Questions tagged [potential-flow]

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

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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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21 views

Find the stagnation point around semi-infinite body (superposition of parallel flow and source)

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 position $x = a$, $y = ...
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23 views

Potential source/sink flow. (Shifted in polar coordinates)

I was wondering how does the equation of velocity for potential source flow shifted from the origin to (R,Alpha)(this are the center coordinates) look like? Can anyone write a formula for this? I was ...
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111 views

Potential flow pressure on a smooth surface

For an incompressible potential flow around a smooth rigid body, is it true that the pressure on the surface of the body is proportional to $a\cos^2\theta+b$ where $\theta$ is the angle the inward ...
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42 views

Can all 2D solenoidal fluid flows be given in terms of a stream function?

Is it true that for any 2D solenoidal fluid flow $\mathbf{u}$ ( i.e one with zero divergence, $\mathbf{\nabla\cdot u = 0}$ ), that $\mathbf{u}$ may be obtained from a stream function? I had always ...
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78 views

Hydroponics Recirculating water flow [closed]

I hope this is the right place to post this, and help would be appreciated. I've have been working on a multi tower hydroponics system for the past couple of weeks. I'm currently trying to figure ...
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90 views

How to determine strain rate for stagnation point flow given properties of fluid and far-field flow

I've seen plenty of derivations for stagnation point flow, but they all use strain rate [1/s] and do not explain how one calculates it. Is there an equation or procedure that is used to find the ...
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27 views

related to fluid mechanics and its velocity variation with respect to area of cross section of pipe through which it's flowing and height

if water is drawn from a tank by two pipes of the same diameter and at the same depth such that one pipe ends at some height and the other reaches the ground in which pipe we can collect the water ...
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Knowing the stream function from the stream lines equation

I've a doubt about my professor's approach on the following apparatus: Consider a stationary, incompressible, potential and bidimensional flow in the duct shown in the figure bellow: $\hspace{...
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Determine the positions of the points on the surface of a cylinder at which the pressure is minimum

I was wondering if anyone could help me with the following problem, as I'm unsure on how to begin. The problem is the following. Two equal line sources of strength $k$ are located at $x=3a$ and $x=-...
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41 views

Determine a relationship for the velocity at the edge of a boundary layer

Consider the flow over a circular cylinder at a high Reynolds number shown here. For the region outside the boundary layer $(y>\delta)$, derive a relationship for the normal pressure gradient $\...
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475 views

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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94 views

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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444 views

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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95 views

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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122 views

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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315 views

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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347 views

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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225 views

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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373 views

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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584 views

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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988 views

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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397 views

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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826 views

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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8k views

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 ...
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1answer
555 views

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 ...
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2k views

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?