Flow In Rough Pipes Research Articles

Closure to “Discussion of ‘Turbulence Structure for Fully Developed Flow in Rough Pipes’” (1973, ASME J. Fluids Eng., 95, pp. 260–261)

Closure to “Discussion of ‘Turbulence Structure for Fully Developed Flow in Rough Pipes’” (1973, ASME J. Fluids Eng., 95, pp. 260–261)

Turbulent Flow in Smooth and Rough Pipes

Fully developed turbulent flow in both smooth and rough-walled pipes is investigated for Reynolds numbers from 30,000 to 480,000. The values of mean velocity, root-mean-square values of the fluctuating velocity components, and cross-correlation values of the fluctuating velocities are presented for flow in a smooth pipe and two sand-roughened pipes, R/ε = 208 and R/ε = 26.4. The quantity R/ε is the ratio of the actual pipe radius to the average sand particle size. The experimental measurements for flow in smooth pipes are in good agreement with those of previous investigations throughout the Reynolds number range considered. Several of the rough pipe turbulence quantities show substantial deviations from the corresponding smooth pipe quantities. For rough pipes, the measured uv cross-correlation values approach those predicted empirically from the Reynolds equations for fully developed, axisymmetric flow as the flow approaches the hydraulically smooth case. However, as the Reynolds number is increased and the flow proceeds through the transition region from smooth to fully rough flow and to the fully rough flow region, the values of the uv cross correlation in rough pipes are significantly lower than the predicted values. This difference between predicted and measured data becomes more pronounced as the Reynolds number is further increased and the flow becomes fully rough. The difference between measured and predicted uv values, and other differences between smooth and rough pipe results, suggests that the accepted reduction of the Reynolds equations for flow in smooth pipes is not valid for flow in rough pipes. Thus, the Reynolds equations are re-examined for flow in rough pipes, and it is shown that these equations can be satisfied by the experimental data if secondary flows and angular variations in the mean velocity are postulated.

Heat Transfer Characteristics of Dilute Polymer Solutions in Fully Rough Pipe Flow

DILUTE polymer solutions which exhibit detectable elastic effects can produce large reductions of fractional drag over fully rough surfaces in the absence of any viscous sublayer1. We have carried out some heat transfer experiments with polyethylene oxide (Union Carbide Polyox WSR301) solution in a rough bore pipe and derived some interesting results.

Turbulent heat transfer from smooth and rough surfaces

Radial temperature profiles have been obtained in a 2-in I.D. rough tube of equivalent sand roughness equal to 0.05 for Prandtl numbers of 0.7, 5.9 and 14.3 over a Reynolds number range 10000–50000. Plots of t + against log y R are linear as in the case of u + for rough and smooth tubes, but the slope depends on Prandtl number and inferentially on the roughness. The t + intercept at log y R = 0 is strongly dependent on the Reynolds number, unlike u + in turbulent rough pipe flow. An expression for the relation between t + and log y R is presented, but the dependence of the slope A R on roughness remains to be determined. The heat-transfer efficiency St/ C F was less in rough tubes than smooth ones for all the fluids studied, but the relative difference becomes smaller at higher Prandtl number and in the turbulent transition region. Friction factors and heat-transfer coefficients have also been measured in seven different 1 2 -in I.D. rough pipes of known surface geometry. Equivalent sand roughnesses ranged from 0.021 to 0.095 for the pipes studied. A semi-theoretical equation based on the temperature profiles obtained in the 2-in pipe predicts the results of the present study and Nunner's air results adequately. It underestimates the water results of Dipprey.

Turbulent Flow in Rough Pipes

Turbulent Flow in Rough Pipes

Similitude theory applied to correlation of flume sediment transport data

A second variant of the method of synthesis, the method of linear proportionalities, is presented and shown to be a powerful device for seeking correlation procedures for sediment transportation data. It is apparent that correlations for sediment transportation data under conditions of quasiuniform flow are of the same basic form as those for rough pipe flow, with some amplification for practical reasons. Certain established correlations are shown to be based on similarity equations from which parametric terms have been omitted, mostly without justification. A rigorous method of correlation compatible with feasible laboratory procedures is presented and illustrated in figure form using available data. It was found that the bulk of the published data was in a form unsuitable for use in a rational correlation. The authors conclude that new experimentation is required and that this could best be done by co‐operation among institutions with the necessary apparatus.

Boundary Flow Along a Circular Cylinder

The Karman-Prandtl mixing-length theory for fluid flow over a flat surface with a laminar sublayer near the boundary is adapted to the flow along an infinite circular cylinder on the supposition that, in the nature of the radial inward convection of momentum towards the boundary, there is no accumulation of the momentum within any arbitrary finite volume of fluid. Experimental results for smooth and rough pipe flows are invoked in order to develop the nature of the boundary flow over a range of conditions from the quasi-smooth to the fully turbulent regimes. The drag coefficient for tangential friction is evaluated as a function of Reynolds number and surface roughness and is shown to lie within the limits 0.002 and 0.02, depending on roughness, for diameter Reynolds numbers greater than 103. Theoretical indications compare favorably with results from towing tests of stranded cables.

THE LAWS OF FLOW IN ROUGH PIPES

THE LAWS OF FLOW IN ROUGH PIPES

Study of Turbulent Flow in Rough Pipes

粗い管及び滑かな管内の乱流に就てその速度変化が同一の方則に従てゐることを見出し、これを基として粗滑両管内の速度分布の異る所以は單に両管内の最大速度の異れる点に存することを示し両管に共通なる速度分布の実驗式を求めた。且粗い管内の最大速度は滑かな管内の最大速度そのものと粗度に関する項とより成ることを見出し、これより平均速度、抵抗等を與へる式を求めた。実驗値としてはNikuradseの報告を取りこれと比較して上記の諸式が実驗値とよく一致することを確め、粗い管内の流れにおける粘性と粗度との影響をある程度明かにすることが出耒た。