what is the application of the bernoulli equation in real life?
347099
I have used the Bernoulli equation to calculate pressure drop through piping and to size pumps (determine required head pressure).  You can't get much more real than that.
892428
To provide a simple answer that does not involve a lot of mathematics, differential equations are used in almost every scientific field to provide a mathematical description of a process.  They are useful because most processes can be described in terms of changes that result from small differences in elements of the process.  When these small changes are represented in mathematical form the result is a differential equation.  Because the changes are small, it is possible to make assumptions that simplify the expression of the process.\n\nFor example, consider the discharge of a capacitor into a resistor.  We know that the charge stored in the capacitor is Q = V*C, where V=voltage on the capacitor, and C is the capacitance.  A small change in charge, dQ will cause a small change in voltage, dV.  The voltage across the resitor will be V, and the current in the resitor V/R.  The current is the amount of charge divided by the time, or change in current is change in charge divided by change in time, or dI = dQ/dt.  (Note: here is the simplifying assumption:) For very small changes in Q, we can assume that the voltage does not change, so that the current is constant in that interval.  Therefore dV=(1/C)dQ = idt = (V/C*R)dt; rewriting this as a differential equation gives\n\ndV/dt = V/(C*R),\n\nwhich describes the discharge of a capacitor into a resistor.  This is a particularly simple example, and differential equations of more complex processes can get very messy, and many cannot be solved explicitly.
702620
Applications huh?  Here's a practical aircraft application.\n\nWell I worked on aircrafts before and our shock struts ( like shock absorbers) are filled with nitrogen.  Depending on the weight of the aircraft the volume may decrease or increase (therefore rising or lowering the aircraft)  So we can ensure that we have enough nitro in there we have a gauge that tells us the pressure.  We compare that pressure to the height of the strut (which gives us the volume) and check our chart (which utilizes boyles law) to ensure or pressure is appropriate for the volume.
110391
There are many practical applications for imaginary numbers. \n\nFirst, nothing in mathematics really EXISTS. Mathematics is just a way of creating a set of rules, then seeing what can be proven from those rules. Applied mathematics is a procedure where a subset of the material from pure mathematics is used to model something in which we are interested, which usually is something in the real world. \n\nIf the rules for manipulating things for imaginary numbers are useful, then that is a good thing. However, they are useful, because they let one solve a lot of problems easier than if we had to make more cumbersome manipulations without them. \n\nFor example, in any problem involving waves and frequencies, they are very useful, because of Euler's formula:\n\ne^(ix)=cos(x)+i sin(x)\n\nThis lets one manipulate trigonometric quantities easily in a compact form. \n\nAll of electrical engineering makes extensive use of this therefore, especially when power is involved, because AC is so prevalent. \n\nSolving many equations are far easier when imaginary numbers are used, even if the initial problem is all real, and so is the final answer. \n\nIntegrals that are used in all application areas are sometimes far more easily solved using complex integration. \n\nAll of quantum mechanics is deepy connected with imaginary numbers. The Schrodinger equation contains imaginary numbers. The answers are complex functions. Their modulus squared produces the real probability functions we use. \n\nImaginary numbers are used throughout physics. \n\n \nTo paraphrase a famous saying, the quickest way to real results is through the complex plane. \n\n(the real quote by Jacques Hadamard is more accurately translated as "The shortest path between two truths in the real domain passes through the complex domain.")\n\nThe more important question underlying this, is, why is mathematics so unreasonably effective at modelling things we are interested in? (see references).
319305
There is a mathmatical equation for the Eiffel tower...this way you have a visual that everyone knows and the info is on-line
78965
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.
478107
It is called the equation of time. It isn't really statistics though.
256452
Modelling actions of natural dacay.\n\nAmortization.  The interest on a loan is calculated on the remaining balance.\n\nFluid dynamics.  The fluid pressure in a silo is a log function of how full it is.  As the level drops, the pressure drops logarithmically.\n\nElectronics.  The time constants of capacitors and inductors\nare logarithmic.\n\nThe list goes on...
73968
I have never used them, but I have heard they have uses in certain kinds of electrical engineering.  I think it involves phase shifts of period functions like sine waves.  Also, there are occasional problems where you start in the real numbers and end in the real numbers, but by doing the problem in the complex domain, certain difficult problems become solvable.  I think Cauchy integrals are used for this purpose.
1118780
Your question is very open.\n\nheat equations very general can be:\napplied heat = specific heat x mass x increase of temperature\napplied heat = heat capacity x increase of temperature\napplied heat = mass x specific melt heat\napplied heat = mass x specific evaporation heat (at boiling point)\nHeat from a supply = power x time.\nCombinations and others are possible.\n\nwave equation can be x = A sin( 2pi t/T)\nThere are more possibilities.
620893
The best way to work this out would be to plot a speed time graph for the information.\n\nOr you could express it as a simultaneous equation.
308356
Bernoulli's Principle.\n\nThe principle states, more or less, that in fluid (or, in your case, air) flow, an increase in velocity occurs simultaneously with decrease in pressure. More specifically, the sum of all forms of energy in a fluid flowing along an enclosed path is the same at any two points in that path. The *only* cause of the change in fluid velocity is the difference in pressures either side of it. \n\nIn a fluid flow with no viscosity, and therefore one in which a pressure difference is the only accelerating force, it is equivalent to Newton's laws of motion.
888996
http://en.wikipedia.org/wiki/Indefinite_and_fictitious_large_numbers\n\nlook at that
84915
The Fourier transform is used throughout physics. All the Fourier representation is, is an expansion of some variable, function or data in terms of sines and cosines.\n\nThis is valuable because:\n1. Simple harmonic oscillators are a very valuable model in physics (in mechanics, quantum mechanics, electromagnetism, etc), and the solutions of the simple harmonic equation are sines and cosines. Therefore sines and cosines are a natural basis to use in physics. \n2. The eigenfunctions of the infinitesimal generator of translations are complex exponentials, which can be expanded easily in the sum of a sine and a cosine by Euler's formula. \n\nTherefore, an expansion in sines and cosines is very valuable, because they can be used as a parsimonius representation of many phenomena in physics. In otherwords, it is a compact way to describe many physical processes. \n\nAnother reason that the Fourier transform is important in physics is that it is very useful for solving equations in physics like the heat equation, Maxwell's equations, fluid mechanics equations, the wave equation, etc. \n\nAnother reason that the Fourier transform is useful in physics is that many important physical properties are captured in things like dispersion relations. This even lead to Schrodinger's equation. Fourier transform pair uncertainty principles are reflected in the Heisenberg uncertainty principle. \n\nHow does the Fourier transform show up in nature? All over the place, such as in the spectra of gases, stars, etc. Rainbows are a visual example of a Fourier transform in nature.
889683
There is, it is called Standarad Deviation, if you have a decent Scientific Calculator it shouyld show how to use it.
76447
p1v1t1=p2v2t2\n\nSee Bernoulli's theorem and Pascals Law
118366
the explicit formula is related to bernoulli numbers