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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48 views

Confusion about airflow resistivity units

What is difference between $\frac{Pa·s}{m}$ and $\frac{Pa·s}{m^2}$? What does that "$2$" after "$m$" mean? I saw both versions,and I dont know if they are same thing or not,no idea what that $2$ is ...
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1answer
136 views

Is Planck angular-frequency equal to 1/Planck-time or $2\pi$/Planck-time?

On wikipedia https://en.wikipedia.org/wiki/Planck_units it states that the angular-frequency is equal to the inverse of the planck time. $$ \begin{align} \omega_p=\frac{1}{t_p}=\sqrt{\frac{c^5}{\hbar ...
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2answers
337 views

Make an equation dimensionless

Suppose the concentration $c(x,y,t)$ inside a reactor evolves the following $$\frac{\partial c}{\partial t}=D\frac{\partial^2 c}{\partial x^2}-kc , $$ where $D$ is the diffusion coefficient and $k$ ...
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1answer
555 views

Find dimensional formula of $\alpha$ [duplicate]

The power delivered by a force is given by the relation $$P=\frac{\alpha}{\beta}e^{-\beta t},$$ where $t$ is time. Find the dimensional formula for $\alpha$. So, $-\beta t$ doesn't make sense for the ...
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1answer
50 views

How should I decide which principal units to use in dimensional analysis based on resulting pi's

Consider an unknown equation involving six different variables: period $T$, in seconds velocity $v$, in meters per second pressure difference $\Delta p$, in Pascal length $L$, in meters volume $V$, ...
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1answer
114 views

Can you simplify dimensional analysis questions before plugging in values?

If I were to solve the equation: $$d=\frac{a^3}{cb^2}$$ and values were given as so: $a=9.7\ \mathrm m$, $b=4.2\ \mathrm s$, and $c=69\ \mathrm{m/s}$. Why would it be wrong for me to use ...
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3answers
133 views

Is it possible to build a tiny solar system model?

I'm working through a chapter about forces and I was wondering about the definition of gravitational force of which things of mass are brought together. When thinking about the solar-system this "...
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1answer
307 views

What is the dimension/unit of a spinor?

I am interested in getting the physical units of a spinor for the usual $(1,3)$ Minkowski spacetime. I am getting 2 different answers, using 2 different approaches! On one hand, using the Lagrangian (...
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3answers
216 views

Path integral kernel dimensions and normalizing factor

I am currently reading Quantum Mechanics and Path Integrals by Feynman and Hibbs. Working on problem 3.1 made me wonder why the 1D free particle kernel: $$ K_0(b,a) = \sqrt\frac{m}{2\pi i \hbar(t_a - ...
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1answer
77 views

Rocket Simulation [closed]

I want to plot the movement of the rocket relative to time ($t$) in the triple dimension $(x, y, z)$. I have all the information about the rocket. I simulate the motion of a rocket. Can you help me to ...
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4answers
114 views

Why we need Watts in electricity if power is done by the Amps?

If: I = V / R And a light bulb needs X amount of electrons flowing per second (I=amps) to create light. Why do we use watts on the first place if all the light bulb cares is the number of ...
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2answers
5k views

How to convert the electron volt into Velocity unit?

About this question,I found this from the Wikipedia:nuclear fission produces neutrons with a mean energy of 2 MeV (200 TJ/kg, i.e. 20,000 km/s), which qualifies as "fast". For my question, I only knew ...
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1answer
208 views

Nusselt Number Correlation of long cylinder in axial flow

What is the Nusselt number correlation of long cylinder in axial (forced) laminar flow? Assume gravity does matter. I have seen numerous sources and lists for cylinders in crossflow which is not ...
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1answer
99 views

Why does the integral for a “generic one-loop snail diagram” in scalar QFT blow up?

I am embarrassed to ask this but I can't figure it out. Say we are in scalar QFT and we have a Feynman diagram like the following (straight from my course notes) Apparently this integral blows up for ...
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2answers
263 views

Units of 1d Poisson equation seem… strange

I'm looking at a problem about the voltage along a 1D line, and the poisson equation comes up: $$ \nabla^2 V(x) = \frac{d^2 V}{dx^2} = \frac{\rho(x)}{\epsilon_0}$$ but if I look at the units of this ...
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2answers
144 views

Uncertainty in multivariable logarithm of a physical quantity

I have a problem in analysis of laboratory data, when I have to take the logarithm of a physical quantity. I know that logarithm is a dimensionless quantity. I have to logarithmize the physical ...
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3answers
685 views

“Dimensional analysis” arguments in quantum field theory

I'm uncomfortable with dimensional analysis arguments made in quantum field theory, particularly those related to renormalization. For example, in section III.2 of Zee's QFT book, it says: Consider ...
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1answer
161 views

Why is the mass dimension of the covariant derivative 1?

I'm reviewing an exam, and I can't figure this one out. I know the covariant derivative, but I'm not seeing how it necessarily has a mass dimension.
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1answer
52 views

Approximations in general

In analysis, a statement like $f(x) \ll g(x)$ (as $x\to x_0)$, has a very precise meaning: $$ \lim_{x\to x_0}\dfrac{f(x)}{g(x)}=0. $$ I was wondering, when physicists write $L_1 \ll L_2$, for, say, ...
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1answer
111 views

Spin Fields in Superstring

The question is the following and it is related to the article of Martinec, Shenker and Friedan, "Conformal invariance, supersymmetry and string theory" (and to many others actually, but just to be ...
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1answer
412 views

Error analysis involving exponential

Given equation $$E(t)=A \exp(-bt)$$ $A$ and $b$ are constant and $E$ is energy $t$ is time If there is an error of say 1.5 percent In measured value of t What is error in value of energy. How ...
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1answer
228 views

Why are physical simulations more accurate with floating point numbers “closer to one”?

I've often heard it said that any sort of "dimensional" (involving length, time, mass, charge, etc.) calculation should be put in a dimensionless form for two reasons Getting a value ~ 1e14 when all ...
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4answers
342 views

Unit of Angular velocity [duplicate]

Why is the angular velocity $\omega$ always written in $rad/sec$? Is there anything wrong if I write it in $degrees/sec$? If no, then why almost all the books have it as $rad/sec$??
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1answer
176 views

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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1answer
380 views

Dimensional analysis with height and time [duplicate]

I'm very new to physic and I'm watching this physic lecture: https://www.youtube.com/watch?v=GtOGurrUPmQ&list=PLyQSN7X0ro203puVhQsmCj9qhlFQ-As8e&index=2 at the 22:05 he talks about ...
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2answers
350 views

Why do quantum effects of gravity become important at the Planck scale?

The standard heuristic argument for why quantum effects of gravity become important at the Planck scale is to consider the length scales at which both quantum field theory (QFT) and general relativity ...
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1answer
358 views

Does second dimension exist? or any other dimension?

Atoms as we know are the structural unit of everything. As i know that atoms are 3D objects, they have length breath and height (they have thickness).Everything is made up of atoms means everything is ...
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1answer
126 views

Why don't there seem to be any dimensionless fields in nature?

Scalar fields have dimension 1, spinor fields dimension 3/2, and vector bosons like the photon dimension 1. According to the principles of renormalizability (along with others), this restricts the ...
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5answers
171 views

Do the units of $G/c^4$ make intuitive sense?

In classical Newtonian mechanics, gravity is explained by: $$F=G \frac {Mm} {r^2}$$ Where $F$ is the force due to gravitation, $M$ and $m$ are the masses of the two bodies in question, $r$ is the ...
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6answers
13k views

Why is it “bad taste” to have a dimensional quantity in the argument of a logarithm or exponential function?

I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although ...
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1answer
130 views

Can Electric Field and Gravitational Field be added vectorially? [closed]

As both fields follow Superposition Principle, can they be added to get a total field at any region?
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3answers
136 views

Why the time period cannot depend upon the angular velocity and angular acceleration of the pendulum?

To derive the time period $T$ of a pendulum using dimensional analysis it is assumed that it depends upon the mass $m$ of the bob, the length of the string $\ell$, the acceleration due to gravity $g$ ...
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1answer
34 views

Converting volume to dimensions

Not sure if this is better posted in mathematics, but I'd like to know the formula used to convert cubic meters to dimensions (eg: 1m height x 1m width x 1m length). I understand that you can turn ...
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2answers
96 views

What does it mean to say that linear momentum has dimension of inverse of length?

Hello i was reading a book written by a physicist about Fourier Transform, and there he says that the momentum space in discrete Fourier transform has it's name because of the value $ p=\frac{2\pi}{...
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0answers
62 views

Dimension of the parameter of SUSY transformation

I'm trying to gain some intuition on the dimension on the parameter of the supersymmetric transformation. Assume I'm creating SUSY from scratch. I am making a wrong choice and defining my ...
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1answer
47 views

Why is Quantum Spin measured in JouleSeconds?

To my knowledge, the unit of quantum spin is h-bar on two. This has units of Joules times seconds divided by radians. The radians part makes sense to me, the Joules Seconds part, does not. Why is ...
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2answers
657 views

Why frequency is a SI-derived unit?

Frequency is a derived SI unit but its unit is 1/s. It uses only time once and no other fundamental quantities. So why is not included in SI base unit?
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1answer
39 views

How would spin of a binary depend on its mass?

I have been reading an article about a code that uses precession analysis on spin of binaries. At the beginning of the article authors describe units of code where they take $c=1$ (speed of light) and ...
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1answer
1k views

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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7answers
3k views

Why are work and energy considered different in physics when the units are the same?

There is a question that explains work and energy on stack exchange but I did not see this aspect of my problem. Please just point me to my error and to the correct answer that I missed. What I am ...
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1answer
66 views

Using dimensional analysis to guess formula ; too many flaws? [duplicate]

A horizontal pipe of uniform cross sectional area A empties into a bucket, filling it at a rate R(unit volume per unit time). The speed of the fluid within the pipe is v. Guess a formula for the ...
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1answer
375 views

Using dimensional analysis to find pressure of a liquid given density and movement speed

Given the density $\rho$ and the movement speed $v$ of a liquid, we are asked to find its pressure. The unit of pressure is $N/m^2$, of density it's $kg/m^3$, and then the unit of speed is $m/s$, the ...
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1answer
382 views

Why does dimensional analysis work? [duplicate]

Suppose we want to calculate a velocity. We identify all the relevant dimensions on which the solution could depend and write out and solve the equation $$l/t= a^x \, b^y \, c^z$$ where $a$, $b$, and $...
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2answers
108 views

In a force model, $F = ma$, how to understand the units?

For instance, in an aerodynamic force model, the force terms can be lift terms, drag terms, both of which have translational velocities as factors in their models; but, velocities are in units of, say,...
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2answers
88 views

Numbers in Dimension Analysis

When I learned dimensional analysis for the first time, I know that the dimension, for example, of the velocity can be written like this $[V]=LT^{-1}$, but in QFT the action for example is ...
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0answers
102 views

How to tell the mass dimensions of couplings and fields in zero dimensional QFTs?

Consider the zero dimensional QFT given by the action $$ I=\frac{1}{2}m^2\phi^2 $$ I want to somehow be able to tell the mass dimensions of the fields and the couplings. Nonetheless, From the action ...
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1answer
68 views

Suppose a particular sound wave momentarily exerts an extra pressure of 10^-4 atm upon a microphone diaphragm [closed]

Suppose a particular sound wave momentarily exerts an extra pressure of $10^{-4}~ \text{atm}$ upon a microphone diaphragm that has an area of $1~ \text{cm}^2$. What total force in newtons does this ...
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2answers
92 views

Is this expression for root mean square velocity dimensionally inconsistent? [closed]

Root mean square velocity for the molecules of a perfect gas (as $P \rightarrow 0$) is given by: $$c = \left( \frac{3RT}{M} \right) ^{\frac{1}{2}}$$ On dimensional analysis, RHS gives $\left( \frac{[...
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5answers
3k views

Why does a calculation to count objects covering a certain area seem to give nonsensical units?

Suppose you want to estimate the number of atoms in a rectangular sheet of graphene. You might estimate the sheet to have $10^{7}$ atoms along one edge and $2*10^{7}$ atoms along the other edge. ...
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1answer
97 views

Dimensions/Units and Matrix Inverses

I was going through a homework problem which is essentially a math review in a kinematics frame. This group of problems start as follows, Given $a_x$, constant acceleration, and initial conditions, ...