Tube flow entry length

The Circular Tube Thermal-Entry-Length, with Hydrodynamically Fully Developed Laminar Flow... 

For the common problem of heat transfer between a fluid and a tube wall, the boundary layers are limited in thickness to the radius of the pipe and, furthermore, the effective area for heat flow decreases with distance from the surface. The problem can conveniently be divided into two parts. Firstly, heat transfer in the entry length in which the boundary layers are developing, and, secondly, heat transfer under conditions of fully developed flow. Boundary layer flow is discussed in Chapter 11. 

Just as for laminar flow, a minimum hydrodynamic entry length (Le) is required for the flow profile to become fully developed in turbulent flow. This length depends on the exact nature of the flow conditions at the tube entrance but has been shown to be on the order of Le/D = 0.623/VRe5. For example, if /VRe = 50,000 then Le/D = 10 (approximately). 

Laminar fluid flow in tubes has been described by Levich [ 3 ]. An entry length, le, is necessary to establish Poiseuille flow, given approximately by... 

Shimizu, A., Echigo, R., Hasegawa, S. and Hishida, M. (1978). Experimental Study on the Pressure Drop and the Entry Length of the Gas-Solid Suspension Flow in a Circular Tube. Int. J. Multiphase Flow, 4, 53. 

In a tube or channel a certain entry length, /e, is necessary before the parabolic Poiseuille flow is obtained (Fig. 8.26). 

Th regioii of flow over which the thermal boundary layer develops and re.iches (he tube center i.s called the thermal entrance region, and the length of this region is called the thermal entry length L,. Flow in the thermal... 

During laminar flow in a tube, the magnitude of the dimensionless Prandtl number Pr is a measure of the relative growth of the velocity and thermal boundary layers. For fluids with Pr = I, such as gases, the two boundary layers essentially coincide with each other. For fluids with Pr > I, such as oils, the velocity boundary layer outgrows the thermal boundary layer. As a result, the hydrodynamic entry length is smaller than the thermal entry length. The opposite is tnie for fluids with Pr < 1 such as liquid metals. 

The entry length is much shorter in turbulent flow, as expected, and its dependence on the Reynolds number is weaker. In many lube flotvs of practical interest, the entrance effects become insignificant beyond a tube length of 10 diameters, and the hydrodynamic and thermal entry lengths are approximately taken to be... 

The entry lengths for turbulent flow are typically short, often just 10 tube diameters long, and thus the Nusselt number determined for fully developed turbulent flow can be used approximately for the entire tube. This simple approach gives reasonable results for pressure drop and heat transfer for long tubes and conservative re.sults for short ones. Correlations for the friction and heat transfer coefficients for the entrance regions are available in the literature for better accuracy. 

How is the hydrodynamic entry length defined for flow in a tube Is the entry length longer in laminar or turbulent flow ... 

S-18C Consider the flow of mercury (a liquid meial) in a tube. How will the hydrodynamic and thermal entry lengths compare if the flow is laminar How would they compare if (he flow uere turbulent ... 

Turbulent Flow. The thermal entry length solutions for smooth ducts for several cross-sectional geometries have been summarized [46]. As for laminar flow, the Nusselt numbers in the thermal region are higher than those in the fully developed region. However, unlike laminar flow, Nu,x and NuxHi are very nearly the same for turbulent flow. The local and mean Nusselt numbers for a circular tube with and boundary conditions are [46] ... 

As a first approximation of geometry, a Y bifurcation using straight rigid mbing may be used. Hie blood may be modeled as a Newtonian fluid without particles. As boundary conditions, the inlet flow may either be considered Poiseuille or uniform across the tube (if a sufficient entry length is included to produce a fully developed flow profile). Steady flow will be used for this model. 

If the velocity profile at the entrance region of a tube is flat, a certain length of the tube is necessary for the velocity profile to be fully established. This length for the establishment of fully developed flow is called the transition length or entry length. This is shown in Fig. 2.10-6 for laminar flow. At the entrance the velocity profile is flat i.e., the velocity is the same at all positions. As the fluid progresses down the tube, the boundary-layer thickness increases until finally they meet at the center of the pipe and the parabolic velocity profile is fully established. 

The hydrodynamic entry length is usually taken as the distance from the tube entrance where the friction factor (pressure loss coefficient, see Section 3.4.1.1) reaches within 2% deviation the fully developed value. In laminar flow, the hydro-dynamic entry length is (Cengel, 2002) ... 

With such a flat plate, the boundaiy layer will increase in thickness in-dcfinitely if slowly (Fig. 1.10(c))l On the other hand if the flow is in a restricted channel (e.g. a circular-tube or a paraltel-plate cell) the boundary layers at the two walls must merge at some point and beyond, a steady-state situation or fully developed laminar flow will result (Fig. Ltl). Fundamental mass transport studies in electrolytic cells are usually carried out in cells with an entry length without electrodes so that the boundary-layer thickness is uniform over the current-carrying surface. 

Influent water enters one end of the pressure vessel and travels longitudinally down the length of the vessel in the feed transport layer. Direct entry into the permeate transport layer is precluded by sealing this layer at each end of the roll. As the water travels in a longitudinal direction, some of it passes in radially through the membrane into the permeate transport layer. Once in the transport layer, the purified water flows spirally into the center collection tube and exits the vessel at each end. The concentrated feed continues along the feed transport material and exits the vessel on the opposite end from which it entered. 

The velocity held is determined by the characteristic length L0, and velocity w0 e.g. the entry velocity in a tube or the undisturbed velocity of a fluid flowing around a body, along with the density g and viscosity rj of the fluid. While density already plays a role in frictionless flow, the viscosity is the fluid property which is characteristic in friction flow and in the development of the boundary layer. The two material properties, thermal conductivity A and specific heat capacity c, of the fluid are important for the determination of the temperature held in conjunction with the characteristic temperature difference Ai 0. The specihc heat capacity links the enthalpy of the fluid to its temperature. 

Consider a fluid moving through a pipe in the laminar flow regime. The wall of the pipe contains an electrode, located at a certain distance from the entry (Figure 4.26). The flow rate at the wall is zero. In the vicinity of the walls, viscous forces slow down the fluid as soon as it enters the pipe. Thus a gradient in flow rate is established across a layer referred to as the hydrodynamic boundary layer. Its thickness increases with the distance from the inlet. The boundary layers of opposing walls eventually meet after a distance L, called the hydrodynamic entrance length. From this point onward, the flow profile is observed to be parabolic. For a tube, Lh has a value of about 70 times its diameter. 

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