Turbulent flow entry lengths

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). 

In turbulent flow, the boundary conditions constant wall temperature and constant heat flux lead to approximately the same mean Nusselt numbers. Correlations in the far turbulent regime (Re> 10 ) are noted here. The hydrodynamic entry length is approximately independent of Re, so that an approximation for fully turbulent flow after length x can be made for... 

In turbulent flow, the intense iqjxing during random fluctuations usually overshadows the effects of molecular diffusion, and therefore the hydrodynamic and thermal entry lengths ate of about the same size and independent of the PflLndil number. The hydrodynamic entry length for turbulent flow can be detennined from [see Bbatti and Shah (1987) and 7.hi-qing (1982)]... 

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. 

Which is greater than 10,000. Therefore, the flow is turbulent and the entry length Is roughly... 

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 ... 

For calculation of the heat and mass transfer it is sufficient to consider turbulent flow to be hydrodynamically fully developed after an entry-length of xe/d 10. Then the small deviations from the end value of the velocity profile hardly affect the heat and mass transfer coefficients. 

You can solve the problem with an inlet velocity that is flat thus you find the entry length it takes to achieve fully developed turbulent flow, and the velocity profile downstream is the fully developed one. When you solve for a kinematic viscosity of 10 m /s (water), diameter of 0.05 m (about 2 inches) and a velocity of 2 m/s (a common optimal velocity), you will obtain a Reynolds number of 10. ... 

Engineering correlations have been presented for pressure drop and entry length in common geometrical flow channels with laminar flow. The correlations differ from their counterparts with turbulent flow (available in handbooks, depending upon density and velocity) since in slow flow the pressure drop is proportional to the velocity and the fluid viscosity. The entry length in laminar flow is also longer than is the case for turbulent flow, which means that some section of flow in microfluidics is in the entry region. 

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] ... 

For turbulent flow, no relation is available to predict the entry length for a fully developed turbulent velocity profile to form. As an approximation, the entry length is nearly independent of the Reynolds number and is fully developed after 50 diameters downstream. 

The pressure drop or friction factor in the entry length is greater than in fully developed flow. For laminar flow the friction factor is highest at the entrance (L2) and then decreases smoothly to the fully developed flow value. For turbulent flow there will be some portion of the entrance over which the boundary layer is laminar and the friction factor profile is difficult to express. As an approximation the friction factor for the entry length can be taken as two to three times the value of the friction factor in fully developed flow. 

Water flows in smooth-walled pipe of 10 meter length and 0.1 m diameter under turbulent flow conditions at a flow rate of 90 1/s. The fluid pressures at the entry and... 

Criterion for hydrodynamic and thermal entry length for turbulent flow ... 

For advanced modeling purposes, the addition of minor loss, flow field switchback, and manifolding effects can be approached analytically. In practice, however, the actual pressure drop in an cell or stack is very difficult to predict with high precision due to the effects of entry length, local turbulence, additional minor losses from switchback, consumption, uptake and other effects. Additionally, in PEFCs and AFCs with a porous diffusion media, there can be unintentional convective flow under the channels, which reduces overall pressure drop, as discussed in Chapter 6. Therefore, a good starting point is to assume the frictional pressure drop dominates (which has been found to be true in certain PFFCs [32]) and calculate an expected loss from Fq. (5.76). For a particular fuel cell, the pressure drop can be correlated as a function of entrance velocity, since this is relatively easy experimental data to obtain. 

Mayer (M7), 1961 Experimental and theoretical study of wavy flow of water in open channel (slopes up to 5°). Data on growth of turbulent spots, local depths, surface velocity, length of entry zone, wave velocities, heights, frequencies, effect of surface-active materials. 

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