# Vector space and 3D flow field

• Leo Liu
In summary, the conversation discusses the concept of mass flow and how it relates to the observed brightness of the sun. It is noted that the sun emits light at a constant speed and power, but due to the decreasing density of photons at distant places, it appears dimmer. The proportionality of mass flow and surface density is also mentioned, as well as the idea of a constant mass flux between two concentric spherical surfaces.
Leo Liu
Homework Statement
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Relevant Equations
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Could someone explain the green highlight to me, please?

The sum emits light of constant speed c with constant power. The emitted photons becomes more sparse at distant places as ##r^{-2}## so the sun is observed more dimmer.

Leo Liu
anuttarasammyak said:
The sum emits light of constant speed c with constant power. The emitted photons becomes more sparse at distant places as ##r^{-2}## so the sun is observed more dimmer.
Thanks for providing some physical intuition. But is it because the surface density of a mass flow is
$$\frac{\dot m}{A}=\frac{\dot m}{4\pi r^2}$$
?

Yes. What's wrong with it ?

anuttarasammyak said:
Yes. What's wrong with it ?
Nothing. Just making sure I understand where this proportionality comes from.

Another perspective: imagine two concentric spherical surfaces of radii ##\rho_1## and ##\rho_2## (##\rho_2 > \rho_1##) which bound a region ##R##. In steady state the mass contained in ##R## is constant, so the mass fluxes into the inner surface and out of the outer surface are equal: ##4\pi {\rho_1}^2 \delta_1 v = 4\pi {\rho_2}^2 \delta_2 v \, \implies \, \delta \rho^2 = \mathrm{constant}##.

Leo Liu

## 1. What is a vector space?

A vector space is a mathematical concept that describes a set of objects (vectors) that can be added together and multiplied by scalars to produce new vectors. In simpler terms, it is a collection of vectors that can be manipulated mathematically.

## 2. What is the significance of vector spaces in 3D flow fields?

In 3D flow fields, vector spaces are used to represent the direction and magnitude of fluid flow at different points in space. This allows for the analysis and prediction of fluid behavior in complex systems, such as in aerodynamics or fluid mechanics.

## 3. How are vector spaces and 3D flow fields related?

Vector spaces are essential in understanding and analyzing 3D flow fields. The vectors in a vector space can represent the velocity, acceleration, or any other physical quantity associated with fluid flow in a 3D space.

## 4. What is a flow field in 3D space?

A flow field in 3D space is a representation of how a fluid (such as air or water) moves and behaves in a three-dimensional space. It is often visualized using vector fields, where each vector represents the direction and magnitude of fluid flow at a specific point in space.

## 5. How are vector spaces and flow fields used in real-world applications?

Vector spaces and 3D flow fields have numerous real-world applications, including in aerodynamics, weather forecasting, and fluid dynamics. They are also used in computer graphics and animation to create realistic fluid simulations.

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