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Fig. 2. Pressure curve for an ideal rubber balloon. When air is first added to the balloon, the pressure rises rapidly to a peak. Adding more air causes the pressure to drop. The two points show typical initial conditions for the experiment. When the valve is opened, the balloons move in the direction indicated by the arrows.
A powerful tool in physics is the concept of dimensional analysis and scaling laws. By examining the physical effects present in a system, we may estimate their size and hence which, for example, might be neglected. In some cases, the system may not have a fixed natural length or time scale, while the solution depends on space or time.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
Some introductory physics textbooks still define the pressure-temperature relationship as Gay-Lussac's law. [ 6 ] [ 7 ] [ 8 ] Gay-Lussac primarily investigated the relationship between volume and temperature and published it in 1802, but his work did cover some comparison between pressure and temperature. [ 9 ]
The Laplace pressure is the pressure difference between the inside and the outside of a curved surface that forms the boundary between two fluid regions. [1] The pressure difference is caused by the surface tension of the interface between liquid and gas, or between two immiscible liquids.
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
In mathematics, the Navier–Stokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using ...
[2] [3] Another problem lies within the mathematical framework of the Standard Model itself—the Standard Model is inconsistent with that of general relativity, to the point that one or both theories break down under certain conditions (for example, within known spacetime singularities like the Big Bang and the centres of black holes beyond ...