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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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 approach estimating correction size in the BK equation?

I am starting to do work in theoretical physics, and as a test, the professor I am working with asked me to estimate the size of a correction to an approximate solution to the BK equation. I am no ...
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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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What is time? Why does it move forward? Can it be manipulated? And if so, how? Does time flow? And if so, what does it flow in respect to? [closed]

Time is a constant - divided by the second, relative to the speed of light, and can be measured. Let s = 1 second or second Let m = meter(s) s = 2.99792458×10^8m The formula s = 2.99792458×10^8m ...
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What is the logarithm of a kilometer? Is it a dimensionless number?

In log-plots a quantity is plotted on a logarithmic scale. This got me thinking about what the logarithm of a unit actually is. Suppose I have something with length $L = 1 \:\mathrm{km}$. $\log L = \...
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Any physical equation with searched behavior [closed]

For my project (related to dimensional analysis) testing I need example of some physical system in which all quantities in equation except one can be measured at home or found in internet, and that ...
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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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660 views

Dimensional Analysis Question

The period of oscillation of a nonlinear oscillator depends on the mass $m$, with dimensions of $M$; a restoring force constant $k$ with dimensions of $ML^2T^2$, and the amplitude $A$, with dimensions ...
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Is displacement vector fundamental or derived quantity?

We know that we have 7 fundamental quantities (all scalars) and length is one of them. I classify velocity as a derived quantity. What about a position displacement vector? How do I classify ...
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Visualizing Physical Units in Phyiscs

I do best in physics when I can make sense of the units that accompany values, and I do this by visualizing in my mind what is happening. Take for instance, $v=\frac{s}{t}$. When I think of velocity I ...
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The dimension of potential and kinetic energy of scalar field in Friedmann equation

From the Friedmann equation $$ H^2=\frac{8\pi G}{3}\rho_m - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}. $$ The dimension of Hubble parameter $H$ is $\frac{1}{\text{time}}$ or $\frac{1}{[T]}$. Therefore, ...
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What justifies dimensional analysis?

Dimensional analysis, and the notion that quantities with different units cannot be equal, is often used to justify very specific arguments, for example, you might use it to argue that a particular ...
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How does the Fourier Transform invert units?

I don't really understand how units work under operations like derivation and integration. In particular, I am interested in understanding how the Fourier transform gives inverse units (i.e. time ...
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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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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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65 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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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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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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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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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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Do smaller aircraft have lower take-off speeds?

Assuming there are two aircraft, each of the same density and each the same shape, am I correct in understanding that the smaller aircraft would have a lower take-off speed? I have explained how I ...
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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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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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The position of a particle at any time $t$ is given by $S = V0/a [1-e^{-at}]$. What are the dimensions of $a$ and $V_0$? [closed]

To find the dimensions of and V0, I must know the dimension of S and e. So I want to know it.
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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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170 views

What is the difference between physical dimensions and physical quantities?

What is the difference between physical dimensions and physical quantities if the dimension of mass is also mass?
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What units for calculating wavenumber of a matter wave?

So I have a problem where I need to calculate the wave number for proton of energy $40~\rm MeV$. I know the formula for wavenumber of a matter wave is $k = \frac{\sqrt{2mE}}{ \hbar}$. But what units ...
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79 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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Drag - Dimensional Analysis / Buckingham $\pi$

I'm working on dimensional analysis and I'm having trouble. Here's a problem from my book I'm working on. I'm supposed to consider a small sphere experiencing acceleration due to gravity $g$. The ...
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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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Why do irrelevant operators require infinitely many counterterms?

As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
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654 views

Renormalizibility by power counting

When testing a theory for its renormalizability, in practice one always calculates the mass dimension of the coupling constants $g_i$. If $[g_i]<0$ for any $i$ the theory is not renormalizable. I ...
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Power counting and (superficial) non-renormalizability

Comment: This stuff is new to me so it doesn't entirely make sense (yet). Question: As I understand from Peskin and Schroeder chap 10 if you have a theory with interaction terms $\lambda \phi^n$ ...
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Relevant interaction terms based on dimension of coupling constants in quantum field theory

For a $\phi^{3}$ quantum field theory, the interaction term is $\displaystyle{\frac{g}{3!}\phi^{3}}$, where $g$ is the coupling constant. The mass dimension of the coupling constant $g$ is $1$ in 4D, ...
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What's the significance of a dimensionless coupling constant?

In the preface to Mark Srednicki's QFT book (an online draft version can be found here http://web.physics.ucsb.edu/~mark/qft.html), Mark mentions that the $\phi^3$ theory in 6 dimensions would be a ...
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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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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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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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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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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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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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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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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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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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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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1k views

Source for Nusselt number correlation for cooling sphere under forced convection

I've been trying to find a Nusselt number correlation for a sphere cooling in a forced gas cross flow where the sphere temperature is much higher than the free stream temperature. I want something ...
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Damping coefficient and damping ratio

I am not sure if I understand the term damping coefficient correctly (I am a high-school student). Here's the link for the info that I learned: http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html ...