Recent content by humphreybogart

Excellent. Got it now. Not seeing 1) is my fault. Not showing 2) in the working is the textbook's. :P

I am working my way through a textbook, and whenever this equation is solved (integrated), the answer is given as: u = f(x) + f(y) I don't understand it. If I integrate it once (with respect to y, say), then I obtain: ∂u/∂x = f(x) -----eq.1 If I integrate again (this time with respect to...

The continuity equation in fluid mechanics is: Do the condition of "constant-density fluid' and 'imcompressible flow' have the same effect on the continuity equation, in that the first two terms disappear? Or is there a difference between these assumptions?

1. Can a fluid which is accelerating down an inclined channel with constant acceleration still satisfy the continuity equation for a constant-density fluid? Since the acceleration will be down the slope, in the streamwise direction, then surely ∇⋅U > 0? 2. Assuming that continuity is satisfied...

Yes, sorry, I thought that's what was meant. It's just that I hadn't stated an initial condition. I'm just considering the general solution, not the particular solution. I'd like to know how I can deal with situations involving "division by zero" in the future, since they arise often in solving...

What do you mean by the initial condition of x=0?

Well, I'm sure I was unsure. :) I think it was a wholly unnecessary digression, however.

…then? I'm not sure what your point was here Ray. "Why are you asking if you are unsure? Don't you know if you are unsure? (That is the effect of using a "?" at the end.)" I said I am not sure. You can take that to mean I'm unsure. There really isn't any other way to interpret my sentence...

Apologies, I've corrected the sign error now. Very frustrating since now, naturally, help with the questions is muddied by correction of the error. :( And also for not being able to count to 3 :P. Regarding: 1) If I don't restrict the constant in this way, I'm saying that y=infinity is a...

Homework Statement Find the general solution to the differential equation: Homework Equations Separation of variables for solving 1st order separable differential equation. The Attempt at a Solution Using separation of variables, I can write: My questions are: 1) Am I correct to...

Transport Phenomena (2nd edition) by https://www.amazon.com/s/ref=dp_byline_sr_book_1?ie=UTF8&text=R.+Byron+Bird&search-alias=books-uk&field-author=R.+Byron+Bird&sort=relevancerank&tag=...

I'd like to purchase one of these books for self-study. The BSLK Introductory Transport Phenomena claims: "Devoting more space to mathematical derivations and providing fuller explanations of mathematical developments—including a section of the appendix devoted to mathematical topics—allows...

Hi, I'm looking for a modern, colourful, illustrative introductory textbook to work through on tensor calculus/continuum mechanics. I'd like one with lots of physical examples, exercises, summaries, etc. I'd like an emphasis on engineering. Something in the mould of Frank White's Fluid...

Thank you. Great! I seen in another post a reference to Bird's Transport Phenomena book. Thanks.

I'm tempted to say 'no', because no fluid enters or leaves a material volume. So the term would disappear. I'd like to see the integral and differential form for conservative, and the integral and differential form for non-conservative.