Entrance length (fluid dynamics)
[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.
Many different entrance lengths exist to describe a variety of flow conditions.
Hydrodynamic entrance length describes the formation of a velocity profile caused by viscous forces propagating from the pipe wall.
Thermal entrance length describes the formation of a temperature profile.
[2] Awareness of entrance length may be necessary for the effective placement of instrumentation, such as fluid flow meters.
[4] For the conservation of mass to hold true, the velocity of layers of the fluid in the center of the pipe increases to compensate for the reduced velocities of the layers of fluid near the pipe surface.
After this region, the velocity profile is fully developed and continues unchanged.
But this is not the fully developed fluid flow until the normalized temperature profile also becomes constant.
[6] In case of laminar flow, the velocity profile in the fully developed region is parabolic but in the case of turbulent flow it gets a little flatter due to vigorous mixing in radial direction and eddy motion.
The velocity profile remains unchanged in the fully developed region.
Hydrodynamic Fully Developed velocity profile Laminar Flow :
, is highest at the pipe inlet, where the boundary layer thickness is the smallest.
[6] In a fully developed region, the pressure gradient and the shear stress in flow are in balance.
[8] Thus, the entry length in turbulent flow is much shorter as compared to laminar one.
In most practical engineering applications, this entrance effect becomes insignificant beyond a pipe length of 10 times the diameter and hence it is approximated to be:
In the case of a non-circular cross-section of a pipe, the same formula can be used to find the entry length with a little modification.
is the Perimeter of the wet part of the pipe By doing a force balance on a small volume element in the fully developed flow region in the pipe (Laminar Flow), we get velocity as function of radius only i.e. it does not depend upon the axial distance from the entry point.
[6] The thermal entrance length is the distance for incoming flow in a pipe to form a temperature profile with a stable shape.
[2] Fully developed heat flow in a pipe can be considered in the following situation.
If the wall of the pipe is constantly heated or cooled so that the heat flux from the wall to the fluid via convection is a fixed value, then the bulk temperature of the fluid steadily increases or decreases respectively at a fixed rate along the flow direction.
At some distance away from the entrance of the fluid, fully developed heat flow is achieved when the heat transfer coefficient of the fluid becomes constant and the temperature profile has the same shape along the flow.
[11] This distance is defined as the thermal entrance length, which is important for engineers to design efficient heat transfer processes.
For turbulent flows, thermal entrance length may be approximated solely based on pipe diameter.
[2] where The development of the temperature profile in the flow is driven by heat transfer determined conditions on the inside surface of the pipe and the fluid.
[13] Constant temperature conditions may be produced by a phase transition, such as condensation of saturated steam on a pipe surface.
[14] Newtons law of cooling describes convection, the main form of heat transport between the fluid and the pipe:
[2] Unlike hydrodynamic developed flow, a constant profile shape is used to define thermally fully developed flow because temperature continually approaches ambient temperature.
[2] Dimensionless analysis of change in profile shape defines when a flow is thermally fully developed.
[2] where Understanding the entrance length is important for the design and analysis of flow systems.
[17] Wind tunnels use an inviscid flow of air to test the aerodynamics of an object.
