write down some physical quantity. It ...
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5answers
215 views

What is the significance of the “squared” in $E =mc^2$? [duplicate]

If $c$ is just an arbitrary constant, why don't we say $E=mc$ and define the value of $c$ to be $\sqrt{299 792 458} \approx 17314$ meters per second? Or, why not use $E=mc^3$?
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153 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
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1answer
52 views

Converting $F^2$ to $C^2$

I'm trying to convert Fahrenheit squared $F^2$ into Celsius squared $C^2$. I know how to convert a value $x$ in $F$ into $C$ with: $\frac{5}{9}(x - 32)$ I also know how to convert a value $x$ in ...
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3answers
161 views

Why are log scales so common?

I am currently reading a very nice book on scales in physics. There is a discussion on the different physical scales which are based on the effect of the corresponding phenomena, the given examples ...
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45 views

Connection between the cosmological constant $\Lambda$ and the cutoff scale $\Lambda$

I'm trying to understand the connection between the $\Lambda$ from cosmology and the $\Lambda$ from QFT. Cosmology: The cosmological constant enters the Einstein equations. In the special case of the ...
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2answers
340 views

Is a vector and a unit vector dimensionless

Lets say I have a position vector $\vec r$. Is it dimensionless or does it have a dimension of length i.e $[L]$. Also does the unit vector $\hat r$ have a dimension?
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1answer
38 views

Dimensional analysis explanation and teacher issues! [closed]

This is going to sound stupid but anyways. I am currently in a physics class and my teacher likes us to use dimensional analysis which I do not understand how to use or what to do with it! So firstly ...
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2answers
122 views

Dimensional analysis, valid reductions of dimensions, and their physical interpretation

So I have been thinking about dimensional analysis and I have been thinking about quantities with components that have negative and positive exponents in the same expression. Two examples: ...
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62 views

Black Hole Entropy Calculation

I was watching "Leonard Susskind on The World As Hologram" ( youtube ). At one point he describes the way Bekenstein calculates the entropy of a black hole. Paraphrasing: Take a minimally sized black ...
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1answer
61 views

Confusion in understanding wave number

The wave number is the number of complete wave cycles in a meter. So, $$K = \frac{1m}{\lambda}$$ and also, $$K = \frac{2\pi}{\lambda}$$ so according to both of the above equation how is $$2\pi ...
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1answer
39 views

Setting constants equal to 1 conditions

I have the following expression for the entropy of an ideal gas in a microcanonical ensemble, $$S=Nk_B\ln \left[ \frac{Ve}{N}\left(\frac{4\pi m e E}{3Nh_0^2}\right)\right] $$ Ideally I would like to ...
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2answers
419 views

Checking units for equation with degree symbol

Using the following equation: $$ U = \left(\frac{B \times L \times \sin(\theta)}{C}\right)^{1/3} $$ I can calcukate the velocity of a flow traveling down a slope. I would like to check that the ...
5
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2answers
272 views

Units inside a logarithm

I have troubles understanding a seemingly simple integral in a physical context. Take a look at $\int_{V_1}^{V_2} \frac{\mathrm{d}V}{V}$ which appears in isothermal expansions (V being the volume of a ...
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1answer
86 views

Deriving (dimensionless) physical constants from theory

The Wikipedia entry on Physical Constants says: With the development of quantum chemistry in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants ...
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626 views

How to indicate that a unit is dimensionless [duplicate]

For my dissertation I am preparing a list of symbols used in the text, which basically is a table that consists of the symbol, a short explanation and the dimension it has as indicated below: ...
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1answer
64 views

I read, some time ago about a dimensionless constant in physics [closed]

and, my terminology is probably off, but, I think I can explain with an example. Take a Newton, which can be described as a KG*Meter/Second^2 - which frankly, written that way, looks confusing to me, ...
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Non-dimensionalizing the “bead on a rotating hoop, with viscous damping” problem

This is not a homework question. Rather, this is an exercise I have taken up on myself. In particular, I am trying to find an algorithmic way to non-dimensionalize known equations, using the ...