# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
### 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: \...