report about the hydraulic analogy. This is an analogy between free-surface waves and compressible flow?
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You can produce free-surface waves for example by dropping a stone at the center of a still mill pond.  The waves that propagate outwards have crests and troughs.  This is analogous to the waves produced in air by sound energy.  For example a trumpet player produces lip vibrations with his/her embouchure that allow the airflow (breath) to be interupted each vibration.  This emits a steady stream of sound waves where the air pressure is slightly above (condensation) and slightly below (rarefaction) atmospheric pressure.  The condensations and rarefactions correspond to the mill pond crests and troughs, respectively. Interestingly, the trumpet player's breath moves very slowly through the instrument (contributing to a slight dopler effect?) while the sound waves travel at the speed of sound (1,100 feet per second).  The sound travels from lip to bell in a tiny fraction of a second and there is even a second wave reflected back toward the lips.  The length of the round trip (and tone produced) depends on the length of horn selected by the trumpet keys (even easier to see in the slide trombone).  The concert A tone is 440 vibrations (trips) per second.  When lip vibrations exactly correspond with the sound wave cycles, resonance occurs and the note is sustained effortlessly.  Beginners try to force the vibrations (without regard for the length of path) and fail.  Singers produce the same type resonating air columns on both sides of the vocal chords, past the teeth and gums and can evey destroy a perfectly good wine glass with resonating energy.  Of course, sound can be emitted from a point source in space and the sound waves are produced as successive growing spheres of condensations and rarefactions similar to surface waves but truly three dimensional in space rather than affecting only a small layer of surface.  The spheres grow at 1,100 feet per second and the energy diminishes as it is spread over a larger spherical surface, although she spheres remain separated by the wavelengths of the pure tone.  A complex tone could better be pictured perhaps as a roller coaster stretched out straight in the directions the spheres are growing.  Your ears can intercept and interpret the roller coasters as song, voice or noise.  Hope that helps a little.
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a drastic change in a medium leading to multiple areas"A shock wave (or simply "shock") is a type of propagating disturbance. Like a normal wave, a shock wave carries energy and can propagate through a medium or, in special cases, through a field such as the electromagnetic field in the absence of a physical medium. Shock waves are characterized by a sudden change in the characteristics of the medium (such as pressure, temperature, or speed) as a positive step function. The corresponding negative step is an expansion wave. A shock wave travels through the medium at a higher speed than a normal wave.\n\nUnlike solitons (another kind of nonlinear wave), the energy of a shock wave dissipates relatively quickly with distance. Additionally, the companion expansion wave from a shock approaches, and eventually merges with the shock, partially cancelling it out. Thus the sonic boom associated with the passage of an aircraft is the sound wave resulting from the degradation and merging of the shock wave-expansion wave pair produced by the passage of a supersonic aircraft.\n\nContents [hide]\n1 Shock waves in supersonic flows \n2 Shock waves due to nonlinear steepening \n3 Analogies \n4 Types of shock wave \n5 External links \n6 See also \n \n\n\n[edit]\nShock waves in supersonic flows\n \nPressure-time diagram at a point for a shock wave propagating past the observerThe shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. Two other methods are isentropic and Prandtl-Meyer compressions. The method of compression of a gas results in different temperatures and densities for a given pressure ratio, which can be analytically calculated for a non-reacting gas. A shock wave compression results in a loss of total pressure, meaning that it is a less efficient method of compressing gases for some purposes, for instance in the intake of a scramjet. The appearance of pressure-drag on supersonic aircraft is mostly due to the effect of shock compression on the flow.\n\nWhen an object (or disturbance) moves faster than the information about it can be propagated into the surrounding fluid, fluid near the disturbance cannot react or "get out of the way" before the disturbance arrives. In a shock wave the properties of the fluid (density, pressure, temperature, velocity, Mach number) change almost instantaneously. Measurements of the thickness of shock waves have resulted in values approximately one order of magnitude greater than the mean free path of the gas investigated.\n\nShock waves are not sound waves; a shock wave takes the form of a very sharp change in the gas properties on the order of a few mean free paths (roughly micro-meters at atmospheric conditions) in thickness. Shock waves in air are heard as a loud "crack" or "snap" noise. Over time a shock wave can change from a nonlinear wave into a linear wave, degenerating into a conventional sound wave as it heats the air and loses energy. The sound wave is heard as the familiar "thud" or "thump" of a sonic boom, commonly created by the supersonic flight of aircraft.\n\n[edit]\nShock waves due to nonlinear steepening\nShock waves can form due to steepening of ordinary waves. The best-known example of this phenomenon is ocean waves that form breakers on the shore. In shallow water, the speed of surface waves is dependent on the depth of the water. An incoming ocean wave has a slightly higher wave speed near the crest of each wave than near the troughs between waves, because the wave height is not infinitesimal compared to the depth of the water. The crests overtake the troughs until the leading edge of the wave forms a vertical face and spills over to form a turbulent shock (a breaker) that dissipates the wave's energy as sound and heat.\n\nSimilar phenomena affect strong sound waves in gas or plasma, due to the dependence of the sound speed on temperature. Strong waves heat the mediu
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In the steady state, water flows out of the aqueduct, leaving the force on the floor&walls unchanged. However, then the barge is first introduced, the displaced water flows as a wave, causing greater forces near the wave-front.
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I wasn't sure of what level of detail you were looking for.\n\nEasier to understand:\nhttp://ga.water.usgs.gov/edu/wwvisit.html\n\nhttp://www.humboldt.edu/~ere_dept/marsh/flow1.html\n\nMore difficult to understand:\nhttp://waterhome.brc.tamus.edu/texasyst/household.html\n\nhttp://www.knovel.com/knovel2/Toc.jsp?SpaceID=10086&BookID=290
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Go to this page and look at the second picture.\nhttp://www.grc.nasa.gov/WWW/K-12/WindTunnel/Activities/Pascals_principle.html\n\nThe water in both tubes is the same amount. When the little box goes down, it forces up the big box. \n(Go here for a demonstration.) http://webphysics.davidson.edu/physlet_resources/bu_semester1/c23_pressure_pascal.html\n\nNow look at the letters on the picture. (W, A, D, F). Note which ones are ones and twos. (F1, F2, etc.) Now look at the formulas below. Don't be scared! Just compare the letters in the picture to the letters in the formula. Do you see which ones are equal? Think about what the letters mean in the formulas.\n\nNow, after you know how to describe the picture, try to read everything on the page.\nOnce you've done that, try the exercises below.\n\nYou have just looked at the hydraulic pump.\nFor another example, go here: http://www3.fhs.usyd.edu.au/bio/fluids/pascal/pp1.html\n\nThe reason why this all works is because the pressure is the same in all directions. (See here for a cool picture) http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Pressure/HydroStatic.html\n\nHope this helps. Just look at the pictures, it helped me. Good luck on your quiz!
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Dear Editor,\n\nI am a student concerned about the recent water supply shortages caused by mismanagement by the water supply authorities.  The shortages have caused me no end of misery.  Not only am I not able to take a shower, or flush my toilet consistently, I am becoming dehydrated from lack of fresh water to drink.  As a result, I can't do my own homework and must instead ask strangers on the internet to do it for me.\n\nI would appreciate it if you could write an editorial on the subject to pressure the authorities to increase the water flow.\n\nSincerely,\n\nMy name, not somebody else that I copied from.
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well, others might have told you it is pressure, and actually even i would have gone for it!\nbut since you have mentioned in particular on a fluid, then this ratio can also be called as Bulk's modulus(though this applies even to solids)\nit can also be the coeff of viscosity taken velocity gradient times\nthere can be various other depictions also
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This is a classic problem from hydrodynamics textbooks. The short answer is, it is approximately simple harmonic motion. You can compute the restoring force caused by the displacement of the liquid if you depress a floating boat (Archimedes principle) and that then, balanced with the weight of the boat, creates the conditions for simple harmonic motion. You can approximate the period and amplitude of motion etc. \n\nHowever it gets more complicated than this of course:\n\na. There are damping forces caused by the motion of the boat through the water and the air\n\nb. The water is not completely incompressible, and the density of the water varies some with depth (a tiny effect)\n\nc. There are surface tension effects and entrainment effects\n\nd. The motion of the boat will be more complicated than simple linear motion in one dimension\n\ne. There will probably be deformation effects on the boat, changing its shape\n\nf. gravity is not constant as the boat is moving up and down a small distance in a gravity gradient\n\nand so on. \n\nHowever, the REASON that sines and cosines are so prevalent everywhere in physics is because simple harmonic motion is such a good approximation for so many things. \n\nWhy is this?\n\nWell consider Newton's Second law: F=ma, where F is force, m is mass and a is acceleration. Newton's second law is not always true, in the quantum world and in relativistic situations, but it is true under many conditions, so it is a good place to start. \n\nIn general, the force F will be some sort of nonlinear function of position x:\n\nF=F(x)\n\nHowever, if x is small, then we can approximate F(x) by a McLaurin series:\n\nF ~ F(0) + x F'(0) + h.o.t. \n\n(h.o.t. is a common acronym for higher order terms).\n\nThis then produces the equation for simple harmonic motion, when substituted into Newton's 2nd law:\n\nF(0) + xF'(0) = m d/dt(d/dt(x))\n\nMany other equations in physics like Schrodinger's equation, or wave equations with forcing, or the heat equation, or the inhomogeneous Laplace's equation include 2nd order derivatives, and can similarly be put in some form where simple harmonic motion is the result. So as strange as it seems when you are just learning about SHM in physics, it really is everywhere in all kinds of unexpected places! \n\n\nOne of my favorites is the waves of heat and cold that are travelling down into the earth from the seasonal forcing produced at the surface. Drilling down, one can observe these waves of hot and cold (with some diffusion) going back many years.
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http://en.wikipedia.org/wiki/Sound_waves
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In air sound moves away from a source at a speed of 333 m/s. That means that the pressure waves in the air that represent the sound move at that speed.\n\nNow imagine an airplane moving faster than the speed of sound. This means that the source of the sound moves faster than the sound itself. The result is that the sound waves no longer travel out ward in circles. Instead they add up to form a shockwave, a broadening cone of  compressed air trailing diagonally from the nose of the plane. When the cone passes through a listener he will here the sonic boom, which is nothing else than the sum of several seconds of airplane sound added up.\n\nThere is a physical analogue to this: a duck swimming in a pond moves faster than the waves that he makes can travel outward.\nThe shock wave is visible as a diagonal trailing outwards from the belly of the duck.
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Your analogy doesn't represent the problem at all.  \n\nWhen we say a particle is treated as a wave it refers to the particle actually not existing at any particular point.  It actually exists at all of points in some region with a certain probability (it is everywhere at once).
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hydrological AND hydrodynamical engineering
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Ocean Waves are mechanical waves that propagate along the interface between water and air; the restoring force is provided by gravity, and so they are often referred to as surface gravity waves. As the wind blows, pressure and friction forces perturb the equilibrium of the ocean surface. These forces transfer energy from the air to the water, forming waves. In the case of monochromatic linear plane waves in deep water, particles near the surface move in circular paths, making ocean surface waves a combination of longitudinal (back and forth) and transverse (up and down) wave motions. When waves propagate in shallow water, (where the depth is less than half the wavelength) the particle trajectories are compressed into ellipses. As the wave amplitude (height) increases, the particle paths no longer form closed orbits; rather, after the passage of each crest, particles are displaced a little forward from their previous positions, a phenomenon known as Stokes drift. A good illustration of the wave motion is given by *Prof. Robert Dalrymple Java applet
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It's similar to the Venturi Principle, where the jet creates a vacuum effect as it punches a "hole" through the air above the water. Since nature proverbially abhors a vacuum, the surrounding air and the water beneath the hole rush to fill it.\n\nYou can create a similar effect by directing the stream from a compressed air blower between two parallel pieces of streamer material. You would think that the pieces of crepe paper would split away from one another; actually, they tend to come together.
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click here:http://www.theenvironmentsite.org/Forum/viewtopic.php?t=663\nhttp://news.nationalgeographic.com/kids/2004/08/waves.html
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Here is a website taken from a book titled "California Rivers and Streams" that does an excellent job of explaining river channel morphology. \nhttp://www.ucpress.edu/books/pages/6664/6664.ch04.html\n\nIt discusses and explains channel cross sections, channel patterns of both single and multichannel rivers, channel patterns in deltas, and includes both diagrams and a list of references. The book is an excellent resource even if you are not specifically interested in California Rivers.
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Its actually derived from Maxwell's Wave Equations, see source. Its too complex and requires mathematic symbols, so I can't type it here.