Pipe Reynolds number

Reynolds dumber. One important fluid consideration in meter selection is whether the flow is laminar or turbulent in nature. This can be deterrnined by calculating the pipe Reynolds number, Ke, a dimensionless number which represents the ratio of inertial to viscous forces within the flow. Because... 

A low Reynolds number indicates laminar flow and a paraboHc velocity profile of the type shown in Figure la. In this case, the velocity of flow in the center of the conduit is much greater than that near the wall. If the operating Reynolds number is increased, a transition point is reached (somewhere over Re = 2000) where the flow becomes turbulent and the velocity profile more evenly distributed over the interior of the conduit as shown in Figure lb. This tendency to a uniform fluid velocity profile continues as the pipe Reynolds number is increased further into the turbulent region. 

The wedge design maintains a square root relationship between flow rate and differential pressure for pipe Reynolds numbers as low as approximately 500. The meter can be flow caUbrated to accuracies of approximately 1% of actual flow rate. Accuracy without flow caUbration is about 5%. 

The constant depends on the hydraulic diameter of the static mixer. The mass-transfer coefficient expressed as a Sherwood number Sh = df /D is related to the pipe Reynolds number Re = D vp/p and Schmidt number Sc = p/pD by Sh = 0.0062Re Sc R. ... 

Value of the discharge coefficient C for a Herschel-type venturi meter depends upon the Reynolds number and to a minor extent upon the size of the venturi, increasing with diameter. A plot of C versus pipe Reynolds number is given in ASME PTC, op. cit., p. 19. A value of 0.984 can be used for pipe Reynolds numbers larger than 200,000. 

This is the basis for establishing the condition or type of fluid flow in a pipe. Reynolds numbers below 2000 to 2100 are usually considered to define laminar or thscous flow numbers from 2000 to 3000-4000 to define a transition region of peculiar flow, and numbers above 4000 to define a state of turbulent flow. Reference to Figure 2-3 and Figure 2-11 will identify these regions, and the friction factors associated with them [2]. 

In fully developed flow, equations 12.102 and 12.117 can be used, but it is preferable to work in terms of the mean velocity of flow and the ordinary pipe Reynolds number Re. Furthermore, the heat transfer coefficient is generally expressed in terms of a driving force equal to the difference between the bulk fluid temperature and the wall temperature. If the fluid is highly turbulent, however, the bulk temperature will be quite close to the temperature 6S at the axis. 

Commercial steel pipes Reynolds number = 105 Williams and Hazen C factor =110... 

The basis for the equivalent L/D method is the assumption that there is some length of pipe (Leq) that has the same friction loss as that which occurs in the fitting, at a given (pipe) Reynolds number. Thus, the fittings are... 

Because the discharge coefficient accounts for the non-idealities in the system (such as the friction loss), one would expect it to decrease with increasing Reynolds number, which is contrary to the trend in Fig. 10-4. Flowever, the coefficient also accounts for deviation from plug flow, which is greater at lower Reynolds numbers. In any event, the coefficient is not greatly different from 1.0, having a value of about 0.985 for (pipe) Reynolds numbers above about 2 x 105, which indicates that these non-idealities are small. 

Primary device Nominal pipe diameter D, in (mm) Beta ratio p Pipe Reynolds number NReD range Coefficient accuracy, %a... 

Coefficient C for a square-edged eccentric circular orifice (with opening tangent to pipe wall) varies from about 0.61 to 0.63 for [3 s from 0.3 to 0.5, respectively, and pipe Reynolds numbers > 10,000 for either vena-... 

An experimentally based rule-of-thumb is that laminar flow often occurs when the pipe Reynolds number, Vdjv, is less than 2,000, or when an open channel Reynolds number, Vhjv, is less than 500, where V is the cross-sectional mean velocity, d is the pipe diameter, v is the kinematic viscosity of the fluid, and h is the channel depth. The diameter or depth that would not be exceeded to have laminar flow by these experimental criteria is given in Table 5.1. 

The empty-pipe Reynolds number is based on the inner pipe diameter and superficial fluid velocity [Eq. (1)]. If the pipe contains a motionless mixer, Eq. (1) needs to be modified to take into account the metal in the mixer, which reduces the effective diameter but increases the fluid velocity (because it blocks part of the cross section). The theoretically sound characteristic dimension for a motionless mixer is the hydraulic diameter, given by... 

Flow Sensor Line Size, Inches (1 in. = 25.4 mm) Beta Ratio Pipe Reynolds Number Range for Stated Accuracy Inaccuracy, Percentage of Actual Flow... 

When the pipe Reynolds number is greater than about 2100, the velocity boundary layer that forms in the entry region eventually turns turbulent as the gas passes down the pipe. The velocity profile becomes fully developed that is. the shape of the distribution ceases to change at about 25 to 50 pipe diameters from the entry. Small particles in such a flow are transported by turbulent and Brownian diffusion to the wall. In the sampling of atmospheric air through long pipes, wall losses result from turbulent diffusion. Accumulated layers of particles will affect heat transfer between the gas and pipe walls. 

When the Reynolds number based on tube diameter is greater than 2100, the boundary layer becomes turbulent at some distance from the inlet. The transition usually occurs at a Reynolds number, based on distance from the entrance, Rcj, of between 10 and 10, depending on the roughness of the wall and the level of turbulence in (he mainstream. As shown in Fig, 4,11, the deposition rate tends to follow the development of the turbulent boundary layer. No deposition occurs until Re is about 10- the rate of deposition then approaches a constant value at Re = 2 x 10 in the region of fully developed turbulence. On dimensional ground.s. the deposition velocity at a given pipe Reynolds number can be assumed to be a function of the friction velocity, if, kinematic viscosity, v, and the particle relaxation time, m/f ... 

Nominal Pipe Diameter D, Beta Ratio Pipe Reynolds Number Coefficient... 

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