Recent content by zeebek

Thank you for your reply. As I said this is not a homework problem. In fact if somebody could help me represent this intergral via some generalized functions this would do. Sorry for the misconception.

This is not really a homework. Homework Statement I am trying to solve one definite integral Homework Equations \int_0^{2 \pi} \frac{\sin^2{t}}{\sqrt{a\cos{t} + b}} dt where a, b are some positive numbers. The Attempt at a Solution I tried integrate by parts, also...

I am reading the definition in wiki ( nothing better at the moment) http://en.wikipedia.org/wiki/Lorentz_space It seems too vague for me, namely what they call "rearrangement function" f^{*}: f^{*}: [0, \infty) \rightarrow [0, \infty]; \\ f^{*}(t) = \inf\{\alpha \in \mathbb{R}^{+}...

Now I understand that I was wrong. A*A is indeed positive semidefinite thanks to everybody

Nevermind, I found contre example.

I have a feeling that for any n x n non-trivial matrix A, trace(A*A) is always positive. Is it true?

Reynolds number is about \frac{U D}{\nu} = 1.7 \times 10^6 This is clearly turbulent and not potential. Bernoulli's equation is not applicable here. The solution is based on the exact statement, that for a steady flow in pipes mean pressure gradient is balanced by the shear at the wall...

sorry if it is too advanced Then follow Doc Al, he gave you basically the same hint. Since there is 180 phase shift you defintely have to subtract smth, because it is the condition for destructive interference. Doc Al gave you hint how to calculate what you need to subtract.

Please, open the book and read under which assumption bernoulli is derived from the Navier-Stokes and where it is applicable. Bernoulli works for potentials flows only. It means no viscosity and vorticity. In pipes both are present.

Formula 2 looks weird. Intensity is just amplitued times its conjugate. Same to say module of amplitude squared. Solution hint I = |A_1 e^{\phi_1} + A_2 e^{\phi_2}|^2 = A_1^2 + A_2^2 + 2|A_1||A_2| \cos(\phi_1 - \phi_2) the rest try to figure out yourself

Start with this \vec {\Omega}. \vec {n} = \lim_{R \rightarrow 0}[\frac {1}{2 \pi R^2} \oint_C \vec {u}.dl] then use Stokes theorem and get in the limit R \rightarrow 0 \vec {\Omega}. \vec {n} = \lim_{R \rightarrow 0}[\frac {1}{2 \pi R^2} \iint_S...

could anyone make a sketch? really hard to imagine what is being asked

as I said bernoulli part is defintely wrong, it just does not work for such flow. For the rest - I will consult with my profs on monday. In principle I can measure what you are asking :)

Here is what I am completely sure of bernouli is not applicable in pipes because the flow is not potential. There is mean vorticity. The head loss in pipes comes from the friction on walls (what you call darcy law). Here is what I am not really sure of, I have to think more if we assume that...

What alxm said + By the definition positive current direction is the direction of positive charge flow. However, like alxm said, it turned out that in most case it is the electrons that are moving and making the current. So the current is kinda "negative". Normally, people speak about current...