Circular tube turbulent flow

Circular Tubes Numerous relationships have been proposed for predicting turbulent flow in tubes. For high-Prandtl-number fluids, relationships derived from the equations of motion and energy through the momentum-heat-transfer analogy are more complicated and no more accurate than many of the empirical relationships that have been developed. 

Liquids in turbulent flow in circular helical coils should be handled the same as for gases or use 1.2 Xhj for straight tubes. 

Derive a relationship between the pressure difference recorded between the two orifices of a pitot tube and the velocity of flow of an incompressible fluid. A pitot tube is to be situated in a large circular duct in which fluid is in turbulent flow so that it gives a direct reading of the mean velocity in the duct. At what radius in the duct should it be located, if the radius of the duct is r l... 

For the most part of the experiments one can conclude that transition from laminar to turbulent flow in smooth and rough circular micro-tubes occurs at Reynolds numbers about RCcr = 2,000, corresponding to those in macro-channels. Note that other results were also reported. According to Yang et al. (2003) RCcr derived from the dependence of pressure drop on Reynolds number varied from RCcr = 1,200 to RCcr = 3,800. The lower value was obtained for the flow in a tube 4.01 mm in diameter, whereas the higher one was obtained for flow in a tube of 0.502mm diameter. These results look highly questionable since they contradict the data related to the flow in tubes of diameter d> mm. Actually, the 4.01 mm tube may be considered... 

An experimental study of the laminar-turbulent transition in water flow in long circular micro-tubes, with diameter and length in the range of 16.6-32.2 pm and 1-30 mm, respectively, was carried out by Rands et al. (2006). The measurements allowed to estimate the effect of heat released by energy dissipation on fluid viscosity under conditions of laminar and turbulent flow in long micro-tubes. 

Hao PF, Zhang XW, Yao FHe (2007) Transitional and turbulent flow in circular micro-tube. Exp. Thermal and Fluid Science 32 423-431... 

As will be shown later, the velocity profile for a Newtonian fluid in laminar flow in a circular tube is parabolic. When this is introduced into Eq. (5-38), the result is a = 2. For highly turbulent flow, the profile is much flatter and a 1.06, although for practical applications it is usually assumed that a = 1 for turbulent flow. 

As mentioned above, two distinct patterns of fluid flow can be identified, namely laminar flow and turbulent flow. Whether a fluid flow becomes laminar or turbulent depends on the value of a dimensionless number called the Reynolds number, (Re). For a flow through a conduit with a circular cross section (i.e., a round tube), (Re) is defined as ... 

For the individual (film) coefficient h for heating or cooling of fluids, without phase change, in turbulent flow through circular tubes, the following dimensionless equation [2] is well established. In the following equations all fluid properties are evaluated at the arithmetic-mean bulk temperature. 

TURBULENT FLOW IN A TUBE OF CIRCULAR CROSS-SECTION... 

Flow in circular tubes is of interest to many corrosion engineers. A large number of correlations exist for mass transport due to turbulent flow in a smooth straight pipe (4,9). The flow is transitionally turbulent at Re 2 X 103 and is fully turbulent at Re 105 (4). The most frequently used expression for turbulent conditions at a straight tube wall is that given by Chilton and Colburn using the analogy from heat transfer (13) ... 

No. 67016 (1967) Forced convection heat transfer in circular tubes. Part I, turbulent flow. 

No. 68007 (1968) Forced convection in circular tubes. Part III, further data for turbulent flow. 

FIGURE 8-19 The relation for pressure loss (and head loss) is one of the most general relations in fluid mechanics, and it is valid for laminar or turbulent flows, circular or noncircular tubes, and pipes with smooth or rough surfaces. 

The head loss /i(, represents the additional height that the fluid needs to be raised by a pump in order to overcome the frictional losses in the pipe. The head loss is caused by viscosity, and it is directly related to the wall shear stress. Equation 8—45 is valid for both laminar and turbulent flows in both circular and noncircular tubes, but Eq. 8-46 is valid only for fully developed laminar flow in circular pipes. 

Water enters a circular tube whose walls ate maintained at constant temperature at a specified flow rate and temperature. For fully developed turbulent flow, the Nusselt number can be determined from Nu — 0.023 Re The correct... 

Based on the observation that the friction factors for turbulent flow in rod bundles differ only little from those of circular tubes, a very simple empirical correlation was proposed [12] ... 

Because of the relatively flat velocity profile in turbulent flow, the channel geometry has only a small influence on the friction factor (as discussed in the previous section) and the Sherwood and Nusselt numbers. The turbulent Sherwood and Nusselt numbers of rod bundles can therefore be related to those of circular tubes. The few experimental data, as compiled by Ref. 6, suggest that for relative pitches between 1.1 and 2.0 (which... 

Because pressure drop measurements are much faster and cheaper than mass transfer or heat transfer measurements, it is tempting to try to relate the Sherwood and Nusselt numbers to the friction factor. A relation that has proved successful for smooth circular tubes is obtained from a plausible assumption that is known as the film layer model. The assumption is that for turbulent flow the lateral velocity, temperature, and concentration gradients are located in thin films at the wall of the channel the thickness of the films is indicated with 8/, 87, and 8., respectively. According to the film model, the lateral velocity gradient at the channel surface equals (m)/8/, the lateral temperature gradient equals (T/, - rj/87 and the lateral concentration gradient equals (c. /, - C , )/8,.. From these assumptions, and the theoretical knowledge that 8//8r Pr and 8//8e Sc (for... 

An additional complication that occurs with oscillating flow is the existence of several regimes of laminar and turbulent flow that are functions of frequency as well as Reynolds number, as shown in Figure 3 for the case of smooth circular tubes [2]. These flow regimes are the subject of much research [3]. They are shown as a function of the peak Reynolds number Nr,peak and the ratio of channel radius R to the viscous penetration depth Sv This ratio is sometimes referred to as the dynamic Reynolds number and is similar to the Womersley number Wo = D 28y). In the weakly turbulent regime... 

The mean Nusselt Num is based on (Aum)tube of the circular tube through which the turbulent fluid flows according to No. la. Both Nusselt numbers are formed with the hydraulic diameter, Num = otmdh/A. The Reynolds... 

E. H. Wissler and R. S. Schechter, Turbulent Flow of Gas Through a Circular Tube with Chemical Reaction at the Wall, Chem. Eng. Sci., 17, 937 (1962). 

Millikan CB (1938) A critical discussion of turbulent flows in channels and circular tubes. In Den Hartog JP, Peters H (eds) Proc 5th Int Congr Applied Mechanics, New York, pp. 386-392, Wiley, New York... 

The flow in the boundary layer on a flat plate is laminar up to Rex = UiX/v 3.5 x 105, and that in a circular smooth tube for Re = a(V)/u < 1500 [427]. For higher Reynolds numbers, the laminar flow loses its stability and a transient regime of development of unstable modes takes place. For Rex > 107 and Re > 2500, a fully developed regime of turbulent flow is established which is characterized by chaotic variations in the basic macroscopic flow parameters in time and space. 

Formulas (1.6.1) and (1.6.2) have formed the basis of most theoretical investigations on the determination of the average fluid velocity and the drag coefficient in the stabilized region of turbulent flow in a circular tube (and a plane channel of width 2a). The corresponding results obtained on the basis of Prandtl s relation (1.1.21) and von Karman s relation (1.1.22) for the turbulent viscosity can be found in [276,427]. In what follows, major attention will be paid to empirical and semiempirical formulas that approximate numerous experimental data quite well. 

In the region of stabilized turbulent flow in a smooth circular tube, the drag coefficient can be estimated from the Prandtl-Nikuradze implicit formula [318]... 

Qualitatively, the picture of stabilized turbulent flow in a plane channel is similar to that in a circular tube. Indeed, in the viscous sublayer adjacent to the channel walls, the velocity distribution increases linearly with the distance from the wall V(Y)/U = y+. In the logarithmic layer, the average velocity profile can be described by the expression [289]... 

More detailed information about the structure of turbulent flows in a circular (noncircular) tube and a plane channel, as well as various relations for determining the average velocity profile and the drag coefficient, can be found in the books [138, 198, 268, 276, 289], which contain extensive literature surveys. Systematic data for rough tubes and results of studying fluctuating parameters of turbulent flow can also be found in the cited references. 

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