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Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables.This technique can simplify and parameterize problems where measured units are involved.
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed.
Quantity (common name/s) (Common) symbol/s Defining equation SI unit Dimension Temperature gradient: No standard symbol K⋅m −1: ΘL −1: Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer
The SI has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m 2), the SI derived unit of area; and the kilogram per cubic metre (kg/m 3 or kg⋅m −3), the SI derived unit of density.
The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma), is a volume-specific quantity defined as the weight W divided by the volume V of a material: = / Equivalently, it may also be formulated as the product of density, ρ, and gravity acceleration, g: = Its unit of measurement in the International System of Units (SI) is newton per cubic metre (N/m 3), with ...
Si 3 N 4 with CNTs 26 °C 9.142 [20] Si 3 N 4 without CNTs 26 °C 8.605 [20] Steel, stainless 304A at 27 °C: 4.2 [15] Pyrolytic graphite, normal to layers 3.6 Steel, stainless 310 at 25 °C: 3.352 [21] Inconel 600 at 25 °C: 3.428 [22] Quartz: 1.4 [15] Sandstone 1.15 Ice at 0 °C 1.02 Silicon dioxide (polycrystalline) 0.83 [15] Brick, common 0 ...
For example, such a regulation might limit the concentration of NOx to 55 ppmv in a dry combustion exhaust gas corrected to 3 volume percent O 2. As another example, a regulation might limit the concentration of particulate matter to 0.1 grain per standard cubic foot (i.e., scf) of dry exhaust gas corrected to 12 volume percent CO 2.