Recent content by C.E

Left hand side: |(u. \nabla )u| Right hand side: (u^2)/D (where D is the diameter of the cylinder). I can now see that if I change the units of distance by a scale factor s then the left hand side changes by a factor of (1/s)^2 and the right actually changes by a factor of (1/s). How does this...

Is what I written in my previous post correct? If so, how does it help? I have had to submit this as a new reply as for some reason it won't let me edit my previous post.

I can see that if I change the distance by a scale factor s then both the right and left hand sides change by a factor (1/s)^2 (assuming the units of time remain the same).

I meant to say that |(u. \nabla )u| is approximately (u^2)/D. Here the vertical lines just mean absolute value of.

Thanks for that, I have now corrected my previous post.

I think I understand it a bit more now, could the characteristic length be chosen to be any length which is uniquely determined by the cylinder? If in the case of a cylinder you select radius instead of the diameter would it then be that u. \nabla |u is approximately equal to (u^2)/2L or...

How do you know what the characteristic length is in a particular case? Is it selected so that |u. \nabla |u is approximately (u^2)/L? In the case of a cylinder of diameter D I cannot see why |u. \nabla |u is approximately (u^2)/D.

Could somebody please clarify a few things about Reynolds number for me? In class the lecturer approximated |u. \nabla |u by (u^2)/L where L is the characteristic length. In a specific example considering flow around a cylinder of diameter D, it was said that L=D. What does the characteristic...

Sorry, but I don't know how a computer monitor would approximate the graph of f, can you please elaborate?

Surely different choices of f would look different wouldn't they? How do this help?

Sorry I probably should have said, the two functions f,g are on the closed real interval [a,b] for some real a,b.

[b]1. suppose f:[a,b]->R is a weakly increasing function, i.e. u<v gives f(u)<=f(v). Show that f is the limit of a sequence of step functions. [b]3. I have no idea how to start this. Please help.

[b]1 Show that the product of two regulated functions is regulated. [b]2. A function is regulated if it is the limit of a sequence of step functions. [b]3. I let f,g be regulated and let a_n, b_n tend to f, g respectivley. I can show that for any x, a_n (x) . b_n (x) tends to...

Oh, yeah, my Algebra was wrong afterall. Sorry about this but I do not actually know what else I can try, any further hints?

Ok, I will try new approaches but just out of interest the comment I made at the end of my last post about the second law do you agree with it? If so what have I done wrong (though it may not show the desired result I still thought my Algebra was correct)?