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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.
Blood resistance varies depending on blood viscosity and its plugged flow (or sheath flow since they are complementary across the vessel section) size as well, and on the size of the vessels. Assuming steady, laminar flow in the vessel, the blood vessels behavior is similar to that of a pipe.
Consequently, if a liquid has dynamic viscosity of n centiPoise, and its density is not too different from that of water, then its kinematic viscosity is around n centiStokes. For gas, the dynamic viscosity is usually in the range of 10 to 20 microPascal-seconds, or 0.01 to 0.02 centiPoise. The density is usually on the order of 0.5 to 5 kg/m^3.
A flow that is not a function of time is called steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Time dependent flow is known as unsteady (also called transient [8]). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference.
Superfluid is the state of matter that exhibits frictionless flow, zero viscosity, also known as inviscid flow. [4] To date, helium is the only fluid to exhibit superfluidity that has been discovered. Helium-4 becomes a superfluid once it is cooled to below 2.2K, a point known as the lambda point. [13]
Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. [1] For liquids, it corresponds to the informal concept of thickness; for example, syrup has a higher viscosity than water. [2]
However, often the non-Newtonian effect is very small due to various reasons. Thus, it is important to know about the blood rheology. One of the characteristics of blood that affects the work required to cause the blood to flow through the arteries is the viscosity of blood. The viscosity of blood is in the range of 3 to 6 cP, or 0.003 to 0.006 ...
For an incompressible and isotropic Newtonian fluid in laminar flow only in the direction x (i.e. where viscosity is isotropic in the fluid), the shear stress is related to the strain rate by the simple constitutive equation = where is the shear stress ("skin drag") in the fluid,