Questions tagged [dimensional-analysis]

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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Dimension of the constant in Born-Infeld nonlinear electrodynamics

As I know, based on the Lagrangian of Born-Infeld electrodynamics, its constant which shows the strength of electromagnetic field should have the dimension of inverse of length, but in some papers I ...
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2answers
54 views

Is separation of variables in the heat equation dimensionally consistent?

This may be a trivial question but is about the statement that the function $U(x,t) $ in the heat equation may be expressed in the form $X(x)\cdot T(t)$. It's that $X$ and $T$ both are functions ...
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1answer
46 views

Method of Dimensional analysis: What does “an expression of product type” mean?

I read in the book Concepts of Physics by HC Verma in the section of Limitations of Dimensional analysis that the method of dimensions cannot lead us to the correct expression sometimes if expression ...
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1answer
47 views

Can a sequence associated with a physical constant lead to natural laws?

I wondered if we know the universal constants (e.g. gravitational constant, etc.) with high enough precision, and try to find a sequence of which it is part of, or a sequence that converges to it, ...
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How to reintroduce $\hbar$ and $c$ into a formula written in natural units? [duplicate]

I am looking for a way to translate formulas written in natural units into either HLU units or SI units. Seeing the Planck constant and the speed of light would help me understand what is going on. ...
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51 views

Strange anomaly in the calculation of the cosmological constant

I was trying to calculate the cosmological constant with two different methods proposed on the internet, that are apparently equivalent but they give different results and different dimensional ...
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1answer
30 views

Differences charge quantity and electric charge

First of all,my english is not well,so sorry for reading. As a senior middle school from China mainland,I am teaching physics about electri field.I with my workmates,get a problem now.We can not get a ...
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2answers
123 views

Is there a name for this dimensionless quantity?

I have an equation with the nondimensional number $\Delta P L / \sigma$. Here $\Delta P$ is a characteristic pressure drop, $L$ is a characterictic length, and $\sigma$ is a characteristic surface ...
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Dimensional Analysis: Determining an empirical equation for problems with three or more pi groups?

For problems with only two $\pi$-groups, $$\tag{1} \pi_1=f(\pi_2)$$ The functional relationship among the variables can be determined by varying $\pi_2$ and measuring the corresponding value of $\pi_1$...
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1answer
52 views

Which quantity has (meter/atm) as its unit?

As m is for distance and atm is for Pressure which quantity has unit m/atm.
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441 views

Units in general relativity

My question is pretty straight-forward: what are the units of the tensors in General Relativity? This should sound easy, but I always studied those in natural units ($c=1$) so I can't figure it out. ...
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48 views

Physical quantity of energy and it's dimension in the article

I am reading an article about Permutation glass by Mobolaji Williams and not sure about the unit (value/dimension) of energy on Fig.3. If $k_BT_c$ is measured in Joules, then I am not totally sure ...
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Does “phase” in physics always have to expressed in radians or degrees?

According to this post What is a phase of a wave and a phase difference? The phase of the wave is the quantity inside the brackets of the sin-function, and it is an angle measured either in degrees ...
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5answers
105 views

Units of variable acceleration

If we have a function, which describes, how a displacement in space along a line varies as a function of time: e.g.: $s(t)=vt$, its units are meters because $[v]=\frac{\text{meters}}{\text{seconds}}$ ...
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2k views

Why revolutions (or turns) are dimensionless?

I think that the reason is because one revolution or one turn is equal to $2 \pi$ rad or to $360$ degrees. We can relate rads and degrees to two units of length that cancel each other. rad $= \frac{...
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1answer
88 views

Reynolds number in a wind tunnel

I would like to understand how to calculate the Reynolds number in the test chamber of a wind tunnel. It is known that the Reynolds number for a pipe is: $$Re = \frac{UL}{\nu}$$ where $U$ is the ...
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1answer
114 views

Undoing problems caused by setting $c = 1$ { or “Undoing $c = 1$” }

In the mathematical derivation of equations for physics, and involving wave propagation in particular, the propagation speed at the start of the derivation is often set to one (c = 1). I am working ...
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2answers
189 views

Why is the equation $E=mc^2$?

The equation $E=mc^2$ never made any sense to me. c is a constant (speed of light), therefore c squared is also a constant. We're not specifying any units so surely the equation should be reduced to ...
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1answer
34 views

Dimensions in the logarithmic form of the Arrhenius equation [duplicate]

The logarithmic form of the Arrhenius equation is: $\displaystyle\ln k=\ln A-\frac{E_a}{RT}$ Here $k$ and $A$ have dimensions whereas $\displaystyle\frac{E_a}{RT}$ is dimensionless. In other words, $...
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Units and measurement

I read on the characteristics of units (i) It should be easily understandable. (ii) It should be changed with change in physical factors. (iii) It should not change with place or time. I want ...
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56 views

Reference request: Oldest dimensional analysis books with exercises?

Per the title, what are some of the oldest dimensional analysis books out there with unsolved exercises? Maybe there are some hidden gems from a long time ago out there.
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1answer
32 views

What is the unit of the current in a square barrier model?

In Quantum Mechanics textbooks, the equation for a electron tunneling through a barrier is $$-\frac{\hbar ^{2}}{2m}\frac{d^{2}}{dx^{2}}\psi \left( x\right) +U\psi \left(x\right) =E\psi \left( x\right)...
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Can we get the values of $G$, $h$ and $c$ to be numerically equal if we use a convenient system of measurement?

The speed of light in vacuum is approximated to be $3×10^8\ ms^{-1}.$ But, if we change the units, we can get a different number. For example, it won't be $3×10^8$ if we used $ft\,s^{-1}$ instead of $...
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Dimensionally inconsistent!

This equation doesn't seem to be correct. Dimensionally inconsistent, in fact! How then, is it established? $$s_{t}=v_{0}+\frac{1}{2}a(2t-1)$$ (In case you don't know, this is the equation used to ...
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1answer
82 views

Question about code units and physical units (hydrodynamics simulations)

I'm working on a code that implements smoothed particle hydrodynamics (SPH) method for solving the equations of magnetohydrodynamics (MHD) with self-gravity. In research papers regarding existing ...
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4answers
86 views

Dimensional analysis with derivatives, logs, exponents and trigonometric functions

How should we do dimensional analysis when we have derivatives, logs, exponents and trigonometric functions in an equation. Should we assume that the operands are pure dimensionless numbers? Coming ...
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Existence of interacting scalar field theory

I saw a comment in Schwartz's introductory text on Quantum Field Theory (cf. Section 14.5) that it is known that $\phi^4$ theory in five dimensions does not exist. In four dimensions it is not known, ...
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2answers
53 views

Can you explain the meaning of base units behind the unit gray?

The gray is a unit that measures energy absorbed per unit of mass. It's defined as one Joule per one kilogram. Which can be simplified to $m^2/s^2$. Can you explain the meaning (interpretation) of ...
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2answers
63 views

Would setting the ideal gas constant to $1$ yield an attractive natural temperature scale? [closed]

In this recent question, there was a comment 'The "zero point" of Kelvin is natural, but the scale is not'. This led me to wonder whether setting $R = 1$ in the ideal gas law would be an attractive ...
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1answer
100 views

How to calculate fractal dimension by fitting on a log-log plot?

I have simulated a DLA pattern by MC method and the data is for fractal dimension. The right column is the number of particle N(r) into radius r and the left column is the radius r. I plotted a log-...
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Units of the Klein-Gordon Propagator in SI Units

What are the SI units of the momentum-space propagator of the Klein-Gordon equation for a free particle?
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1answer
39 views

Why is angles given at the end of fundamental units? [closed]

In my study material, there is a chart of the fundamental units. In that solid angle and angle are separated by a line from the other fundamental units. What is the reason for that?
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About irrelevance in dimensions & about absorptive and spectral absorptive power

I have read that spectral absorptive power(a) is a dimension less term and total absorptive power(a) is just a ratio hence it is also dimension less. But I have also seen expression in many books that ...
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1answer
108 views

Is there a physical observable with the same units as $c/G$?

Dividing the speed of light $c$ by the gravitational constant $G$ yields the dimension mass*time/area or mass/(length * speed) Is there a physical quantity used in textbooks with this dimension? I ...
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What Dimensionality Reduction method I can follow on a dataset that has Physics Parameter?

I am trying to model data related to Locomotive Train. We have a various set of parameters and we have the possibility to generate a few more parameters from this. Our model is currently using a lot ...
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1answer
120 views

Why coupling constants with negative mass dimensions lead to non-renormalizable theories?

can somebody explain or point to the relating mathematics showing Why coupling constants with negative mass dimensions lead to non-renormalizable theories?
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1answer
61 views

Problem in the continuum limit of a Kronecker delta

I am having troubles in understanding how to correctly perform the continuum limit of a double sum containing a Kronecker delta. Imagine to integrate a function depending on $t$ and $t'$, both ...
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1answer
73 views

What is the dimension of the weak gauge field couplin constant NOT in natural units?

What is the dimension of g and g', NOT in natural units, but in terms of mass, length, time, and permittivity?
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135 views

Why does electrical resistivity have units of $\Omega \cdot \mathrm{m}$ rather than $\Omega \cdot \mathrm{m}^3 ?$

Electrical resistivity has units of $\Omega \cdot \mathrm{m} .$ However, since resistivity can be described as the resistance of a unit cube, shouldn't the units therefore be $\Omega \cdot \mathrm{m}^...
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1answer
74 views

What are the units of dark energy?

Popular literature seems to equate dark energy with the cosmological constant of the Einstein field equations. We know however that the dimensions of any constituent of the field equations is ${\rm ...
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1answer
75 views

Why can we multiply different units but not add them? [duplicate]

Like units can be added together or, subtracted from one another. However, multiplication and division of units does not have such boundations. multiplication is just repeated addition, similarly ...
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1answer
56 views

Why does the universe manifest scale?

I'll try outline my question in clear terms, articulating specific aspects that are its primary motivators. I'm just beginning in my exploration of physics as a student, but a persistent question that ...
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1answer
70 views

Size of a raindrop

Thinking about the fact that raindrops come with a typical size I was wondering how this can be determined. I am pretty sure that the friction with air and the quantity of water in the clouds are ...
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65 views

What's does square root of number of atoms mean?

Number of atoms $N$ was counted in 3 dimension. $x,y,z$. However, when calculate it, i.e. in many cases such as refractive index , people take the square root of it, i.e. in reflective index $n=\sqrt{...
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27 views

How to introduce dimensionality in a dimensionless framework?

This question is an extension of this one. I have been told that to introduce dimensionality in a dimensionless quantity I need to multiply with suitable parameters. For instance, for velocity I have ...
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3answers
116 views

How to find the corrsponding expression after working with natural units $\hbar=c=1$?

If one does long calculations in natural units how does one find the right expression in let's say SI units in the end? I know that natural units make the calculations easier and also help to show ...
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2answers
90 views

Electrostatic in 2D: dimensional analysis

After reading this very interesting post about the electric field and the electric potential of a point charge in 2D and 1D, I've understood that, for the $2D-$case, the following formulas hold: $$ \...
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1answer
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How to deal with motion on a 2-D lattice in terms of dimension?

I am reading a paper titled: Random walks of molecular motors arising from diffusional encounters with immobilized filaments. There the authors consider the molecular motor moving on a 1-D protein ...
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149 views

Why does $\sqrt{\frac km}$ represent angular velocity and not frequency?

When I break down $\omega = \sqrt{\frac km}$ (angular velocity for a simple harmonic oscillator) into its units, I get: $$\omega = \sqrt{\frac{kg * \frac {m}{s^2}}{kg *m}}$$ which simplifies to: $$\...
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1answer
33 views

Is cross-sectional area over length classified separately from length?

The ratio of cross-sectional area to length (or its reciprocal) appears in several formulas, including those for electrical resistance and capacitance in terms of the resistivity and permittivity. ...