Questions tagged [dimensional-analysis]

The study of the relationships between physical quantities by identifying their units of measure and fundamental dimensions. It is used to convert from one set of units to others such as from miles per hour to meters per second, or from calories per slice of cake to kilocalories per whole cake.

What questions should have this tag? Questions which are related to the conversion between different units of measurement or fundamental dimensions (for example, converting speed from miles per hour to meters per second).

What are the basic methods? The factor-label method for converting units involves first creating a series of ratios equaling 1 from known identities and using those to multiply your input, cancelling dimensional units which appear both in the numerator and denominator until the result is in the desired dimensions.

For example, $10 \frac{\text{miles}}{\text{hour}} = 10\frac{\text{miles}}{\text{hour}}\times 5280\frac{\text{feet}}{\text{miles}}\times \frac{1}{3600}\frac{\text{hour}}{\text{second}} = 14.\overline{6}\frac{\text{feet}}{\text{second}}$

Important links:

Dimensional Analysis (chem.tamu.edu)

Wikipedia: Dimensional Analysis

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What is $5^\circ \mathrm{F}$ minus $5^\circ \mathrm{F}$?

Is it $0^\circ \mathrm{F}$ or is it $0\,\mathrm{K}$ (Kelvin)? From an arithmetic standpoint, it seems like it should be $0^\circ \mathrm{F}$, but that seems inconsistent because the result represents a delta ($0 \,\Delta^\circ \mathrm{F}$ perhaps)…
Brent
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Do there exist dimensionless quantities in dimensional analysis?

In physics and science in general researchers use dimensional analysis and they often state that some quantities are dimensionless like for example the number of some objects but I don't think this is true here's why. Consider a typical problem, a…
user746545
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How is the dimenionality of the nonlinear diffusion equation in Perona-Malik filter satisfied?

The diffusion equation is given by, $\partial h /\partial t = \nabla \cdot (c \cdot \nabla h) --(1)$. But in the Perona - Malik nonlinear diffusion equation the choice of c given by two forms PM1 : $c = e ^{(-(|\nabla h|/\lambda)^2)} --(2)$ and PM2…
skyfall
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Intuitive explanation of Buckingham Pi Theorem?

I'm currently taking a class about model building in applied math. We spent quite a bit of time on Buckingham $\Pi$ theorem. I understand it on a shallow level. I know how to solve the homework and quiz problems but I just don't understand why it…
Bain
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Dimensional Analysis of dimensionless groups

I would have posted this in Chemical or Petroleum Engineering board, but they don't exist. The following webpage (http://www.fekete.com/SAN/WebHelp/Piper/WebHelp/c-te-pressure.htm) gives the calculation of $N_{vl}$ (Liquid Velocity Number)…
Adrian
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Form of Buckingham Pi Function

Per https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem#Statement, the conclusion of the Buckingham Pi Theorem involves a function depending only on the so-called dimensionless "pi terms": $$ F(\pi_1,\pi_2,...,\pi_p)=0$$ Question 1: Does the…
FreshAir
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Area dimensions

I cannot seem to comprehend why the dimensions of area are length squared. Area is the number of square units in a plane surface and is measured in terms of squares of sides of unit length. In short , I cannot fathom the meaning of a length times a…
Musab
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Is Gaussian function dimensional or non-dimensional?

The Gaussian function is $$g(x,y,\sigma) = \frac{1}{2\pi \sigma^2}\exp\left(-\frac{x^2+y^2}{2\sigma^2}\right)$$, from a perspective of dimensional analysis, can I say that $x,y,\sigma$ have the same dimension $L$ for length? If so, $g$ should have…
avocado
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Dimensional analysis for Safety Stock formula not matching

I have a question regarding the dimensions of one of the Safety Stock formulas. "D" stands for "Demand" and "LT" for "Lead time". We can assume that Demand is in Quantity per day and Lead time is in days. $$SS =…
OBT
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Formalization of dimensional analysis - how did I do

I attemted to create a formal definition of dimensional analysis. Here were the results. What is good and bad about this formalization, and what problems are there? Let $\mathbf{F}$ be a set of fundamental units. Then the unit space of $\mathbf{F}$…
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Determining points on a n-spiral

I'm trying to generate points on a n-dimensional helix. I'm using a fix angle and maintaining the radius equals to 1. Is there a formula/pattern to determine the points in more than 3 dimensions? Regards.
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Dimensional Analysis in Vertical Throw Problem

Problem 1.5: Vertical throw You throw a ball directly upward with speed $v_{0}$. Use dimensional analysis to estimate how long the ball takes to return to your hand (neglecting air resistance). Then find the exact time by solving the free-fall…
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Can I scale (non-dimensionalize) a variable with another variable?

Can I scale (non-dimensionalize) a variable with another variable? For example I have a velocity function, u(x,t), which gives velocity of a flow field and has spatial and temporal variations (function of time and position). Suppose that I scaled …
sfe
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Terminology in non-dimensionalization

I am reading the paper "Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios" by C. L. Frenzen and P. K. Maini, where they nondimensionalize a system of differential equations. They keep writing "unit order…
lala_12
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Calculating distance in n dimensions

Does this method work up to any spacial dimension? (5d, 10d etc) http://freespace.virgin.net/hugo.elias/routines/r_dist.htm p.s. If I'm getting this all fundamentally wrong somehow, please say.
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