Circulation Definition and 83 Threads

Got a friend with a boat he's storing over the winter. He wants to discoruage misture and mold build up by keeping air circulating. He puts a box fan in the companionway, (and presumably opens the fore hatch). All other things being equal, is it better to point the fan into the companionway...

Greetings The exercice consist of calulating the circuitation of the Field F along a the borders of the region omega my problem was how they found that y goes from 0 to h ( for 0 it´s clear but the mystery for me is h) Thank you!

Hi, I just had a quick question about conventions in potential flow theory: Question: What is the convention for ## \Gamma ## for the streamline ## \Psi = \frac{\Gamma}{2\pi} ln(\frac{r}{a} ) ## and how can we interpret the Kutta-Jukowski Theorem ## Lift = - \rho U \Gamma ##? Approach: For the...

Homework Statement:: What is the convention for ## \Gamma ## for the streamline ## \Psi = \frac{\Gamma}{2\pi} ln(\frac{r}{a} ) ## and how can we interpret the Kutta-Jukowski Theorem? Relevant Equations:: ## v_{\theta} = - \frac{\partial \Psi}{\partial \theta} ## [Mentor Note -- moved from the...

Fig1: Fig2: We haven't covered this topic yet, but they expect us to solve it and I'm not 100% sure what I'm doing. a) ##C_r =\oint{\vec{v}*\vec{dl}} = \int{\omega*r*dl} = \omega*\int{r*r*d\phi} = \omega*r^2*2pi## b) Now here I begin to struggle. If v is constant, can I simply pull it out of...

Homework Statement Homework Equations The Attempt at a Solution I am stuck trying to figure out why there are three different alphas and why in the equation we are supposed to use has a theta and what that means. If I can set up the Fourier series I can properley I know how to solve it for...

These two things seem to be exactly the same (even down to the same formula), so I'm having difficulty understanding why they are two different terms. Is circulation just the work done as you go around a circle once?

Hi, I was wondering if anyone has any links or documents of some challenging projectile motion and circular motion questions. Also, if you have any regarding 'Energy' and roller coasters and pendulums and Hooke's law they would be great too. I am in year 11 and am looking to do some extra study...

Homework Statement Find magnetic flux density B circulation in closed contour. The countour consists of square with a perimeter of 4b. It includes a square conductor with a perimeter of 4a. A homogenic current flows through a conductor with a current density of j. Homework Equations...

Why do white blood cells die and what cause them to destroy within a few (20-30) hours? I have an other question also that if red blood cells remain within capillaries, veins and arteries then how do they pass onto liver cells for the breakdown or they die within veins, capillaries and arteries?

Hi I am trying to understand what forces are at work to slow a liquid flowing in a circular pipe As an example the above torus pipe fully filled with an incompressible low viscosity liquid. This is rotated until the fluid achieves solid body rotation and then the pipe is suddenly stopped...

What is the reason that the pressure drops in the central circulation?especially if you go from arteries to arterioles you get a huge pressure drop. If you look what is changing if you go from arteries to arterioles then it is that you get many many branches this leads to an increase of total...

Circulation of a magnetic field = closed loop integral ∫c B ⋅dl = μ0I B is mag field strength, dl is small line element, I is current Im imagining both B and dl point in the same direction from the diagram. So the dot product here, I picture as cosθ = cos0 Is that correct way to...

I know that the circulation is defined as the counter clock wise integral around the closed curve of the flow velocity component along the curve but what is its meaning in real life? I mean what does circulation actually refer to in real life? Also could someone explain the above image? What is...

(Edited to make an answer more likely) So first let's quickly summarize what this is. If you have some closed curve c(t) around a set of fluid elements, Kelvin's circulation theorem says that the circulation around this curve is constant as the curve and its corresponding fluid elements move...

Homework Statement Find the circulation (line integral) of y2dx+x2dy for the boundary of a triangular region contained within x+y=1, x=0, and y=0. Homework Equations Green's theorem The Attempt at a Solution I think I actually already got the solution; I used the Green's theorem to get the...

Suppose I have an overhead tank that heats hot water by natural circulation via a thermosiphon (& a Heat Exchanger with some source of waste heat), is there a limitation on how tall this loop can be? e.g. Can there be an elevated tank at 30 feet with a heat exchanger at ground level that heats...

Homework Statement Using Kelvin’s circulation theorem, find the qualitative and quantitative relation between the circulation around an airfoil and the circulation of the starting vortex. Homework Equations Kelvin's circulation theorem: DΓ/Dt=0 The Attempt at a Solution I don't really know...

Actually i have to calculate the make up water capacity of cooling tower . M= E+B+W . but while calculating the particulars , i am needing the circulation flow rate . i searched it in internet also but it simply showing 18000 so getting confused . Is it 18000 a constant or anything there to...

Homework Statement [/B] Consider F = (y - z)i + (z - x)j + (x + z)k Find circulation of F in the clockwise direction as seen from above, around the boundary of surface S defined by z = 4 - x2 - y2 0 ≤ z ≤ 4 Homework Equations ∫∫ ∇xF • k dA The Attempt at a Solution ∇xF = i - 2j - 2k...

Homework Statement F = y2z3i + 2xyz3j +3xy2z2k Find the circulation of F in the clockwise direction as seen from above, around the ellipse C in which the plane 2x + 3y - z = 0 meets the cylinder x2 + y2 = 16 Homework Equations ∫ F (dot) dr = ∫∫ (∇xF) (dot) k dA The Attempt at a Solution z...

Homework Statement From my notes: "In an irrotational flow, Γ = 0 for any curve lying wholly within the fluid. But circulation around a wing (airflow) is possible! Why?" The Attempt at a Solution The obvious answer is that the air around the wing isn't irrotational. But that seems a bit too...

I've noticed that a FEW of the electrical vehicles have no front grill. I am quite surprised that they do not have one, because the condenser of the AC unit needs to have heat taken away from it (in other words, the condenser needs a heat exchanger). So, in view of the fact that E-vehicles don't...

Other laws in terms of circulation and flux Why others vector fields no are studied like the magnetic and electric fields? In other words, why others vector fields, like the gravitational and the hydrodynamic, haven't "supreme laws" based in the circulation/flux or curl/divergence?

I know what is circulation by a mathematical point of view, but in the reality (in the physical world), what is circulation? I'm thinking that the electrical current through of a circuit, that the water current through of an pipe or of an river, that the water vortex formed over a drain or that...

Exist circulation in a system/circuit/vector field/anything where the path of circulation is open? Is possible to compute the circulation of a system/circuit/vector field/anything with an open path of integration?

Homework Statement I am having issues with some problems relating to a plant theoretically shut down on natural circulation, and calculating the core ΔT and natural circulation flow rate.. Can anyone provide some equations or theory I could use to assist me? I'm not familiar with this...

1st which is the math definition for circulation (##\Gamma = \int_s \vec{f}\cdot d\vec{s}##)? And 2nd, what means positive, null and negative circulation?

Hello. My first time posting here. So... My question is kinda hard to explain but I will try to. So we all know about the Kelvin-Stokes theorem (not talking about manifolds here) : And we also know about Ostrogradsky/Gauss Theorem ...

Hello, My name is Tom and I had a theoretical question about general air pressure and circulation. i have attached an image to diagram the system I am describing. In this closed system loop there is one part of a loop filled with water and the other part filled with air at a higher...

Homework Statement Can someone guide me through solving a problem involving the circulation of a vector field? The question is as stated for the vector field E = (xy)X^ - (x^2 + 2y^2)Y^ , where the letters next to the parenthesis with the hat mean they x y vector component. I need to find...

Here's my work: http://i.imgur.com/9ik31P5.png I need confirmation that the vector fields I found for parts 1) and 2) are correct. I also need to figure out how to find the flux in part 2) when the problem doesn't give any boundaries to evaluate. For part 1), the answer can be found by...

Here's my work typed in Microsoft Word: http://i.imgur.com/jWPqBDh.png I have trouble believing the answer is 0 for part c. All I did was use the curl of F from part a and dot it with dr which came out to be 0.

Homework Statement Compute the circulation of the vector a = yi+x2j - zk around the contour L: {x2 +y2 = 4; z = 3}, a) directly and b) via the Stokes Theorem. Plot the contour and show its orientation. Homework Equations Stokes theorem is \ointF.dr = \int∇ X F . n dS The Attempt...

Homework Statement So a, b, and c are points in the plane. Let nab, nbc, and nca be vectors perpendicular to ab(vector), bc(vector), and ca(vector) respectively, and point towards the exterior of the triangle abc. Also, |nab|=|ab(vector)|, |nbc|=|bc(vector)|, and |nca|=|ca(vector)|. Show...

Homework Statement A fluid as velocity field F(x, y, z) = (xy, yz, xz). Let C denote the unit circle in the xy-plane. Compute the circulation, and interpret your answer.Homework Equations The Attempt at a Solution Since the unit circle is a closed loop, I assumed that ∫ F * dr = 0 (the ∫ symbol...

Hello there, I've got a vector field which you can see here: Sketch of the vector field . It is: \vec{v} = \cos(x)\,\sin(y)\vec{i}-\sin(x)\,\cos(y)\vec{j} Say I want to find the circulation around the square formed by -\frac{\pi}{2} \, \leq x \leq \, \frac{\pi}{2} and -\frac{\pi}{2} \...

Homework Statement In a xyz cartesian coordinate system, a thin vortex filament with constant circulation Gamma, forms a square (in the xy plane), with each side of the square having length L. You are told that an infinitesimal segment del (vector) of this filament induces an infinitesimal...

I've encountered a problem in learning about the curl of a vector field. (My learning material is the "Div, Grad, Curl and all that" from H.M. Shey.) Introduction to problem: The curl of a field F is defined as: ∇×F = i (∂Fz/∂y - ∂Fy/∂z) + j(∂Fx/∂z - ∂Fx/∂x) + k(∂Fy/∂x - ∂Fx/∂y)...

The vector field \vec{F} = <\frac{-y}{x^2 + y^2},\frac{x}{x^2 + y^2},0> has a zero curl, which means its circulation is zero. However \int \vec{F}.d\vec{s} around a unit circle on the xy plane is equal to (+/-)2\pi and not zero Is it because F is undefined at (0,0)? No, because Stoke's...

Homework Statement consider the vector field v(x,y,z)=(-h(z)y,h(z)x,g(z)) wherer h:R->R and g:R—>R are differentiable .Let C be a closed curve in the horizontal plane z=z0.show that the circulation of v around C depends only on the area of the reion enclosed by C in the given plane and h(Z0)...

Homework Statement A giant wheel, 40m in diameter, is fitted with a cage and platform on which a man can stand. The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by the man on the platform is equal to his weight. The speed of the man is: X is located...

Hi, This is my first post. So if I made any mistakes that is the way I asked the questions, kindly let me know. The work done so far Circulation: C {0,0,1} to {1, pi,1} C eq: {y=pi*x, z=1} dr={dx, pi*dx, 0} F={cos(y/z), -x/z*sin(y/z),xy/z^2*sin(y/z)} F.dr = -dx [dot product and...

"cold shutdown" that doesn't require coolant circulation? I was wondering what is preventing a plant being built that can be truly shut down and not require coolant circulation. Is it that efficiency would be reduced to unacceptable levels?

Homework Statement Let F(x,y) = ( P(x,y), Q(x,y)) be a vector field that is continuously differentiable along the closed smooth curve C : x2+y2 = 1. Moreover let -F(x,y) = F( -x, -y)≠ 0 and P(x,y) = -P(-x,y) and Q(x,y) = Q(-x,y). Determine all the possible values of the circulation...

I have never really thought why an air embolus can restrict the passage of blood, until now, and I don't really understand. Why can't the circulation pressure just push the air embolus forward until it is eventually expelled in the lungs? Or why can't it dissolve the embolus? In a plant is...

Homework Statement I'm trying to find sketches that demonstrate ,the general circulation patterns of the atmosphere and the cells in atmosphere of a planet.3 cases must be considered:a slow rotating ,a fast rotating and a non rotating planet. Homework Equations The Attempt at a...

After looking into the lift force i hve been able to calculate most of the things i know. I have however been told that i need to use circulation and vorticity to show that the air flows faster over the wing than below it. I need to show this mathematically by derviving an equation but i am...

I have attached a file with all needed information including the function and path of integration. My work seems right to me, but the correct answer is a^2. Will someone please take a look and show me where my misstep is.

How is the net driving pressure difference within a PWR a function of T and H delta P = delta T(Core) * g * partial Rho(T, P(RCS))/partial T * delta H I get how this correlates to the pressure differential and is found with bernoulli's equation but how does the temperature dependence get...