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In non ideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section.
In free space, where ε = ε 0 and μ = μ 0 are constant everywhere, Maxwell's equations simplify considerably once the language of differential geometry and differential forms is used. The electric and magnetic fields are now jointly described by a 2-form F in a 4-dimensional spacetime manifold.
For materials without polarization and magnetization, the constitutive relations are (by definition) [9]: 2 =, =, where ε 0 is the permittivity of free space and μ 0 the permeability of free space. Since there is no bound charge, the total and the free charge and current are equal.
A medium with a permeability of 1 darcy permits a flow of 1 cm 3 /s of a fluid with viscosity 1 cP (1 mPa·s) under a pressure gradient of 1 atm/cm acting across an area of 1 cm 2. Typical values of permeability range as high as 100,000 darcys for gravel, to less than 0.01 microdarcy for granite. Sand has a permeability of approximately 1 darcy ...
The lumped parameter model consists in a system of ordinary differential equations that adhere to the principles of conservation of mass and momentum balance. The model is obtained exploiting the electrical analogy where the current represents the blood flow, the voltage represents the pressure difference, the electric resistance plays the role of the vascular resistance (determined by the ...
The concept of permeability is of importance in determining the flow characteristics of hydrocarbons in oil and gas reservoirs, [4] and of groundwater in aquifers. [5]For a rock to be considered as an exploitable hydrocarbon reservoir without stimulation, its permeability must be greater than approximately 100 md (depending on the nature of the hydrocarbon – gas reservoirs with lower ...
This is a very important mechanism in biology where fluids inside a blood vessel need to be regulated and controlled. Permeation can occur through most materials including metals, ceramics and polymers. However, the permeability of metals is much lower than that of ceramics and polymers due to their crystal structure and porosity.
Differences in vascular permeability between normal tissue and a tumor. Vascular permeability, often in the form of capillary permeability or microvascular permeability, characterizes the capacity of a blood vessel wall to allow for the flow of small molecules (drugs, nutrients, water, ions) or even whole cells (lymphocytes on their way to the site of inflammation) in and out of the vessel.