Search results
Results from the WOW.Com Content Network
In the case of laminar flow, for a circular cross section: =, =, where Re is the Reynolds number, ρ is the fluid density, and v is the mean flow velocity, which is half the maximal flow velocity in the case of laminar flow. It proves more useful to define the Reynolds number in terms of the mean flow velocity because this quantity remains well ...
In a flow distribution network that progresses from a large tube to many small tubes (e.g. a blood vessel network), the frequency, density, and dynamic viscosity are (usually) the same throughout the network, but the tube radii change. Therefore, the Womersley number is large in large vessels and small in small vessels.
In that case, the velocity of flow varies from zero at the walls to a maximum along the cross-sectional centre of the vessel. The flow profile of laminar flow in a tube can be calculated by dividing the flow into thin cylindrical elements and applying the viscous force to them. [5] Another example is the flow of air over an aircraft wing.
Poiseuille flow in a cylinder of diameter h; the velocity field at height y is u(y).. Murray's original derivation uses the first set of assumptions described above. She begins with the Hagen–Poiseuille equation, which states that for fluid of dynamic viscosity μ, flowing laminarly through a cylindrical pipe of radius r and length l, the volumetric flow rate Q associated with a pressure ...
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
Often expressed in cm/s. This value is inversely related to the total cross-sectional area of the blood vessel and also differs per cross-section, because in normal condition the blood flow has laminar characteristics. For this reason, the blood flow velocity is the fastest in the middle of the vessel and slowest at the vessel wall.
In fluid mechanics and transport phenomena, an eddy is not a property of the fluid, but a violent swirling motion caused by the position and direction of turbulent flow. [4] A diagram showing the velocity distribution of a fluid moving through a circular pipe, for laminar flow (left), time-averaged (center), and turbulent flow, instantaneous ...
A schematic diagram of the Blasius flow profile. The streamwise velocity component () / is shown, as a function of the similarity variable .. Using scaling arguments, Ludwig Prandtl [1] argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge of the plate).