Dimensional analysis physical quantity, defined

A related concept to dimensional analysis is quantity calculus, a method we find particularly useful when it comes to setting out table header rows and graph axes. Quantity calculus is the handling of physical quantities and their units using the normal rules of algebra. A physical quantity is defined by a numerical value and a unit ... 

Because the quantitative analysis of transport processes in terms of the microscopic description of turbulence is difficult, Kdrmdn suggested (K2) the use of a macroscopic quantity called eddy viscosity to describe the momentum transport in turbulent flow. This quantity, which is dimensionally and physically analogous to kinematic viscosity in the laminar motion of a Newtonian fluid, is defined by... 

This step is one of the most difficult and is, of course, extremely important because all pertinent variables have to be included in the analysis. The term variable includes any physical quantity, dimensional and apparently non-dimensional constant that plays a role in the phenomenon under investigation. The determination of the variables must take into account practical knoivledge of the problem as ivell as the physical laivs governing the phenomenon. Variables typically include the parameters that are necessary not only to describe the geometry of the system (such as the diameter of the pipe in the example beloiv), but also to define the fluid properties (such as the density, viscosity, thermal capacity, thermal conductivity of the fluid, the diffusion coefficient for one species in the working fluid, etc.) as well as to indicate the external effects that influence the system (such as the driving pressure drop in the further discussed cases). 

Unit for temperature The SI unit system defines a base unit for temperature kelvin with the dimension ( ). The physical origin of this definition is the thermodynamic temperature scale where the temperature unit is defined as being proportional to the kinetic mean energy of the molecules in a system of matter. Therefore, for dimensional analysis it is admissible to use the same unit for temperature quantities as for energy, if this is expedient. In this case, the dimension for temperature is (L MT ). 

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