What is Saint-Venant’s Principle?
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Saint-Venant’s principle is often invoked to justify approximate solutions to boundary value problems in linear elasticity.  For example, when we solve problems involving bending or axial deformation of slender beams and rods in elementary strength of materials courses, we do not prescribe loads in any detail.   Instead, we specify the resultant forces acting on the ends of a rod, or the magnitudes of point forces acting on a beam.  We rely on Saint Venant’s principle to justify this approach. In this context, the principle states the following.  Suppose we calculate the fields in a slender rod due to two different (self equilibrating) traction distributions which act on the ends of the rod.  If the two traction distributions exert the same resultant force and moment on the rod, then the difference between the two states at a point distant from the ends is an order of magnitude smaller than either state.\n\n \n\nSaint-Venant himself limited his principle to the problem of extension, torsion and flexure of prismatic and cylindrical bodies.  There have been various attempts to generalize the principle, some more successful than others. The most satisfactory statement is due to Sternberg, who shows rigorously that\n\n \n\nIf the forces acting on an elastic body are confined to several distinct portions of its surface, each lying within a sphere of radius  , then the stresses and strains at a fixed interior point of the body are of a smaller order of magnitude in  as  when the forces on each portion are in equilibrium than when they are not.
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If it's just a moving point, there is no "final" position, but there is a position as a function of time.  Specifically, the position at any time t will be (x + ut, y + vt).  If we are talking about a point moving in a force field, so that u and v are actually functions of x and y, it becomes much more complicated.  You have to treat u as x-dot and v as y-dot ("dot" as in differentiation with respect to time), and then you have to integrate to see if you can get x and y as functions of time.  In this case, one or both coordinates may converge to a finite value as t --> infinity, and then you would have a final position.
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At any given point in a fluid, yes, pressure is equal in all directions.  However, a given point is likely along a pressure gradient, meaning that the pressure changes in places directly adjacent to the first.\n\npressure is a scalar quantity, not a vector quantity.  Vectors have direction; scalars do not.
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So Archimedes was lying in one of those Greek bathhouses when he suddenly realized that (besides the rise in water level) he was FLOATING.\n\nThen he came up with his principle in buoyancy, that the weight of water displaced equals the weight of the buoyant object.  This has many uses in the calculations of forces and whether or not an object would float. (You would like to know if your boat can float before getting on, wouldn't you?)
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1. The bouyant force of the water on the object is the difference in the reading, i.e. BF=(.0554-.0370)g\n                                   =0.0184gN\n\nBased on Archimedes' Principle, BF =Volume*Density of water displaced.\n \n0.018g=Volume*1000g\nVolume=.018/1000\n            =1.8*10^-5m3\n\n2. Density of Object=Mass/Volume\n                                =.0554/1.8*10^-5\n                                =3078kg/m3
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a) zero momentum, as velocity on top is zero. p=mv\n     p=0.100kg * Om/s\n\nb) Vf = Vi + at\n      0=15+(-10)t\n     t=1.5ec (to reach maximum height)\n\nDivide by 2 for halfway up .i.e 0.75ec\n\nVf = Vi + at\nO=15 + (-10)(0.75)\nVf = 7.5m/s\n\np=mv   (p = momemtum)\n\np = (0.100kg)(7.5m/s)\np = 0.75kg*m/s, upwards (Direction is important)
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http://en.wikipedia.org/wiki/Liskov_substitution_principle click the link to know in detail.
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Le Chåtelier's principle - when a system at equilibrium is disturbed by application of a stress, it attains a new equilibrium position that minimized the stress.\n\nif a liquid substance is added, regardless if the substance is acidic or basic, the shift in equilibrium would be to the right\n\nBecause there would be a net movement of molecules from the liquid phase to the vapor phase, the number of liquid molecules has decreased.  The equilibrium has therefore shifted to the right
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Archimedes LAW of buoyancy states that any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force the magnitude of which is equal to the weight of the fluid displaced by the body.. also, the density of the ship( and the air inside it) is lesser than the density of water. \n\nBernoulli's principle explains why airplanes fly: air/water traveling at faster speed has lower pressure in it.\nthe shape of the airplanes wing is like half of a water drop. therefore the air flowing at the top/above the wing of an airplane is faster compare to the air underneath creating enough pressure to lift the airplane.
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coz the principle of bouyancy comes into action. that is there is a space with air in the bottom part of the ship/boat n hence it doesnt allow it to sink.. n that too that a greater surface area is there so the pressure is distributed over a larger area. \n u can also call it Upthrust.\nexplanation-\nArchimedes discovered the law of bouyancy. It states: on everybody emersed in water (or fluid in general) there acts an upward force with magnitude equal to the wieght of displaced water/fluid.\n\nthere are 3 scenarios for a body in water:\n\n1. floats on the surface; gravity of the body equals bouyancy and equals exactly the amount of weight of the displaced water\n\n2. the body is entirely emersed in water; again gravity = bouyancy\n\n3. the body sank; gravity = boyancy + normal reaction of the floor.
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Set up the equation\n\nP = dRT\n\nAssuming P to be constant,\n\ndT = d'T'\n\nor d' = 0.76*273/298 = 0.696 g/l.
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Bernoulli's Principle \nThis is an important principle involving the movement of a fluid through a pressure difference. Suppose a fluid is moving in a horizontal direction and encounters a pressure difference. This pressure difference will result in a net force, which by Newton's 2nd law will cause an acceleration of the fluid.  \n\nBernoulli's principle thus says that a rise (fall) in pressure in a flowing fluid must always be accompanied by a decrease (increase) in the speed, and conversely, if an increase (decrease) in , the speed of the fluid results in a decrease (increase) in the pressure. This is at the heart of a number of everyday phenomena. As a very trivial example, Bernouilli's principle is responsible for the fact that a shower curtain gets ``sucked inwards'' when the water is first turned on. What happens is that the increased water/air velocity inside the curtain (relative to the still air on the other side) causes a pressure drop. The pressure difference between the outside and inside causes a net force on the shower curtain which sucks it inward. A more useful example is provided by the functioning of a perfume bottle: squeezing the bulb over the fluid creates a low pressure area due to the higher speed of the air, which subsequently draws the fluid up.
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Is that the same principle as two negatives making a positive?\nThen the answer would be yes.
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Gotta approach this using basic principles.\n\nEnergy is the integral of force applied over a distance.\nTheres two sets of forces working:\nfluid and gravitational.\n\nSo you make your control volume, and look at it.\nYou want to raise the water in it, thats mgh or rho*v*g*h\n\nYou also have to exert a pressure to push against the water ahead of it.  The downward pressure acting on your control volume is f/a so the force you must overcome is p*a and you are traversing distance h so the energy is p*a*h\n\nTherefore to raise the fluid vertically against a down pressure and against gravity the minimum energy (real world is lossy) is \nE = h*(mg+pa)
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http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation
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Newton's First Law of Motion:\nI. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.  \n\nThis we recognize as essentially Galileo's concept of inertia, and this is often termed simply the "Law of Inertia". \n\nNewton's Second Law of Motion:\nII. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.  \n\nThis is the most powerful of Newton's three Laws, because it allows quantitative calculations of dynamics: how do velocities change when forces are applied. Notice the fundamental difference between Newton's 2nd Law and the dynamics of Aristotle: according to Newton, a force causes only a change in velocity (an acceleration); it does not maintain the velocity as Aristotle held. \n\nThis is sometimes summarized by saying that under Newton, F = ma, but under Aristotle F = mv, where v is the velocity. Thus, according to Aristotle there is only a velocity if there is a force, but according to Newton an object with a certain velocity maintains that velocity unless a force acts on it to cause an acceleration (that is, a change in the velocity). As we have noted earlier in conjunction with the discussion of Galileo, Aristotle's view seems to be more in accord with common sense, but that is because of a failure to appreciate the role played by frictional forces. Once account is taken of all forces acting in a given situation it is the dynamics of Galileo and Newton, not of Aristotle, that are found to be in accord with the observations. \n\nNewton's Third Law of Motion:\nIII. For every action there is an equal and opposite reaction.  \n\nThis law is exemplified by what happens if we step off a boat onto the bank of a lake: as we move in the direction of the shore, the boat tends to move in the opposite direction (leaving us facedown in the water, if we aren't careful!).
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Conservation of momentum\nP = mv before must equal mv after\nmass remains the same\nvelocity is a vecor quantity (magnitude and direction)