What is Boundary: Definition and 999 Discussions

In physics and fluid mechanics, a boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. The liquid or gas in the boundary layer tends to cling to the surface.
The boundary layer around a human is heated by the human, so it is warmer than the surrounding air. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boundary layer is the air layer (~ 1 km) near the ground. It is affected by the surface; day-night heat flows caused by the sun heating the ground, moisture, or momentum transfer to or from the surface.

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  1. T

    Solving Boundary Conditions for One-Dimensional Heat Flow Equation

    I have done most of a question except for the most important part, putting in the boundary conditions, I can't really interpret them. The question is: I managed to solve this, with -c^2 as a separation constant, and I got: T(x,t) = X(x)F(t) = (A_{1} \cos{\frac{cx}{\sqrt{\kappa}}} + A_{2}...
  2. M

    What Are the Steps to Solve a Boundary Condition Problem with Three Conditions?

    Hi, this question has been bugging me for weeks and any help would be greatly appreciated. In lectures we derived a general expression for the potential distribution across the xy half plane (y>0) in terms of a known potential distribution along the boundary defined by the x-axis where the...
  3. M

    Boundary Layers Of An Aerofoil

    :confused: :confused: hi everyoone I am carrying reasearch on BOUNDARY LAYERS OF AN AEROFOIL. I have been looking around for information but so far everything as been in vain. I will really be grateful if someone could help. Please urgent :confused: :confused:
  4. A

    My essay on the atmospheric boundary layer

    3 pages double spaced. Can someone please comment on it before Sunday? That would be nice. Thanks! the file located at http://students.washington.edu/achen89/3_boundarylayer.doc . Please feel free to e-mail corrections to hemaalpha@gmail.com Human civilization (and biological phenomena) has...
  5. M

    Boundary Conditions and Hilbert Space

    Hey all, Last year, I took my university's undergraduate QM sequence. We mainly used Griffiths' book, but we also used a little of Shankar's. Anyway, I decided to go through Shankar's book this year, in a more formal treatment of QM. After the first chapter, I already have some questions that...
  6. D

    SHO with a fixed boundary

    How to solve the time-independent Schodinger equation with the following potential: U(x)=x^2 for x>x0 U(x)=infinity for x<x0 ?
  7. D

    Solving Light Refraction Boundary Conditions: Find T^-1

    Can someone please help me with this question: Light with frequency \omega in media 1 ,with refractive index n_{1} , is incident (normal) to an interface of media 2, with refractive index n_{2}, and then is incident on a second interface with refractive index n_{3}. Using boundary conditions...
  8. K

    Solving Non-Linear Boundary Problems: Challenges and Numerical Methods

    Let's suppose we have a Non-linear operator (supposing is self-adjoint and all that) so: cos(y'')+(y')^{2}y+xy=g(x) with the boundary conditions for some a and be real y(a)=0 and y(a)+2y(b)=0 then the "superposition principle" can't be applied so how the hell do you solve it :mad: :mad...
  9. K

    How do different hull treatments affect water flow and boat speed?

    Hi Sailing 30 yrs ago we used to wax and polish hulls to maintain a protective and as gloss a surface as possible. However some say that anything that beads water such as wax causes more drag than a smooth surface that water will sheet over. Note Racing rule 53 " SKIN FRICTION A boat...
  10. W

    Diff EQ with the boundary conditions

    I took an ODE course last year, but I seem to have forgotten some stuff. I need to solve this equation: \frac{d^2u}{dt^2} + {\omega}^2u = f_osin({\mu}t) with the boundry conditions: u(0) = 0, du/dt(0) = 0 When I tried to solve the homogenenous equation first, I got...
  11. S

    Appropriate boundary conditions ?

    "Appropriate boundary conditions"...? I am stumped by a question in my Electromagnetism asignment that asks, after determining the potential (V) and electric field (E) of a hollow conductive sphere containing a point charge system, to "show that E and V satisfy the appropriate boundary...
  12. X

    Proof that the boundary and the closure of a subset are closed.

    Hello, I am currently working on proving the following theorem The boundary \partial A and the closure \overline{A} of a subset A of \mathbb C are closed sets. Proof: Let A \subset \mathbb C. We want to show the set \partial A \cap \overline{A} is closed. To show that \partial A...
  13. B

    Boundary Questions: Can a Set Include Interior Points?

    Is it possible for a set's boundaries to contain some interior points? I can't think of an example off-hand...one would be nice.
  14. A

    Stability for turbulent boundary layer

    concerning fluid flow past a body, i know that if the boundary layer is laminar then the flow becomes unstable when the Reynold's number of the flow is greater than the critical Reynold's number. is this also true when the boundary layer is turbulent? tia
  15. D

    Boundary value problem involving eigenvalues

    I need a bit of help with these boundary value problems. I'm trying to find their eigenvalues and eigenfunctions and although I pretty much know how to do it, I want to exactly WHY I'm doing each step. I attached part of my work, and on it I have a little question next to the steps I need...
  16. P

    How Does Film Thickness Affect Mass Flow Rate in Laminar Liquid Boundary Layers?

    Here is the problem: (From sabersky, problem 8.9) Vapor condenses on a vertical surface to form a liquid film. The film moves under gravity and forms a laminar liquid boundary layer. Derive an expression for the mass flow rate dm/dt as a function of the local film thickness \delta. Neglect...
  17. J

    Neumann boundary with finite differences

    I tried to solve laplace equation for the steady state temperature over a rectangle with both neumann and dirichlet boundary conditions. For the part of the rectangle with neumann boundary condition(normal derivative = 0) i used U(k,p)=(2*U(k+1,p)+U(k,p+1)+U(k,p-1))/4 Is this correct...
  18. A

    How Does Object Shape Influence Water Flow Patterns?

    I have a physics project and i chose the topic of fluid dynamic (i don't know of it is really fluid dynamic but i think that is close enough). My level is only a high school student for information, in order to avoid any over complicating explenation. The concept is simple: first pour a...
  19. A

    Electrostatic boundary conditions

    Im having trouble following how this is derived: The normal component of the electric field is discontinuous by an amount sigma/epsilon_0 at any boundary (when you cross a continuous surface charge). They talk about taking a little box so that the surface integral E dot da = 1/epsilon_0 * sigma...
  20. M

    Boundary Conditions for Waves in Joined Strings with a Knot of Mass

    I'm given the fact that two strings under tension T are joined by a knot of mass m... I'm supposed to find the appropriate boundary conditions. I know that the tensions are the same in both ropes and that the boundary will be continuous. I know the "trick" in this problem is knowing the...
  21. M

    Show that the boundary conditions X(b)=wX(a) +zX'(a)

    I need a little help getting started here, Show that the boundry conditions X(b)=wX(a) +zX'(a) and X'(b) = yX(a) + dX'(a) on the interval a<=x<=b are symmetric if and only if wd-zy=1 i know that the a set of boundries are symmetric if f '(x)g(x) - f(x)g'(x) = 0 evaluated at x=a and...
  22. G

    Boundary condition (Electromagnetics)

    I got some problem about using boundary conditions,especially in the fifth pics,those sentences marked by red.I really don't know how to use Js=An x H,since I don't know the fields well enough.Some questions of mine are illustrated in the sixth pic by different colors. I'm sorry the pics are...
  23. Clausius2

    Solving z(r) Equation with Boundary Conditions

    I am looking for the general solutions of this equation in z(r) If someone remembers well, this equation arises in surface tension physics. z(r)=\frac{1}{r}\frac{d}{dr}\left[\frac{z_r r}{(1+z_r^2)^{1/2}}\right] subject to the boundary conditions z_r(0)=z_{ro} and z(\infty)=0 I only...
  24. S

    What is the solution to the boundary value problem using Green's Theorem?

    Let D be a domain inside a simple closed curve C in R2. Consider the boundary value problem (\Delta u)(x,y) = 0, \ (x,y) \in D, \\ \frac{\partial u}{\partial n} (x,y) = 0 , \ (x,y) \in C. where n is the outward unit normal on C. Use Green's Theorem to prove taht every solution u...
  25. S

    Reconciling the Use of Periodic Boundary Conditions in Solid State Physics

    I'm taking solid state, and again and again we use the periodic boundary conditions, that the wavefunction should be unchanged by displacements of the length of the sample, L (assume 1D for simplicity). The argument was that the surface is so far away that it shouldn't have an effect on the...
  26. B

    Boundary conditions for charged cylinder

    Hello, Charge density \sigma(\phi) = k \sin 5\phi (where k is a constant is glued over the surface of an infinite cylinder of radius R with axis along the z-direction. Find the potential inside and outside the cylinder. Two things I'm having trouble with: 1. Is the potential of an...
  27. P

    Boundary of the union of two sets

    is it true that: \partial(A\cup B) = (\partial(A)\cap \mbox{int}(X-B))\cup (\partial(B)\cap \mbox{int}(X-A)) ? (where \partial(A) is the boundary of A, int(A) is the interior, and A and B are two subsets of the topological space X) I can prove that: \partial(A\cup B) \subset...
  28. P

    Magnus force and boundary layer equations

    First of all I am trying to find a "derivation??" for the Magnus force that affects rotating cylinders and spheres passing moving through air. By derivation, if it is not correct, I mean a proof, something showing how the function was created. I have found the magnus force quite easily by...
  29. kakarukeys

    Orientable Manifold with Boundary

    How does the orientation on M induce an orientation on the boundary of M? I follow the book Lectures on Differential Geometry by Chern, do not understand the proof. The proof is the Jacobian Matrix of the transformation between coordinates of two charts has positive determinant (oriented...
  30. wolram

    Does BH Mass Boundary Vary with Matter Type?

    For a BH to form it must have a mass boundary, but does this boundary vary with differing types of matter?
  31. P

    Sphere Boundaries: Does a Sphere Have Any?

    Hi, we are doing the Divergence Theorem/Stokes' theorem and the teacher said a sphere has no boundaries...what does this mean? Help will be appreciated.
  32. P

    Imposing boundary conditions on a string

    I need to know how different boundary conditions on the DE representing a string under a force can be physically implemented. For example, if you need y(0)= 0, just tie the string to y=0 at that end. If you need y'(0)=0, attatch it so that it can freely slide up and down a pole at x=0. But...
  33. N

    What's the difference between initial conditions and boundary conditions?

    As the thread title says: What's the difference between initial conditions and boundary conditions? Thanks in advance for helpful replies. :)
  34. H

    Chapter 4: The Boundary Problem for Experiencing Subjects

    Liberal Naturalism Having rejected physicalism as a viable ontological framework in which to house p-consciousness, Rosenberg now begins the task of exploring possible alternatives. He will not investigate substance dualism; rather, he will seek to develop a version of Liberal Naturalism...
  35. O

    Fresnel Equations Boundary Conditions

    I'm having trouble with the meaning of the boundary condition in the derivation of fresnels quations, namely that the component of E tangental to the surface is continuous across the boundary. My trouble is, what physically does this corresspond to. Is it something to do with the divergence...
  36. H

    Solve AP Physics Problem: Reflection & Refraction at a Boundary

    AP PHYSICS PROBLEM...i forgot the formula, someone help me solve! This won't take lon Light of frequency 6.0 x 1014 hz strikes a glass/air boundary at an angle of incidence, ø1. The ray is partially reflected and partially refracted at the boundary as shown. The indices are shown. (a)...
  37. M

    Boundary Value Problem for Electrostatic Potential in a Channel

    I need some help starting off on this question. Electrostatic potential V (x,y) in the channel - \infty < x < \infty, 0 \leq y \leq a satisfies the Laplace Equation \frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2}= 0 the wall y = 0 is earthed so that V (x,0) = 0...
  38. W

    How does turbulence affect the boundary layer and create drag on swimsuits?

    hi, I'm just currently doing some research on swimsuits and how they work. i have found that 1 type of swimsuit makes water "stick" to the suit longer so the water doesn't separate and cause drag. i notice this is very similar to how golf balls work with the dimples making the air stick longer...
  39. A

    Behavior of two liquids in contact and a boundary

    Hi, I have a problem that talk about the behavior of two liquids in contact and a boundary that appears between them. I am lack of theory about this situation do anyone of you could help me to find some paper of articles that talk about this? Thank you, Aron
  40. C

    Understanding the Chandrasekhar Boundary: Exploring Its Significance

    What does the Chandrasekhar boundary (or line, I'm not sure about it) means?
  41. R

    What's the boundary between micro and macro?

    Thermodynamics treats with macroscopic systems, where statistical mechanics make sense. In these systems there is an arrow of time following the second law. On the contrary, temporal reversibility is generally seen at microscopic level. What is the limit (magnitude order in number of...
  42. Clausius2

    Electromagnetic boundary layer.

    I want to comment with you this imaginary problem. I have not formulated it yet. But I would want your qualitative opinion about this. It is not anything new or revolutionary, because electromagnetic control of boundary layers have been proved yet. But I would want to understood mathematically...
  43. L

    Green function and the boundary conditions

    Hello there, I am glad that I found this forum. Because I have a little bit trouble with theoretical physics. :yuck: The problem is the Green function in theoretical electrodynamic. I try to understand the difference between the Dirichlet Condition and the Neumann Condition. I...
  44. M

    Expanding manifold with constant boundary

    OK. Suppose you have a surface with a closed curve as a boundary. Then suppose that surface grows like a soap bubble but the boundary is stationary like the orifice through which air passes to make the bubble grow. It would seem that the 2D surface grows in both dimensions in the middle of the...
  45. C

    Inhomogeneous Initial, Boundary Value Theorem Proof

    I think my lack of background in proofs is showing. From "Partial Differential Equations of Mathematical Physics and Integral Equations" by Ronald B. Guenther and John W. Lee, pp. 107 problem 4-3.10. Prove: For the inhomogeneous, initial, boundary value problem...
  46. T

    He wrote a book called Geons, Black Holes, and Quantum Foam: A Life in Physics

    Everyone keeps discussing some forms of the big bang models for the creation of the universe, however upon reading hawkings The theory of everything, he discussed many models for the creation of the universe. One, that i found particularlly interesting was the idea of the No-Boundary Universe...
  47. V

    Exploring Stephen Hawking's No Boundary Proposal

    Stephen Hawking and the No Boundary Proposal The no boundary proposal has been around for quite some time now, and in some ways it seems to relate to the concept of forever that's been around for hundreds or thousands of years. It's a theory that appears to shed light on imaginary time...
  48. E

    What is the difference between surface boundary and point-set boundary?

    I'm having trouble understanding how to find the boundary in the sense of boundary of a surface, as opposed to boundary in the sense of boundary of a point-set. From what my professor said, it seems as though for surface boundaries, you just stare at the surface and figure out its boundary, but...
  49. Norman

    Solving Electric Field Boundary Conditions Across a Dipole Layer

    This is a homework question so please do not just tell me the answer, but please point me in the right direction. A dipole layer, D(y,z), exists on the plane x=0. Find the boundary conditions (discontinuities, if any) for [phi](x,y,z), E_x(x,y,z), E_y(x,y,z), and E_z(x,y,z) across the...
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