Abstract
In this chapter we apply the macroscopic balance equations that have been developed in Chap. 3 to study a few important problems. First, the pipe flow of a Newtonian fluid is considered in Sect. 5.1; then, in Sects. 5.2 and 5.3, this case is generalized to non-Newtonian fluids, stressing how the velocity profiles and the consequent pressure drops are functions of the fluid constitutive equations. In Sect. 5.4. we analyze the flow of a fluid across porous media, stressing when and how a fixed bed becomes fluidized. Then, in Sect. 5.5 we start considering non-stationary flows, introducing the Quasi Steady State (QSS) assumption that will be used extensively in the following. Finally, in Sect. 5.6, we study capillary flows, i.e. the fluid flows that are driven by surface tension effects.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Named after Jean Léonard Marie Poiseuille (1797–1869), a French physicist and physiologist.
- 2.
This notation can be misleading, as in aerodynamic applications the dynamic pressure is the kinetic energy per unit volume of a uniform stream.
- 3.
Named after Maurice Marie Alfred Couette (1858–1943), a French physicist.
- 4.
Named after Eugene Cook Bingham (1878–1945), an American chemist.
- 5.
The exponent in Eq. (4.2.2) is generally indicated by n, despite the fact that it is not an integer. Also, note that K is not a viscosity, unless n = 1.
- 6.
It refers to the fluid flowing through preferential channels or rivulets within the medium, where it encounters a smaller resistance than elsewhere.
- 7.
Named after Henry Philibert Gaspard Darcy (1803–1858), a French engineer.
- 8.
The coefficient κ is sometimes denoted as Darcy permeability, to distinguished it to the mass transfer coefficient, having the units of a velocity, that in the biomedical literature is, unfortunately, also called permeability.
- 9.
The mean velocity in porous media is often called superficial velocity and denoted by v s .
- 10.
With this definition, the hydraulic radius coincides with the radius of the cylindrical tubes. Note that in many textbooks the hydraulic radius is defined as V w /S w .
- 11.
Sometimes it is preferable to use the Carman-Kozeny equation, where the coefficient 150 is replaced by 180.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Mauri, R. (2015). Laminar Flow Fields. In: Transport Phenomena in Multiphase Flows. Fluid Mechanics and Its Applications, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-15793-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-15793-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15792-4
Online ISBN: 978-3-319-15793-1
eBook Packages: EngineeringEngineering (R0)