Laminar flow smooth pipes

For laminar flow (Re < 2000), generally found only in circuits handling heavy oils or other viscous fluids, / = 16/Re. For turbulent flow, the friction factor is dependent on the relative roughness of the pipe and on the Reynolds number. An approximation of the Fanning friction factor for turbulent flow in smooth pipes, reasonably good up to Re = 150,000, is given by / = (0.079)/(4i e ). 

In laminar flow,/is independent of /D. In turbulent flow, the friction factor for rough pipe follows the smooth tube curve for a range of Reynolds numbers (hydrauhcaUy smooth flow). For greater Reynolds numbers,/deviates from the smooth pipe cui ve, eventually becoming independent of Re. This region, often called complete turbulence, is frequently encountered in commercial pipe flows. The Reynolds number above which / becomes essentially independent of Re is (Davies, Turbulence Phenomena, Academic, New York, 1972, p. 37) 20[3.2-2.46ln( /D) ... 

Fluid flow is also critical for proper operation of a hydraulic system. Turbulent flow should be avoided as much as possible. Clean, smooth pipe or tubing should be used to provide laminar flow and the lowest friction possible within the system. Sharp, close radius bends and sudden changes in cross-sectional area are avoided. 

As in any other pneumatic-conveyor system, special attention must be given to the piping or ductwork used to convey the dust-laden air or gas. The inside surfaces must be smooth and free of protmsions that affect the flow pattern. All bends should be gradual and provide a laminar-flow path for the gas. 

For developed laminar flow in smooth channels of t/h > 1 mm, the product ARe = const. Its value depends on the geometry of the channel. For a circular pipe ARe = 64, where Re = Gdh/v is the Reynolds number, and v is the kinematic viscosity. 

With turbulent channel flow the shear rate near the wall is even higher than with laminar flow. Thus, for example, (du/dy) ju = 0.0395 Re u/D is vaHd for turbulent pipe flow with a hydraulically smooth wall. The conditions in this case are even less favourable for uniform stress on particles, as the layer flowing near the wall (boundary layer thickness 6), in which a substantial change in velocity occurs, decreases with increasing Reynolds number according to 6/D = 25 Re", and is very small. Considering that the channel has to be large in comparison with the particles D >dp,so that there is no interference with flow, e.g. at Re = 2300 and D = 10 dp the related boundary layer thickness becomes only approx. 29% of the particle diameter. It shows that even at Re = 2300 no defined stress can be exerted and therefore channels are not suitable model reactors. 

Figure 7.4 Representations of hydrodynamic flow, showing (a) laminar flow through a smooth pipe and (b) turbulent flow, e.g. as caused by an obstruction to movement in the pipe. The length of each arrow represents the velocity of the increment of solution. Notice in (a) how the flow front is curved (known as Poiseuille flow ), and in (b) how a solution can have both laminar and turbulent portions, with the greater pressure of solution flow adjacent to the obstruction.

However, the flow regime of a film cannot be defined uniquely as laminar or turbulent, as in the case of pipe flow, due to the presence of the free surface. Depending on the values of AFr and JVw , the free surface may be smooth, or covered with gravity waves or capillary or mixed capillary-gravity waves of various types. Thus, under suitable conditions, it is possible to have smooth laminar flow, wavy laminar or turbulent flow, where the wavy flows may be subdivided into gravity or capillary... 

For Newtonian fluids flowing in smooth pipes, the friction losses can be estimated for laminar flow (Re < 2100) using the Fanning friction factor, f. The Reynolds number, Re, is given by ... 

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],... 

Circular Cross-section Pipes. In contrast to nozzles and apertures, the calculation of gas flow through tubes (/ d) has to take the effects of gas viscosity into account. For smooth-walled tubes, gas fluxes less than q l3 and laminar flow conditions, the well-known expression for p F-throughput, can be obtained ... 

The constants in this relation will be different for different critical Reynolds numbers. Also, the surfaces are assumed to be smooth, and the free stream to be turbulent free. For laminar flow, the friction coefficient depends on only the Reynolds number, and the surface roughness has no effect. For turbulent flow, however, surface roughness causes the friction coefficient to increase sevcralfold, to the point that in fully turbulent regime the friction coefficient is a function of surface roughness alone, and independent of the Reynolds number (Fig. 7-8). Tliis is also the case in pipe flow. 

In transitional flow, the flow switches between laminar and turbulent randomly (Fig. 8-5). It should be kept in mind that laminar flow can be maintained at much higher Reynolds numbers in very smooth pipes by avoiding flow disturbances and tube vibrations. In such carefully controlled experiments, laminar flow has been maintained at Reynolds numbers of up to 100,000. 

Fully Developed Flow in Smooth Circular Pipes (a) Laminar flow (Re < 2300)... 

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

The shear rate at the wall for the flow of power law fluids in smooth pipes under laminar conditions can be calculated as follows (15) ... 

When a gas enters a smooth pipe from a large reservoir through a well-faired entry, a laminar boundary layer forms along the walls. The velocity profile in the main body of the How remains flat. The velocity boundary layer thickens with distance downstream from the entry until it eventually fills the pipe. If the Reynolds number based on pipe diameter is less than 2100, the pipe boundary layer remains laminar. The flow is said to be fully... 

It is well known that the turbulent flow in a pipe is changed into a laminar flow if the velocity or the Reynolds number is reduced below a certain value. This value may be taken to be i = 1160 (c. g. s.). A laminar flow may, on the other hand, be maintained even if the Reynolds number is raised considerably above the critical value, provided the inlet end of the pipe is smooth and all disturbances of the flow are otherwise avoided. In the experiments here considered the edges of the pipe or channel were deliberately kept sharp in order to secure in every case a well defined transition from a laminar to a turbulent flow. 

A typical velocity distribution for a newtonian fluid moving in turbulent flow in a smooth pipe at a Reynolds number of 10,000 is shown in Fig. 5.3. The figure also shows the velocity distribution for laminar flow at the same maximum velocity at the center of the pipe. The curve for turbulent flow is clearly much flatter than that for laminar flow, and the difference between the average velocity and the maximum velocity is considerably less. At still higher Reynolds numbers the curve for turbulent flow would be even flatter than that in Fig. 5.3. 

THE FRICTION-FACTOR CHART. For design purposes, the frictional characteristics of round pipe, both smooth and rough, are summarized by the friction-factor chart (Fig. 5.9), which is a log-log plot of / versus For laminar flow Eq. (5.18) relates the friction factor to the Reynolds number. A log-log plot of Eq. (5.18) is a straight line with a slope of — 1. This plot line is shown on Fig. 5.9 for Reynolds numbers less than 2100. 

Two different types of fluid flow are usually considered in hydrodynamic problems (Figure 9.2.1). When the flow is smooth and steady, and occurs as if separate layers (laminae) of the fluid have steady and characteristic velocities, the flow is said to be laminar. For example, the flow of water through a smooth pipe is typically laminar, with the flow velocity being zero right at the walls (because of friction between the fluid and the wall) and having some maximum value in the middle of the pipe. The velocity profile under these conditions is typically parabolic. When the flow involves unsteady and chaotic motion, in which only on the average is there a net flow in a particular direction, it is termed... 

It should be noted that the horizontal portions of the curves to the right of the broken line are represented by Nikuradse s [60] correlation, which is presented in Table 5.9. The downward-sloping line for the smooth turbulent flow is represented by the PKN correlation shown in Table 5.8. The downward-sloping line for laminar flow is represented by Eq. 5.17. Relative roughness e can be obtained from Table 5.10 for a variety of commercial pipes. 

Example 11.3. Water is flowing in a 3-in ID smooth pipe, with an average velocity of lOft/si How far from the wall are the edge of the laminar sublayer and the edge of the buffer layer What is the average velocity at each of those points I... 

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