studiot

Hi Acme, the Columbia river huh? Canada to Frisco? You don't give any clue as to whereabouts, but the CR is an very important north american river and could easily move such a boulder many miles when in spate. Do you know where the parent rock is located?

And your point is....?

Not at all. The sequence 'increases without limit' Which roughly means that consider any proposed limit, m then take n>m and the series has a term n which is greater than the proposed limit m which is a contradiction. So the sequence has no limit. The OP has been banned but since the subject is of such fundamental importance we can continue to discuss it if you wish.

Hello Bruno and welcome to ScienceForums. I'm sorry the site was down yesterday afternoon so my earlier answer was lost. It would be useful learn what you already know, since limits are very very important and many struggle at the beginning. Limits are usually a student's first encounter with infinity. Is this High School level? Do you know what a 'set' is in mathematics? As already mentioned, your teacher's example was one of Zeno's paradoxes. Zeno was an Ancient Greek and they did not understand limits in their mathematics. https://www.google.co.uk/?gws_rd=ssl#q=zeno%27s+paradoxes To start here are some important facts about limits. Firstly a limit is not a property of a single number. It is a collective property of a whole bunch of numbers. We call a bunch of numbers a set of numbers. So the number 1 or 2 or zero are not, by themselves limits. But when we introduce a whole bunch of numbers for example the reciprocals of the counting numbers and place them in (decreasing) order [math]\left\{ {\frac{1}{1},\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5}.......} \right\}[/math] We see that the collection gets closer and closer to zero, the further we go along the list. We say that the limit of this sequence is zero. But waitup. Consider a different sequence of the same numbers [math]\left\{ {1,2,3,4,5............} \right\}[/math] This sequence gets larger and larger the further we move along it. We say the first sequence is convergent and the second divergent. Such Divergent sequences do not have a limit. We say that the limit does not exist. So a limit may or may not exist for a given situation, depending upon the circumstances. An important requirement is that the limit be the same sort of mathematical object as all the others in the set or sequence. Infinity is not a number. Note that the limit number does not have to belong to the set or sequence. In the first example zero is not in the sequence. If either of these are the case then we can never reach the limit. That is the limit is not accessible. But if the limit number is an element of the set or sequence then we can reach it. It is not true to say that we can never ever reach a limit. Sometimes we can, sometimes we can't. Sometimes even stranger things can happen, but these are best shown graphically and I will leave that part to next time if you are still interested. Also our set need not be about numbers but may be about any suitable mathematical object. For example as we draw regular polygons of an increasing number of sides, the closer the polygon gets to a circle. Being geometers, the Ancient Greeks did explore this aspect of limits and came up with a respectable value for [math]\pi [/math].

Interesting 'photo' in a recent German magazine about European centres. Any ideas on how the trick works?

RiceAWay I owe you an apology. I didn't respond to your post#24 because I found the claim hard to believe but it has now been independently verified so I, for one, have learned something. Thank you.

Would a numerical integration method not do nicely?

Top to bottom of all three layers or just the top one? You need at least two electrodes to inject a current. So you need the electrode spacing. How about a sketch?

Thank you again Acme, now that the tone of the discussion has definitely taken a turn for the better. I was not aware of such rules about traps in your part of the world. The UK does not actually specify the physical details of the trap only the depths of the water seal for different purposes. If you think about it, both P and bottle traps must eventually become elongated S traps unless the connection is to a larger diameter pipe. We usually consider a P trap for a horizontal outlet and an S trap for one that goes down. Sometimes the geometry of the construction constrains what connections are possible. Isn't it strange how a particular physical arrangement that works well in one part of the world (and may even be mandatory) can be illegal in another. I have always thought it ironic that in the UK it is illegal to earth (ground) the consumer neutral, but in the US it is illegal not to.

I think the folks have nailed the reason for your 'bottom water' Perhaps if you had posted some photos and/or sketches more complete advice could have been forthcoming. Thanks to Acme for the diagram of a P trap. However it is quite likely to be a bottle trap rather than an S or P trap. These are favoured by builders as they are smaller, cheaper and easier to fit. They do unfortunately clog up more easily than pipe type traps since the fluid path is not smooth.and regular. Please note on the bottom of Acme's diagram a 'cleaning eye' is shown as a bump. You should find out the type of trap and check youtube for cleaning and maintenance instructions.

I have already noted that we do not know if Larry Hills was referring to the cross sectional or longitudinal flow pattern, and that I assumed the more difficult cross sectional question. Rectangular/square cross sections are usually used for gaseous flow rather than for liquids for a number of reasons. Further this flow is often turbulent rather than laminar, at least in the longitudinal direction. I note the presentation quoted in post#17 is an elementary presentation, slanted towards liquids (water in particular) in round sectioned pipes. In the quote below, from the Karlsruher Institute I have highlighted the classic 8 vortex pattern for square ducts and, As the professor says cross sectional profiles are less abundant than longitudinal ones. The patterns of eddies are known as disturbed flow. It is also called secondary flow in that it is distinct from the main flow of the bulk fluid. If you would like me to explain the various flow terminology I will happily oblige. But it is important to distinguish between pathlines, which have one more dimension than streamlines, streaklines and streamlines themselves. Further important terms are steady/unsteady and uniform/nonuniform flow, turbulent, laminar and disturbed flow and to know which is the 'opposite' of which. Edit there is one other important flow distinction viz compressible v incompressible, obviously important in water v gas as the fluid.

If you are going to make claims here it would be wise to ensure their correctness. The original post was over 5 years ago. some time before I actually joined SF. I did not in fact join the discussion until recently, when I did indeed offer a novel answer to the OP's question "Where did the half come from" in my post#39. If you are actually interested to learn anything you might be interested to know that there is another energy formula containing the factor of one half. Strain energy = 1/2 stress x strain. This also causes difficulty when folks first meet it. I think both these difficulties are caused by over emphasis of the formula work energy = force x distance in early learning of physics.

Fibre reinforced composites are relatively new materials and many users do not understand them properly. So inappropriate manufacturing design is applied. This can be in several forms. a) Physical Inappropriate stress concentrations. Inappropriate shear transfer devices b)Chemical Insufficiently clean and dry manufacturing conditions leading to premature chemical degradation. Check out 'osmosis' in grp boat hulls. http://www.anchormarinesurveys.co.uk/osmosis.php Excessive material thicknesses causing internal overheating during curing.

Reflections on the political year in Parliament.

@RiceAWay Since you won't clarify, I will. 1) is incomplete. 2) is just plain wrong since V2 = V1 + at, a = (V2-V1) divided not multiplied by t 3) is also wrong since it implies that kinetic energy is independent of mass, amongst other issues.

I thought aeronautical engineers used spherical chickens to test the robustness of jet engines. One should also beware the subtle and not so subtle differences in terminology used by different authors at different times. Streamlines constitute a direction field and must either extend to infinity or form closed loops. Either way if you can draw streamlines it is possible to predict where the flow will go next from any point. That is not turbulence, where it is impossible to predict the next destination from any particular point. Remember also that there are two kinds of vortex, one with net vorticity and one without. The vortex sheets shown in the Wikipedia article are actually a result of Kelvin's theorem and the above statements. They are the loop closers required by Kelvin to generate the vorticity (circulation) to generate the lift.

Here is a simple analogy. But beware analogs are never exact, but they can offer enough correspondence to promote understanding. Right so SR is 'flat or euclidian' GR is not. Going down to 2 dimensions for the analog consider a plane and a sphere, both of which have two dimensions, X and Y for the plane, Latitude and Longitude for the sphere. Remember a sphere is mathematically a surface, not a solid. The plane is flat like SR. The sphere corresponds to GR. The plane only approximates a small portion of the surface of the sphere with any pretention to accuracy. The smaller the curvature ( ie the larger the sphere) the greater is this 'patch'. A function or transformation that maps points on the plane to points on the sphere is called a chart. Clearly a chart good at the equator is not good for mapping the polar regions. This is what is meant by local. In fact no single transformation will put every point of any given sphere into one-to one correspondence with a point on the plane. There will always be at least one sphere point left out, when every available point on the plane has been used up. Proving this is the subject of topology. So the planar grid can never be a global coordinate system for the surface of a sphere. You have to 'cover' the sphere with reference to at least two different planes. Of course the sphere is the simplest most regular 2 D surface in 3D. The real universe is quite irregular so the only global grid is the universe itself, which is effectively saying there is no global grid. That is enough for now, but does it help?

The following fractal is used to model lightening patterns, amongst other things. Diffusion Limited Aggregation fractal https://www.google.co.uk/search?q=diffusion+limited+aggregation+fractal&hl=en-GB&gbv=2&prmd=ivns&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjiqdLRlcLRAhWMI8AKHd2YBrIQ_AUIBQ

Yes a modern version can be accomplished with a video camera and a screen. In fact both the infinite regression that is described and the opposite infinite expansion play huge roles in modern theory. Infinite regression leads to chaotic behaviour and infinite expansion to positive feedback. Another entirely separate case is geometry behind the stereographic projection, non linear Riemannian geometry and the so called extended complex plane. https://www.google.co.uk/?gws_rd=ssl#q=extended+complex+plane

Perhaps you would like to clarify these? I have added the numbering for reference clarity.

Hello Sarah and welcome to ScienceForums. This is a good and perceptive question and you should confirm the actual meaning with your tutors as the wording is a bit lax. +1 for spotting it. Normal practice in the scientific world for mixtures, solutions etc is to refer to % by mass ( or volume) of the mixture, not of any of the consituents so I would expect they meant your second answer. However strictly if they simply said add 20% by mass then your first answer is correct. The technical word for adding 20% is to add 20% to the admixture. They really need the word mixture in there somewhere to make it plain.

Well here is an offer to test if you are serious. There used to be a brand of liquid coffee essence called camp coffee. It came in a bottle and on the label was a picture of a butler holding a silver tray with a coffee cup and a bottle of camp coffee on it. I used to wonder what was on the picture on the label on that bottle on the tray and if the pictures went on forever, with smaller and smaller pictures of the coffee bottle. https://www.google.co.uk/?gws_rd=ssl#q=camp+coffee This type if geometry is known as scale invariant geometry and is very important in modern theory. https://www.google.co.uk/?gws_rd=ssl#q=scale+independent+geometry Over to you.

I like the way this thread panned out. +1 guys.

Personally I read this to mean transverse to the flow. That is to say flow in ducts of rectangular section. Bends, restrictions etc were not mentioned. Perhaps I was wrong but it certainly wasn't clear. However since Larry has not returned to this site since he wrote the OP I wonder if he has lost interest? I would like to extend a welcome to Ned, whilst pointing out that streamlines should not end as shown in post#6. I call the reverse flow circulating in the corners simply 'eddys'. Such flow is not turbulent since full streamlines can be drawn at all points.

This question/discussion proposal was inspired by the discussion in this thread, but is not directly on topic there. http://www.scienceforums.net/topic/102170-an-issue-i-have-with-gr-physics-versus-newtonian-physics/page-2#entry966276 It appears to me that accepting universal expansion has-implications-for/constrains acceptable coordinate systems. Consider static points on the classic 2D manifold surface of a balloon. As manifold expansion occurs: 1) For xyz coordinate systems all of x and y and z will be different before and after expansion. 2) For cylindrical coordinate systems the angle will remain unchanged, but r and z will be different. 3) For spherical coordinate systems both angles will remain unaltered but r will change. Only option (3) has two invariable coordinates (latitude and longitude or HA and azimuth) that we can use to keep the points in the 'same place' as the balloon expands. Since the expansion takes place over time my question for discussion is how does the choice of coordinate system affect the 'arrow/reversibility of time' and the block universe?