studiot

It is always sad to hear of someone else's difficulties. Keep strong.

I expect you are thinking only of gases? There are many other states of matter, called phases in thermodynamics. How would you derive the phase rule from your quantities? And how did you get on with my questions in post#2? I am having some difficulty understanding where you are coming from. Have you , for instance, done a course in statistical thermodynamics ? Perhaps if you asked for some explanation, rather than made sweeping generalisations someone could help more. Thermodynamics is a wonderful subject, and worth a deal of effort.

Go on. If you apply a force to a moving object to change its momentum by say gravity or electromagnetic means there is a reaction on the mass of the generator which alters its momentum by a corresponding amount is there not? Normally we discount this since the generator is highly massive or attached to something that is. Alternatively if I hit a cricket ball with a cricket bat both suffer a change of momentum and there is an impact force to take into account. I am using the word 'balance' in the engineering sense, ask captain panic, he is a chemical engineer and they do lots of momentum balances, includng the forces acting on control volumes.

I don't know what sort of proof you are looking for. You have provided scant data to work with (pun intended). Let us say that your data, when plotted, comprises a series of increasing ordinates, but increasing at an apparently ever decreasing rate. If you can find a convergent mathematical sequence, each term of which, produces an ordinate larger than corresponding ordinates in your data, then you have a mathematical proof that your data is convergent, over the range taken. You should look up the comparison test and ratio test for series/sequences. However be warned these can produce an infinite range of data, yours cannot so the conclusion to infinity would be extrapolation. This may not be the case in reality. For instance in reality measuring the output of an electrical power supply has the above characteristic. As you increase the load on the supply the output slowly 'droops' until it suddenly falls to zero as the supply protection kicks in.

Momentum is conserved whether the system is open or closed. Open systems allow a mass flux, which carries additional momentum into or out of the system. This must be accounted for in the balance. Total momentum, with due allowance for these fluxes, is a system property. You don't need to go to the ends of the universe to find momentum popping into or out of existence though, just to your local fire station or car wash. Consider a water jet impinging on the side of a wall or car. The jet has considerable momentum normal to the wall. All of this disappears in applying a force to the wall, which appears as the stagnation pressure on the wall. Parallel to the wall momentum suddenly appears and is carried away with the draining fluid. Or consider two identical blocks of identical mass sliding towards each other at identical speeds along a common line on a frictionless surface. What happens when they meet? Well each block had momentum, but the total momentum of the system is zero, although each individual block has momentum before the collision. Remembering that momentum is a vector quantity mv + m(-v) = 0 before collision. At and after collision total system momentum remains at zero so the blocks collide and become still.

In a word no. Classical thermodynamics is much more complicated than that. Suppose I told you that I had 1 mole of substance A in a container, open to the air at the top, of 1 litre volume. What can you tell me about its thermodynamics? Can you identify substance A, or even tell me what state it is in?

Do you have a mathematical model of whatever this data is about?

Is the target at the same elevation as the gun or launcher? Are you asking what is the difference between the hypotenuse and the other two sides of a right triangle?

An Argand Diagram show two axes, x and y. It shows all numbers of the form x+iy, When y=0 all the numbers are of the form x+i0 = x. That is they are real numbers without an imaginary part. So this represents the x axis. When x=0 all the numbers are of the form 0+iy = iy. This is, of course the y axis. The numbers long this axis are purely imaginary they have no real part. All other numbers are complex numbers with both an imaginary and a real part and they cover the rest of the complex plane represented by the Argand Diagram. For any value of x, y the argument = arctan(y/x).or inverse tan(y/x) So you are looking for angles that have a tangent of -1. What angles do you know that have this value? This angle then defines a line through the origin, but not including it, on the Argand Diagram, every point of which has y/x=-1. I say not including the origin since this has no argument since you x=y=o and you can't form the quotient y/x. How many of these will be complex and how many real?

pretty well all new theory is an extension of what went before and usually reduces to it in simple everday cases. Quantum mechanics is not exception. This is an interesting idea but have you considered the 'forbidden rotations' and axial vectors, both of which are available to classical mechanics? The uncertainty principle also applies in classical mechanics. Which brings me to a point. The equation [math]{x^2} - 5x + 6 = 0[/math] is only true for two particular values of x. It is not true for all values of x. This is very old and well known. In physics we really want equations that are true for as many values of x as possible, preferably a continuous range of them. So for instance Newton's second Law P = ma applies (in Newtonian mechanics) to any value of acceleration we choose, we can find a value of P that will provide this acceleration. However more advanced classical physics has equations, often to do with energy, that are more like the quadratic I showed. That is they are only true for certain values, but not all, and not even certain ranges. This is the development (beginnings) of quantum theory out of classical theory. The realisation that some quantities can only take specific values. This is the origin of the word 'quantum', which means just that. The difference between two specific values. We usually take the dividing line between classical and quantum as being centered on the year 1900, with overlap so that the boundary is between about 1890 and 1910. That was the time when physical phenomena that required such mathematics was being examined. Subsequently effects, such as quantum tunneling, were discovered that have no counterpart in pre 1900 physics. Thus was our knowledge of the physical world extended.

Good job you finished your post, michel, before I finished mine. I can give a better reply. The original post asked for the optimum placement of the umbrella. Your sketches do not show this. For example the walker in the third sketch would be better protected at the rear if he held the umbrella higher and more nearly vertical. As I said at the end of post#9, my analysis answered the specific question posed. However it can also be used and adpated to answer all sorts of variations and 'what if' questions depending upon the variation of velocities, heights, size of umbrella, and so on. It can show that the faster the walker goes the further line AC penetrates under the canopy so provides a limit where AC would actually coincide with OP. It can show that the closer the umbrella is to the walker's head the better he is protected, ie he should not hold it high in the air. You diagram shows that the curvature of a real umbrella provides a measure of slant protection without tilting the umbrella in any case.

That is a very pretty picture of a venturi. Where did it come from? This is homework help. Have you been asked to explain as a homework question? We do not do your homework for you, but since you seem to be having trouble with basic understanding; There are two physical principles involved. The law of conservation of mass. The law of conservation of energy. (In this case mechanical energy) What do you know about these? You can answer the question, without maths, using these two physical principles.

I hope they can explain themselves more fully than you have done. Did you have a question?

Try a PM to a mod. dave is online right now.

OK so there are two approaches to integration. The anti derivative is linked to the area approach by what is known as the Fundamental Theorem of Calculus. This theorem is difficult and therefore not normally studied until advanced courses in calculus. Here is the simple route to area. Note this is 'intuition' only, not a formal proof since this is a very quick answer. Consider any general curve (function) as drawn. Divide it into strips by drawing verticals. The strips are almost rectangular. It is obvious from elementary geometry that the area of any strip is greater than the area generated by multiplying the low side by dx and less than the areas generated by multiplying the high side by dx. An approximation can be obtained by using the average value of y1 and y2 (low side and high side) times dx. Equally the total area between any two x values can be obtained bu adding up (summing) the areas of all the strips. So if we let the strip beocme very thin (dx tends to zero) and the number of them very large we obtain an infinite sum. We can write this in limit form for a formal proof, but it demonstrates the principle of why the Area = Integral ydx Does this help?

How were you introduced to the definite integral, or for that matter any integral? I need to start from what you know, and proceed to what you want to know.

What purpose does this serve? My objective is calculation not drafting perfection. How do I draw a velocity to scale? This is an instantaneous picture. The velocities are linked by formulae. I have modelled my human as a vertical straight line, since this line will meet the rain before any other part of the human. I have no idea what you mean by draw the rain behind. Again I have no idea what you mean. Raindrops falling from the perimeter ? All the raindrops have reached terminal velocity and are falling at the same constant speed. These were the explicit conditions stated by the OP. Water splashes, water from another source, etc are all outside the scope of this model. But then so is the slope of the ground, the partial evaporation of rain drops and other phenomena present in the real world.

Here is my analysis of the situation. The notation provides a basis for futher discussion. Here is some explanation. OP is the projected length of the umbrella on the horizontal. This blocks all rain from passing. As the front edge, B, moves forwards it covers rain that has already fallen below the level of the umbrella. This rain continues to fall vertically, impacting the ground between C and D. C is the point where rain falling when the umbrella edge was at A strikes the ground. These points create a diagonal line BC, separating the area under the umbrella into two zones. Quad OBCP where is it totally dry and triangle, BCD where it is still raining. Thus any walker behind line AC cannot get wet under any circumstances Further, although there is rain in triangle CED, none of this is accessible to the walker, since it will have fallen to the ground by the time the walker arrives. Thus only the rain in triangle BEC could ever hit the walker. Now since BD is constant the longer AB is the smaller the slope of CB and therefore the smaller the triangle BCE. But the condition for making AB as long as possible is for it to be horizontal. This answers the original question, but an interesting further exercise is to superimpose the area within BCE that the walker is going fast enough to enter. This is the point of line A'B'E'C' and the velocities. When the rain is vertical and the umbrella horizontal the they meet at 90 degrees. If the umbrella is now tilted at x from the horizontal, the rain and umbrella are now at (90-x) to each other.

Sorry I can't agree with this. No rain can fall directly down through the horizontal projection of the umbrella, wherever it is. The umbrella creates a 'dry zone' immediately in front of the walker. The walker is always walking into this zone. Since the horizontal position maximizes the shadow it maximizes the size of this dry zone. The umbrella travels with the walker. So yes, the walker is walking into the rain, but the only rain that she can encounter has already fallen below the level of the umbrella, before the umbrella has arrived. So it becomes a race between the speed of the walker and the speed of falling drops. Yes the vertical projection of the umbrella will push the drops in the upper level out of the way. But this projection must be small to keep off the drops still falling vertically above the walker. The walker will still catch any drops that have already fallen below this level on the lower part of their body, shoes etc, if he walks fast enough. The risk of that is minimised by maximizing the dry zone and therefore the horizontal projection. This is unlike the situation of an open topped sports car, which is going much faster, so a (near) vertical windscreen will push the drops in the upper half away and the car's speed will carry you past the vertically falling drops before more can fall. Further the driver is protected at low level by the bodywork.

The rain is falling vertically so there is no wind. In these circumstances you should hold the umbrella vertically. The umbrella cast a 'dry shadow' over the holder which is maximal at the vertical umbrella position, whether the umbrella is moving or stationary. At any other angle the shadow is oblique and equal to the projection of the umbrella area onto the horizontal. This is very much like the question, "Is the normal reaction at an angle when on object moves over its support?"

Ask a mod to move this topic to speculations. Get a surveying textbook and find out about deflection angles. Surveyors often have to measure or set out curves, only part of which, are accessible and the centre is too far away to be accessible. There are other methods than deflection angles .

Did I not mention high rate of discharge? The outflow is controlled solely by the outflow geometry and configuration. Once the siphonic action is initiated the inflow exerts no control over the outflow, rather like the toilet flush I referred to in post2. Do you understand this? The inflow in not going to be constant, which you originally stated. Of course perhaps this might be the only absolutely constant, naturally occurring flow, in existence. As a matter of interest have you heard of Turloghs in the Burren in County Claire in Eire? You should look these up.

The condition under which my diagram will act as a siphon or simply an overflow depend upon the inlet and outlet conditions. I thought I had already explained that, did you not understand it? The diagram was meant to be able to reproduce this stated behaviour, which it could do in suitable circumstances. Here is a modified drawing, exaggerated to demonstrate the point. Water enters the initially empty chamber and fills it to level CC a total of volume 3 There is no outflow at this stage. Further inflow fills the volume marked 2 plus the left hand pipe of the siphon. When the water reaches level AA it starts to trickle out over what you have dubbed a weir. So long as the inflow remains low it will trickle out over this weir. However inflow is variable and a sudden influx of water equal only the the small additional volume 1 and taking the level to BB will initiate the siphonic action. The siphon will now discharge through the outflow until the level falls to CC. That is the whole of volumes 1 and 2 will discharge continuously in a sudden rush. There will then be a dry period where volume 2 recharges, the duration will depend upon the size of volume 2 and the inflow rate. The siphon is then reset ready for action. Note that unlike the cup and straw siphon in the video the intake for the outlet is not at the bottom (though it could be) so volume 3 is never discharged once filled. The straw emptied the cup completely since one open end went to the bottom. Note also that this mechanism is capable of providing a much larger temporary sudden discharge, plus a lower base rate flow, depending upon the geometry. All it requires is volume 1 to be much smaller than volume 2.

Thank you so much for the link, I got sidetracked by the pop pop boats. Ideal for some younger relatives! The siphon is full immersed in the cup so completely empties it. If the outlet is to one side and does not reach the bottom then it will not completely empty. I should have noted that an anticline is tension dominated, whereas a syncline is compression dominated. This is because the outer top is stretched in an anticline, leading to cracking and weakness in an otherwise impervious layer, allowing a route for water entry.

#First let me apologise for the poor quality of my hasty sketch. This may have led you astray. Start with the chamber or porous zone empty. Water percolates in and the chamber collects until the level reaches B Percolation continues, but the water still cannot escape until its level is such that it is enough to initiate the siphonic action, which I have shown as A. In fact there will be a small discharge as soon as the level reaches the lower part of the outlet, you have shown as C. Once the water between my A and B has been discharged the level will be too low to sustain siphonic action so only this water will exit. The water below B will remain. Of course other factors which affect the discharge are the rate of influx and the available rate of eflux. A heavy rainshower, for instance, will rapidly charge up a finite chamber, but the outlet may be restricted so the eflux will occur in sudden heavy bursts. As I said the most likely situation is that the collection is not in an open chamber but in porous material that is bent around an anticline (upfold). Does this make it any clearer?