Turbulent flow in pipes

Most of the results available for turjbulent boundary layers have been found by measuring time-average velocities at various points in flow in pipes or over flat plates and by attempting to generalize the velocity profiles. For various experimental reasons it is easier to make such measurements in pipes, so most of the results are pipe results. Now we consider the turbulent flow in pipes for one section, and then we return to the turbulent boundary layer. 

As discussed in iSec. 6.4, turbulent flow differs from laminar flow in that the 

As discussdd in Sec. 6.3, the velocity profile for laminar flow in a tube is parabolic. For turbulent flow it is much closer to plug flow, i.e., to a uniform velocity over the entire pipe cross section. Furthermore, as seen from Fig. 11.7, as the Reynolds number is increased, the velocity profile approaches closer and closer to plug flow. At the wall the turbulent eddies disappear so the shear stress at the wall for both laminar and turbulent flow of newtonian fluids is given byj dVJdy. Although it is ve difficult experimentally to 

Prandtl showed that each of the different turbulent-flow curves in Fig. 11.7 could be represented fairly well by an equation of the form 

Velocity distribution in laminar and turbulent flow in smooth, circular pipes. [From J. Nikuradse, Gesetzmaessigkeiten der turbulenten Stroemung in glatten Rohren (Regularities of turbulent flow in smooth tubes), Forschungsheft 356 (1932). Reproduced by permission of the publisher.] 

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A typical combination of these numbers is that for turbulent flow in pipes ... 

Ryan, N.W. and Johnson, M.M., Transition from laminar to turbulent flow in pipes, AIChE Journal, 5, pp. 433-5 (1959). 

Chapters 13 and 14 deal primarily with small deviations from plug flow. There are two models for this the dispersion model and the tanks-in-series model. Use the one that is comfortable for you. They are roughly equivalent. These models apply to turbulent flow in pipes, laminar flow in very long tubes, flow in packed beds, shaft kilns, long channels, screw conveyers, etc. 

Colebrook, C. F., Turbulent Flow in Pipes, Journal of the Institute of Civil Engineers, London, February 1939. 

More complex equations have been developed for the flow of power-law fluids under turbulent flow in pipes [85,86,90], The foregoing applies to smooth pipes. Surface roughness has little effect on the friction factor for laminar flow, but can have a significant effect when there is turbulent flow [85],... 

In forced convection, the fluid is moved over the surface by a pump or blower neglecting natural convection are usually neglected. The study of forced convection is of great practical importance and vast amount of data have been amassed for streamline and turbulent flow in pipes, across and parallel to tubes, across plane surfaces, and in other important configurations such as jackets and coils. 

An exclusively analytical treatment of heat and mass transfer in turbulent flow in pipes fails because to date the turbulent shear stress Tl j = —Qw w p heat flux q = —Qcpw, T and also the turbulent diffusional flux j Ai = —gwcannot be investigated in a purely theoretical manner. Rather, we have to rely on experiments. In contrast to laminar flow, turbulent flow in pipes is both hydrodynamically and thermally fully developed after only a short distance x/d > 10 to 60, due to the intensive momentum exchange. This simplifies the representation of the heat and mass transfer coefficients by equations. Simple correlations, which are sufficiently accurate for the description of fully developed turbulent flow, can be found by... 

Colebrook CF (1939) Turbulent Flow in Pipes, with particular reference to the Transition Region between Smooth and Rough Pipe Laws. J Inst Civ Eng 12(4) 133-156... 

For turbulent flow in pipes the velocity profile can be calculated from the empirical power law design formula (1.354). 

Nikitin, N. V., Direct numerical modeling of three-dimensional turbulent flows in pipes of circular cross-section. Fluid Dynamics, Vol. 29, No. 6, pp. 749-758, 1994. 

C. Wang, On the Velocity Distribution of Turbulent Flow in Pipes and Channels of Constant Cross Section, J. Appl. Mech., (68) A85-A90,1946. 

C. F. Colebrook, Turbulent Flow in Pipes with Particular Reference to the Transition Region between the Smooth and Rough Pipes Laws, 7 Inst. Civil Eng., (11) 133-156,1939. 

For laminar boundary layers, as for laminar flow in a pipe, it was possible to calculate the flow behavior from a set of plausible assumptions and then to show experimentally that the flow behaved as calculated. For turbulent boundary layers, as for turbulent flow in pipes, no one is yet able to calculate the flow behavior without starting with experimental data. However, from experimental measurements it has been possible to make some generalizations, which can then be used to extrapolate to other conditions. 

C. F. Colebrook, Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws, J. Inst. Civ. Eng. 11 133-155 (1938-9). 

Research has shown that the flushing regime for lead pipes has a considerable effect on the lead concentration (Vewin, 1987). If the flow in the pipes is turbulent Re > 2300) the lead concentration is higher than after flushing with laminar flow. This is probably due to the release of particulate lead. In practice, consumers draw water with an average flow rate of 5 litres/minute, which corresponds to turbulent flow (in pipes of 19 mm diameter. Re > 5000). 

A each stage, considerable effort has been made to present the most reliable and generally accepted methods for calculations, as the contemporary literature is inundated with conflicting information. This applies especially in regard to the estimation of pressure gradients for turbulent flow in pipes. In addition, a list of specialist and/or advanced sources of information has been provided in each chapter as Further Reading . 

Ambrose, H.H. (1960). Turbulent flow in pipes with artificial roughness. Department of Civil Engineering. University of Tennessee Knoxville. 

Sec. 2.10 Design Equations for Laminar and Turbulent Flow in Pipes... 

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