By Josef Kunes
Dimensionless amounts, comparable to π, e, and φ are utilized in arithmetic, engineering, physics, and chemistry. in recent times the dimensionless teams, as established intimately right here, have grown in value and significance in modern mathematical and desktop modeling in addition to the normal fields of actual modeling. This e-book deals the main finished and recent source for dimensionless amounts, offering not just a precis of the amounts, but additionally a rationalization in their actual ideas, components of use, and different particular houses throughout a number of appropriate fields. proposing the main whole and obviously defined unmarried source for dimensionless teams, this e-book can be crucial for college students and researchers operating around the sciences.
- Includes nearly 1,200 dimensionless quantities
- Features either vintage and newly constructing fields
- Easy to exploit with transparent association and citations to appropriate works
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Additional resources for Dimensionless Physical Quantities in Science and Engineering
It is especially applied in chemical technology. Its inverse value is called the Smoluchowski number Sm (p. 86). Info: [A29],[A35]. Martin Hans Christian Knudsen (p. 420). 32 Mass Fraction M mA M5 P mi mA (kg) À mass of substance A; mi (kg) À mass of individual substances. It characterizes the mass fraction of partial components, for example, in mixing. Physical chemistry. Info: [C85]. 33 Mole Fraction xi xi 5 ni Ni 5 n N ni (À) À number of moles of ith substance; n (À) À total number of moles in a mixture; Ni (À) À number of molecules of ith substance; N (À) À total number of molecules in a mixture; NA (À) À Avogadro number (p.
75 Void Fraction ε ε5 Va Vm Va (m3) À volume of void space; Vm (m3) À total or bulk volume of material including the solid and void components. Physics and Physical Chemistry 33 It expresses the ratio of the void space volume in the material to the total material volume. Physics. Fluid mechanics. Flow through a porous material. Drying. 19 In a dimensionless shape it expresses the wave length. The expressions (1) and (2) are different forms only. For example, the expression (3) is used with electromagnetic waves.
Heat) (p. 37). For flowing fluid, it expresses the inertia-to-friction ratio. It characterizes the hydrodynamic influence of the inertia and friction forces of the streaming fluid in a chemical reaction. The relation of the Schmidt number (p. 263) and the Prandtl number (p. 197) to the Damk˝o hler numbers (p. 36, 38) is obvious from the expressions (2) and (3). Info: [A4],[A23],[A26],[A29],[B11]. Gerhard Friedrich Damko˝ hler (see above). ) time Ah3 (p. 35). ) Contact Dj, Ko Dj 5 k1 ϕ1 ðck Þτ 5 τ τr k1 ϕ1 (ck) (s21) À unit speed at a given concentration; k1 (À) À virtual speed constant of direct reduction process; ck (À) À concentration; τ (s) À contact time; τ r (s) À decay time.