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In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities.
A Newtonian fluid is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate: = These fluids have a constant viscosity, μ, across all shear rates and include many of the most common fluids, such as water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.
Log-log linear models are widely used in various fields, including economics, biology, and physics, where many phenomena exhibit power-law behavior. They are also useful in regression analysis when dealing with heteroscedastic data, as the log transformation can help to stabilize the variance.
Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity. Mechanical power is also described as the time derivative of work.
The red curve shows the power in the load, normalized relative to its maximum possible. The dark blue curve shows the efficiency η. The efficiency η is the ratio of the power dissipated by the load resistance R L to the total power dissipated by the circuit (which includes the voltage source's resistance of R S as well as R L):
The Stefan–Boltzmann law gives the power emitted per unit area of the emitting body, = (,) Note that the cosine appears because black bodies are Lambertian (i.e. they obey Lambert's cosine law ), meaning that the intensity observed along the sphere will be the actual intensity times the cosine of the zenith angle.
The wind profile power law relationship is = where is the wind speed (in metres per second) at height (in metres), and is the known wind speed at a reference height .The exponent is an empirically derived coefficient that varies dependent upon the stability of the atmosphere.
In physics and many other areas of science and engineering the intensity or flux of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. [a] In the SI system, it has units watts per square metre (W/m 2), or kg⋅s −3 in base units.