Questions tagged [potential-flow]

In fluid dynamics, potential flow describes the velocity field as the gradient of a scalar function: the velocity potential.

30 questions
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Calculate the stream line, which goes through the stagnation point and defines the surface of the semi-infinite body

$\require{cancel}$ Background The flow field around a half-infinite body is defined by a potential flow consisting of a parallel flow with velocity $u = U_{\infty}$ and a source of magnitude Q at ...
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Equipotential Lines in Circuit Analysis

I found this while studying about the symmetry method of determining equivalent resistance. But, I cannot understand on what basis they are coming into this conclusion; how they are calling these ...
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Fluid flow described by a complex potential

Given this complex potential $$\phi(z)=(\cos \alpha-i\sin \alpha)z$$ $\alpha>0$ Find the equations of the streamlines Find the components $V_x$ y $V_y$ of the velocity vector at $(x,y)$.What angle ...
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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 ...
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How can we define $\Gamma$ (circulation) around a point vortex?

I'm having trouble understanding something in a book that I'm reading (Chorin & Marsden intro to fluid mechanics): Next we shall examine a model of incompressible, inviscid flow. We imagine the ...
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Can a streamline have simultaneously two different values for the stream function?

Consider for example a two-dimensional potential flow: a line of sources with volumetric flow per line length, $m$, centered on the origin. For this type of flow, the associated complex potential is: ...
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Potential flow past a rotating sphere [closed]

Consider a ball of radius $R$, fully immerged in an infinite incompressible fluid. We will suppose that the density of the fluid is equal to the density of the ball so that the ball is neutrally ...
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Vorticity and circulation in potential flow

There is a plenty of situations where the vorticity $\vec{\omega} = \nabla \times \vec{u}$ is zero all over the system (i.e. potential flow) and yet the circulation $\Gamma$ is nonzero (e.g. ...
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multipole moments of dipole with finite spacing

Can a dipole with finite spacing between poles be represented by pure multipoles centered at the origin? Say for example that I have a dipole with finite spacing $2\epsilon$ between the poles. I ...
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How do I find a stream function given a volumetric flow rate?

How do I find a stream function given a volumetric flow rate? The flow only occurs in one direction, between 2 plates, and I have no knowledge of velocity. I know that volumetric flow rate = ...
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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 ...
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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 ...
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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 $\vec \Psi$ ...
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What causes angular deformation in an inviscid free vortex?

We can describe a two-dimensional (i.e. planar), inviscid, irrotational, free line vortex in cylindrical coordinates with the stream function $\psi = -K\ln{r}$, velocity potential $\phi= K\theta$, ...
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Calculate Potential [closed]

$\vec{w} = \begin{pmatrix}w_r \\ w_{phi} \end{pmatrix} = \begin{pmatrix}\frac{Q_0}{2 \pi r} \\ 0 \end{pmatrix}$ 1) Show that the flow satisfys the continuity equation 2) Show that $\vec{w}$ has ...
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By what mechanism is lift produced on a rotating cylinder in an inviscid flow?

I am taking some introductory fluid dynamic classes, and have become very confused by the Kutta-Joukowski theorem. One of the conclusions that can be derived by applying Kutta-Joukowski is that a ...
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What is “full clutching flow” in fluid-dynamics with regards venturi design?

As the title says, what is "full clutching flow" in fluid-dynamics with regards venturi design? I came across this reference a few times and can not find any further info on it, I'm currently ...
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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 ...