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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Dimensional analysis of Stokes equation $\mathrm{div} \sigma = f$.

Consider the stationary (i.e, independent of time) Stokes equations $$\mathrm{div}~ \sigma = f$$ where $\sigma$ is the stress tensor, $f$ is the external force. Denote by $M,L,T$ the mass, length, and time, respectively. Then the dimension of…
user171342
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Do all physical equations have a polynomial and a non-polynomial part?

Let $Q,Q_1,...,Q_n$ be $n+1$ physical quantities associated with some physical dimensions. Assume, the physical equation $$Q = f(Q_1,...,Q_n) $$ is true. While discussing methods of dimensional analysis, my professor noted, that all physical…
Joker123
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Dimensional analysis on $v=kF^xl^ym^t$

The velocity V of a wave moving in a stretched string can be written as, ( $v=kF^xl^ym^t$ ). where $F$ is the tension in the string, $l$ is it's length and m is the mass of the string and $k$ is a dimensionless constant. DETERMINE THE VALUES OF $x,…
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Why does the conversion factor method works? (dimensional analysis).

In many textbooks, the unit factor method for converting units is described in this way: In dimensional analysis, a ratio which converts one unit of measure into another without changing the quantity is called a conversion factor. For example, kPa…
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What is the dimension of a heap?

Heap is a kind of data structure used in computer science. But what is it dimension? An array can be 1-D 2-D...etc Young's tableaux is 2-D But what about heaps?
latra
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In dimensional consistency checks is $\mathrm{M}=\sqrt{3}\mathrm{M}$ true?

When checking an equation with dimensional consistency, if I get $\mathrm{M}=\sqrt{3}\mathrm{M}$ should I be worried? or the coefficients don't matter because we are concerned about dimensions?
Loli
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Dimensional analysis / units for best fit curves

I am doing a lot of curve fitting from experimental and modelling data. If I have a polynomial of the form which takes a temperature T and outputs a pressure Pa (Temp^2 + Temp + constant) = Pressure then of course the units of left and right hand…
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Does the absolute value operator pick up dimension?

My specific question is whether the quantity $\rho = k\times | xyz|$, has the dimension of $k$, or it has the dimension of $k\times xyz$?
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Non-dimensionalising the mass-spring system

I'm trying to non-dimensionalise the equation for the mass-spring system $$m\ddot{y}+ky=0$$ I've made a list of the constants and their dimensions, including the one I've added which is $g$. $$\begin{array}{ll} \text{Constant} & \text{Dimension}…
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Are all dimensions in an N-dimensional set homogeneous?

Hello and please excuse me if the title of the question makes little mathematical or English sense, my level in Maths is rather low and I am not a native English speaker, so I don't always choose the most appropriate words. I hope I'll be able to…
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Proof for the conversion of nanometers to inverse centimeters

This is probably an elementary question, but I can't seem to figure it out. How does one convert nm to inverse cm? For example, if I start with 10 nm, my first step would be to flip the fraction so it becomes 1/(10 nm)then just proceed normally. But…
Nova
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Is this equation nondimensionalized?

the question as mentioned in title. i want to know how this equation is dimenssionless as my efforts didn't give me the answer the equation is: $$z=(L/ \hbar) \cdot \sqrt{2m \cdot (E+V_o)}$$ as i tried in draft i found : [z]=m.Kg.s^-1 but in the…
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Calculating average pace from multiple known distances and speeds

A person ran 4 km total. For the first 2 km she ran at 12.5 km/hr, for the second 1 km she ran at 11 km/hr, for the next 0.5 km she ran at 7 km/hr, and for the final 0.5 km she ran at 10 km/hr. How do I determine the equations for the following,…
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Please help me solve this equation (Dimensional Analysis)

I have an equation I need help solving. This is an mechanical engineering question about calculating leak rate. If possible could you walk me through the process to solve this because I want to learn how to do it and not just get an answer. Here is…
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How much of 1 Planck Length goes into 1 inch?

I am writing a program(this is not a programming question) this program calculates how small an inch needs to get until it reaches 1 Planck Length of an inch. I know there are 1,587,999,999,999,999,744,856,664,160,920,216 Planck Lengths in 1 inch,…
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