In fluid dynamics, potential flow describes the velocity field as the gradient of a scalar function: the velocity potential.
Questions tagged [potential-flow]
56 questions
11
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What is a Physically Accurate Explanation for the Kutta Condition?
Countless arguments between highly intelligent people have been waged (on this very site in fact) as to exactly how lift can be explained in an experimentally and mathematically rigorous way. Taking the potential flow approximation and invoking the…
Bryson S.
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Physical meaning of multipole moment
Is there a physical interpretation for multipole moments?
For a quantity governed by the Laplace equation ($\nabla^2 \omega = 0$), I understand that the general solution is given by the multipole expansion. In 2D, the exterior multipoles are given…
Ragnar
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2 answers
Given a terrain, how to draw the stream flow path?
Assuming I have a terrain, as usual the terrain has ridges, creeks and all the characteristics that you can find on a real life map. Water flows from the top of the mountain into lower area, the path that water flows is termed stream flow path.
The…
Graviton
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What causes angular deformation in an inviscid free vortex?
We can describe a two-dimensional (that is, planar), inviscid, irrotational, free line vortex in cylindrical coordinates with the stream function $\psi = -K\ln{r}$, velocity potential $\phi= K\theta$, tangential velocity component $v_{\theta} =…
darthbith
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Can the irrotational vortex be described using spherical harmonics?
THE BACKGROUND:
The irrotational vortex is an ideal fluid flow that can be represented via the following expressions in cylindrical $\{R,\psi,z\}$ and spherical $\{r,\theta,\varphi\}$ coordinates:
$$\vec{v} = \frac{B}{R}\hat{\psi} =…
aghostinthefigures
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Origin of spin and direction in the magnus effect
If you solve the Bernoulli equation:
$$p=p_0-\rho_0{v^2 \over 2}$$
using a complex flow potential for a flow around a cylinder:
$$W(z)=v_0 z + {v_0 R^2 \over z} - {\Gamma \over 2 \pi } \ln(z)$$
you get the forces per length $\vec f$ by using an…
Kuhlambo
- 950
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2 answers
Helmholtz decomposition allows incompressible flow with an irrotational component?
A vector field can be written in terms of irrotational and a divergence-free components. Using a 2D velocity field as an example,
$ \vec v = -\nabla \phi + \nabla \times \vec \Psi$
Where $\vec \Psi$ is a vector potential, which in fluid mechanics is…
wil3
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3 answers
Is there any solution to the potential flow around a square cylinder?
Potential flow around a circular cylinder is a classic solution. But I am wondering if there is any solution similar to this for the flow past a square cylinder?
Daniel
- 613
2
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1 answer
Stokes stream function derivation
I want to know a concrete derivation of 3D Stokes stream function.
The statement is, for example in 3D spherical coordinates (with symmetry in rotation about the $z$-axis), if
$$\nabla \cdot u=0\tag{1}$$
which is
$${1\over r^2}{\partial \over…
Zjjorsia
- 291
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1 answer
Waterflow / Watercooling Question
This is probably a very basic question, but I was not really sure how to look it up.
I am thinking of watercooling some CPUs with one loop. I can either create one loop with T-Connectors (green design) or use distribution plates (red). Also a mix…
Jaster
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Simple analytical model for fluid flow in "Mushroom cloud"
In potential flow theory there are simple analytical models (formulas) for velocity-field of elementary features (like source, sink, dipole, vortex etc.)
Is it possible to write simple analytical expression for flow (i.e. velocity field $\vec…
Prokop Hapala
- 1,007
2
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2 answers
Rotational flow and irrotational flow
I can understand the difference between the definition of rotational and irrotational flow if the flow is in a straight pipe. But in case of circular flow, that confuses me.
Let's consider a flow that is rotating about the origin point $O$.
In both…
2
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Why does Flow always occur from Higher Potential to Lower Potential?
This is a sort of a generalized question and not just referring to the flow of current. This includes fluids and many other such entities.
But why does this flow occur. For example if I consider current, then the definition of potential at any point…
Arnav Mahajan
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Kutta-Joukowski theorem applied on a Joukowski airfoil (derivation)
I have a doubt about the derivation of the Kutta-Joukowski theorem for a Joukowski airfoil. I know the results, but my main objective is to know how get these ones.
Consider for the initial plane a cylinder centered on $\zeta_0$, with a circulation…
Élio Pereira
- 1,102
2
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1 answer
Why does (potential) fluid flow bend around a solid surface in the flow?
Potential flow obeys Laplace's equation with certain boundary conditions (i.e. no fluid penetrates the solid body in flow, and far away from the body, the flow is uniform with a given velocity and pressure).
So let's condider the potential flow…
Dipole
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