# 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.

669 questions
Filter by
Sorted by
Tagged with
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 ...
136 views

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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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.
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, ...
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 ...
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 ...
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 ...
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 $rad/sec$??
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?
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 $g$ ...
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 ...
96 views

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,...
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 ...
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 ...
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 ...