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.
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Can the differential be unitless while the variable have an unit in integration?
Apologies for terminology inconsistencies, as I'm reading a Chinese statistics and probabilities textbook while looking up intrinsics on an English encyclopedia.
This arose when I was reading the ...
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What are the units of a product whose factors themselves contain seperate and distinct units?
Okay so I understand that dividing miles by hours gives us "miles-per-hour", with the logic being that we're splitting up a quantity over a group. But what happens if we keep the same ...
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What is the dimension of this set of points?
The following set of points in $\mathbb{R}^n$ is full-dimensional ($n$-dimensional):
$$\{(x_1,\ldots,x_n)| 0\leq x_i \leq 1 \text{ for all }i\in[n] \}$$
What is the dimension of the following set - is ...
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Solving for a linear equation from a nondimensionalisation
Whilst doing my homework I came across the following question and got particularly stumped at question c). I do not know how I could possibly derive a precise linear relationship. Any help?
When a ...
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Nondimensionalizing and normalizing a partial differential equation
I am trying to understand how to normalize the partial differential equation below. I know how to make it dimensionless but I do not fully understand how to normalize it. I know you're supposed to use ...
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What's wrong with applying our intuition for the behavior of objects in low dimension to high dimension [closed]
The following text is taken from the a book about linear programming that I'm reading:
A graphical illustration is useful for understanding the notions and procedures of linear programming, but as a ...
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Non-Dimensionalizing a Traffic Flow PDE for Physics Informed Neural Network Issue
I'm working on analyzing a traffic flow model described by the following partial differential equation (PDE):
$V_{\max} \left(1 - \frac{2\rho}{\rho_{\max}}\right) \frac{\partial \rho}{\partial x} + \...
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How to "non-dimensionalize" this expression?
As an example, take the following expression:
$\frac{x^2}{k(\frac{x^2}{2k^2}+\frac{5y^2}{4})}-k$
Then:
Define a new variable $K := \frac{ky}{x}$ such that $k = \frac{Kx}{y}$
Plug k into expression ...
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Dimensional analysis of Laplacian
Given a function $$f(x, y): \mathbb{R} \left[kg \right] \times \mathbb{R} \left[K \right] \mapsto \mathbb{R} \left[m \right]$$ where the units of the variables $x, y$ and of the function $f(x, y)$ are ...
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What are the Units of Flux and How do They Relate to Their Physical Meaning
While taking Calculus III, which included some vector calculus, we defined the flux of a vector field $\mathbf{F} \colon \mathbb{R}^3 \to \mathbb{R}^3$ through a surface $S \subset \mathbb{R}^3$ as $$\...
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Calculating coordinates of vertices, given dimensions in an architectural floorplan
So, one of my friend is trying to learn autocad. They were given a floorplan. The floorplan had the dimensions. And they were asked to find the coordinates of the all the vertices of the plan. So we ...
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Dimensional analysis and differential entropy
Differential entropy is a form of entropy that refers to the calculation of continuous distributions. Despite the fact that differential entropy does not have the same properties as the (discrete) ...
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"Axioms" of dimensional analysis
I wondered if there are any theoretical backgound or "formalization" of dimensional analysis. I had an attempt on doing this, by providing some axioms and then "deriving" how ...
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Nondimensionalizing Fourth Order Differential Equation for an Elastic Beam Under Tension
I am going through the textbook A First Look At Perturbation Theory 2nd ed. by James G. Simmonds and James E. Mann Jr.
Exercise 1.14 states: "An elastic beam of section modulus $EI$, resting on ...
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Nondimensionalizing an DE
I am struggling to understand the validity of what is done when you have a differential equation with dimensional variables and you are able to turn it into a differential equation with less ...
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