# 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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### Bohr's atoms model

Why might Bohr have been especially curious about the possible values of the angular momenta of electrons in quantum mechanics? What looks special about them?
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### Unit vector in displacement

When we use vectors in physics why does the unit vector (for displacement) equals magnitude of 1 or magnitude of 1m?
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### Possible fundamental dimensions in Pi Buckingham theorem

While the Pi Buckingham is often taught in a fluid dynamics context, in which the relevant fundamental dimensions are generally : Mass, Length, Time and Temperature, it can obviously be applied to ...
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### Non-dimensionalization of Navier-Stokes equations multiphase flows

I am currently dealing with multiphase flows and have to use the non-dimensional form of the Navier-Stokes equations (NSE). In the scientific literature I found various formulations (and almost no ...
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### Whats the dimension of no of molecules per unit volume

I know its trivial but still i am confused,i know that no of molecules per unit volume (n) is dimentionless but my confusion is what if we describe it by total number of molecules by total volume(n=N/...
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I am reading an article (Nonspreading wave packets, by Michael Berry, Am. J. Phys. 47, 264 (1979), author eprint), and I have some questions about the maths within. First of all they take a wave ...
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How does this formula work, from a dimensional analysis perspective? $$v_\text{escape} = \sqrt{\frac{2GM}{R}}$$ The way I'm thinking about it is that $G$ is in units $\text{N} \cdot \text{m}^2/\... 2answers 98 views ### How to put$c$back into relativistic equations? Many books set the speed of light$c=1$for convenience. For example, Weinberg in his textbook "Gravitation and Cosmology" (though$Gis still left as a constant): \begin{align} \mathrm{d}\tau^2 &... 1answer 91 views ### why we can use dimensional analysis to discover formulas? if I want to discover the time duration (t) of a object falling from an heigh (h) to the ground in a gravitational field (g), I can guess that t is proportional to h, g and the mass (m). ... 1answer 75 views ### Dimensional analysis of vectors, possible? Usually we use dimensional analysis to find the dimension of acceleration or force, but can we do the same thing to find the dimension of the vector acceleration, and the vector force, or we can't ... 2answers 107 views ### Question about Radian as a unit I'm having a hard time trying to understand the units between angular velocity and basic velocity of a circle. For angular velocity the units are Radian(s) per second(s) or degree(s) per second(s). ... 2answers 106 views ### Is the International System of Units complete? Are there any known (measurable continuous) physical quantities, which are neither base quantities of SI, nor are derivable from the base quantities? In other words, are there any quantities which ... 1answer 119 views ### 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}. $$The dimension of Hubble parameter H is \frac{1}{\text{time}} or \frac{1}{[T]}. Therefore, ... 3answers 54 views ### Scaling of force between cubes? [closed] I found an interesting problem online which has been confusing me for quite a while. Basically, two solid cubes of side length a touch each other along one of their faces, and I am to find how many ... 1answer 57 views ### Does it make sense to multiply a unit by a negative number? I was thinking about the way our system of units of work, and I realized that we have been multiplying units (such as for lengths) by negative numbers, when dealing with vector quantities; positive ... 3answers 340 views ### Magnetic H field unit in cgs system I'm studying an old E&M textbook which uses cgs unit system. I'm re-writing the formulas in SI unit. The book says \vec{H}=\vec{B}-4\pi\vec{M}. So I guessed that H should have same unit as ... 4answers 470 views ### Why does this paper use 1/cm for units of frequency? Reading this paper from 1963 ^*, they use units of cm^{-1} for frequency. Here is an excerpt: It doesn't seem like wave number, as they clearly call it frequency. What's going on here? ^* ... 2answers 138 views ### Infinite plane gravity: what is “mass density per unit area”? Recently I learned that the gravity of an infinity plane is independent of the distance from that plane. In fact it is$$g = 2\pi G \sigma$$where \sigma is "the mass density of the plane per unit ... 1answer 82 views ### How can we use zero in physics [duplicate] Is better to say the e.g. kinetic energy is 0 joule or kinetic energy is 0 ? since 0*joule equals 0.Is a mathematical concept behind because in many books i find both ways. 1answer 161 views ### Height of a water tower, using Pascal's Law [closed] This is a problem on Brilliant.org which asks, if you want to receive 400kPa of water pressure to a house that is at the foot of a water tower, how tall must the water tower be? It provides you with ... 0answers 60 views ### Why are the Planck charge and Planck mass values so much larger than observed particles? [duplicate] The Planck charge and mass values seem rather unusual. Is this an indicator that there is a lack of understanding in current theory, or is there a logical explanation for the magnitude of these two ... 2answers 78 views ### Keeping track of units I'm not quite sure how keep track of physical units when differentiaion is involved. I find it important to keep track of units because I want to be able to check the units afterwards. I will discuss ... 4answers 1k views ### How do we recover units of force from units of gravitational potential? The gravitational potential G_\text{pot} has units of energy per unit mass:$$ \bigg[\rm\frac{J}{kg}\bigg] = \bigg[\rm\frac{kg\cdot m^2}{s^2\cdot kg}\bigg] = \bigg[\rm\frac{m^2 }{s^2}\bigg].$... 1answer 247 views ### Why we can't multiply two extensive quantities together? I have read that regarding the equation of state$PV=nRT$, since$V$is an extensive quantity$P$should be an intensive one because the product of extensive quantities is inherently non-linear. ... 1answer 284 views ### Biot number - Heisler chart correlation Hello I have a question about Biot number. I know that if Bi > 0.1 we're using Heisler chart to calculate heat transfer else Lumped capacitance method can be used. However can we use Heisler chart Bi &... 2answers 81 views ### How to interpret resistivity and its unit? I was wondering which interpretation could we find for the resistivity, what image correspond to the concept. Furthermore, how to interpret its unit$\Omega \:\rm m$. Why is it more logical than a$ ...
I'm trying to replicate the results of a paper, and they use the quantity $l$ to denote the length of the recirculation zone behind a cylinder for a problem regarding fluid flow past a cylinder. Early ...