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In many engineering applications the local flow velocity vector field is not known in every point and the only accessible velocity is the bulk velocity or average flow velocity ¯ (with the usual dimension of length per time), defined as the quotient between the volume flow rate ˙ (with dimension of cubed length per time) and the cross sectional area (with dimension of square length):
In fluid mechanics, plug flow is a simple model of the velocity profile of a fluid flowing in a pipe. In plug flow, the velocity of the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe. The plug flow model assumes there is no boundary layer adjacent to the inner wall of the pipe.
Four pulsatile flow profiles in a straight tube are shown. The first graph (in blue) shows the pressure gradient as a cosine function, and the other graphs (in red) show dimensionless velocity profiles for different Womersley numbers. The pulsatile flow profile is given in a straight pipe by
In fluid dynamics, the entrance length is the distance a flow travels after entering a pipe before the flow becomes fully developed. [1] Entrance length refers to the length of the entry region, the area following the pipe entrance where effects originating from the interior wall of the pipe propagate into the flow as an expanding boundary layer.
The velocity profile should be referred to as the axial velocity profile. As the velocity vector can be resolved into three mutually orthogonal components, the velocity profile only represents the axial component of velocity. fig.(2) showing the Swirl Angle which explains the definition of flow swirl and swirl angle.
The point where the velocity profile essentially reaches the asymptotic velocity is the boundary layer thickness. The boundary layer thickness is depicted as the curved dashed line originating at the channel entrance in Figure 1. It is impossible to define an exact location at which the velocity profile reaches the asymptotic velocity.
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.
In incompressible flow, the velocity profile is linear because the fluid temperature is constant. When the upper and lower walls are maintained at different temperatures, the velocity profile is more complicated. However, it has an exact implicit solution as shown by C. R. Illingworth in 1950. [6]