Fluid mechanics, dimensionless numbers

Dimensionless numbers are not the exclusive property of fluid mechanics but arise out of any situation describable by a mathematical equation. Some of the other important dimensionless groups used in engineering are Hsted in Table 2. 

Heat Transfer In general, the fluid mechanics of the film on the mixer side of the heat transfer surface is a function of what happens at that surface rather than the fluid mechanics going on around the impeller zone. The impeller largely provides flow across and adjacent to the heat-transfer surface and that is the major consideration of the heat-transfer result obtained. Many of the correlations are in terms of traditional dimensionless groups in heat transfer, while the impeller performance is often expressed as the impeller Reynolds number. 

The behavior of the gas as it flows down the tube is controlled by fluid mechanics and a complete investigation wouldbe lengthy and outside the scope of this book. It is enough to say that the Reynolds number, which is a dimensionless parameter that characterizes the... 

There are three techniques of developing the dimensionless similarity parameters. The use of Buckingham s pi theorem can be found in most fluid mechanics books, where the variables of importance are used to determine the number of dimensionless parameters that should describe an application and help to identify these parameters. One difficulty with Buckingham s pi theorem is the unspecified form of the dimensionless numbers, which can result in unusual combinations of parameters. 

The second technique is physical insight into the problem, where ratios of forces or mass/heat transport determinants are factored to develop dimensionless numbers. This technique can also be found in most fluid mechanics texts. 

Rn Reynolds number a fluid mechanics term. It is a dimensionless ratio of... 

The most important dimensionless number in fluid mechanics is the Reynolds number (Re), which is defined as... 

Boucher D. F. and Alves G. E. (1959) Dimensionless numbers for fluid mechanics, heat transfer, mass transfer, and chemical reaction. Chem. Eng. Prog. 55, 55-64. 

Incidentally, Bowes discussed in his book, Self-Heating Evaluating and Controlling the Hazards , some dimensionless numbers, such as the Grashof number, the Reynolds number and the Prandtl number, which are all used in order to discuss the convective flow in fluid mechanics. 

In order to understand the fluid mechanics in microchannel systems one has to calcrdate the Reynolds numbers in a given system. The dimensionless Rejmolds number (Re) is the ratio of the inertial forces to the viscous forces acting on a small element of fluid, and can be seen as the ratio of shear stress due to turbulence to shear stress due to viscosity. 

The Reynolds number is undoubtedly the most famous dimensionless parameter in fluid mechanics. It is named in honour of Osborne Reynolds, a British engineer who first demonstrated in 1883 that a dimensionless variable can be used as a criterion to distinguish the flow patterns of a fluid either being laminar or turbulent. Typically, a Reynolds number is given as follows ... 

Boucher DF, Alves GE (1959) Dimensionless Numbers for Fluid Mechanics, Heat Transfer, Mass Transfer and Chemical Reaction. Chemical Engineering Progress 55 (9) 55-64... 

In dealing with viscoelastic fluids, especially under turbulent flow conditions, it is necessary to introduce a dimensionless number to take account of the fluid elasticity [29-33], Either the Deborah or the Weissenberg number, both of which have been used in fluid mechanical studies, satisfies this requirement. These dimensionless groups are defined as follows ... 

Euler number (Eu) - A dimensionless quantity used in fluid mechanics, defined hy Eu = Ap/pv, where p is pressure, p is density, and V is velocity. [2]... 

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