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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Flow Past a Spherical Obstacle: azimuthal symmetry
For a flow passing a spherical obstacle, I don't really understand why the azimuthal term $\frac{1}{r^2 sin^2 \theta} \frac{\partial^2 \phi}{\partial \varphi^2}$ of $\vec{v} = - \nabla \phi$ is 0.
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Low Reynolds number flow and Potential flow
In an experiment conducted in my lab, we observed a low Reynolds number flow between two parallel plates with narrow gap between them resemble Potential Flow which is quite counter-intuitive as low ...
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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
$$\nabla \cdot u=0\tag{...
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A standard irrotational flow: is there an intuitive derivation?
It is said that a flow is irrotational if $\nabla \times \textbf{v}=0$ for the velocity profile. I know that there's a whole lot of vector calculus involved in "properly" writing the ...
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How can the vortex be an elemental potential flow if there is a point of curl?
Aero is not my speciality at all so apologies if missed anything. But when looking at potential flows, i thought the whole point is for there to be no rotation at any point and its that reason the ...
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No-slip condition tangential and normal component decomposition
No-slip condition on a corrugated surface (modelled by a sinusoidal function $b(x)$))
$\vec{ u} (x,b(x)) =u \vec{i}+ w \vec{k} = 0 \vec{i} + 0 \vec{k}$
expressing in terms of the stream function :
$$\...
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Which are the incompressible flows around a sphere with no azimuthal vorticity?
Assume fluid velocity $\vec{u}(r, θ, φ)$
radial distance: r ≥ 0,
polar angle: 0° ≤ θ ≤ 180° (π rad),
azimuth : 0° ≤ φ < 360° (2π rad).
At r much larger than sphere radius the flow is $\vec{u}=u_0 * ...
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Fluid-mechanics: Scalar field associated with velocity field
I have just started studying fluid mechanics (without a proper physics education :) and came across the following equation for incompressible steady-state fluids.
$$
\nabla\cdot \mathbf{u} = 0
$$
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Potential flow involving a sphere
I am currently working on a problem involving a sphere being dragged through a fluid at constant velocity.
Working in the rest frame of the sphere I'm told the potential is of the form:
$$\frac{k\cos(\...
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Meaning of potentials in Helmholtz decomposition
I am trying to understand the meaning of the potentials $U$ and $A$ arising in the Helmholtz decomposition of a vector field $\vec{V}$:
$\vec{V} = \nabla U + \nabla \times A$
Let's focus on the curl-...
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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)...
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Organized structures in rapid flows: Vortices, Rollers, Air Entrainment (Reference request)
Water flows in rivers show a wide variety of organized structures due to the interaction of the flow with its boundary. In whitewater, people give these features names like rollers, vortices, holes, ...
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Potential function in fluids
Question: Show that the potential function is a non-exact differential (or a non-analytic function) for two-dimensional rotational flow.
Doubt: I know what a potential function and its relation with ...
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Velocity induced by a straight vortex filament
Consider a straight vortex filament as shown below. At each point, there's a point vortex of strength $\it T$. Consider that a point $P$ is there on the outermost circle of flow induced by the vortex ...
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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 ...
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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 ...
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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 ...
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When does the stream function vanish?
I don't really get the physical meaning of the constant value that the stream function can take on. I mean, I know when $\psi = \text{const}$ that means that along that path the velocities are tangent ...
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Rotational, Potential Flow
The short answer is "by definition, potential flow is irrotational", but please hear me out.
I was working through "Fundamentals of Aerodynamics" by Anderson, and I noticed the following when he ...
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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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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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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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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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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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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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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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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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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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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 = change ...
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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 (that is, 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 ...
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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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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?
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