Pipe flow friction factors

Alternatively, the following simple equation can be used to obtain approximate values for the friction factor for flow in smooth pipes for Reynolds numbers less than... 

FRICTION FACTOR IN FLOW THROUGH CHANNELS OF NONQRCULAR CROSS SECTION. The friction in long straight channels of constant noncircular cross section can be estimated by using the equations for circular pipes if the diameter in the Reynolds number and in the definition of the friction factor is taken as an equivalent diameter, defined as four times the hydraulic radius. The hydraulic radius is denoted by r and in turn is defined as the ratio of the cross-sectional area of the channel to the wetted perimeter of the channel ... 

Compare the form of this friction factor with the familiar Fanning friction factor for flow through pipes.)... 

Considering an aqueous clay suspension III (Table 3-9) with a mixture density of 1440 kg/m (SG = 1.44), a yield stress of 20 Pa, and a coefficient of rigidity of 32.8 mPa s as reported by Caldwell and Babbitt (see references of Chapter 3), determine the friction factor for flow at 2.5 m/s in a 63 mm ID pipe, using the Darhy method. Determine aiso the pressure drop per unit length. 

The Fanning friction factor for flow through pipes is found from commonly available charts (Perry and Green, 1984). A generalized equation is also available to calculate the friction factor directly, or for spreadsheet use (Chen, 1979) ... 

If we had operated our vacuum cyclone with the same absolute mass flow rate of dust that reported to our reference cyclone, then the dust concentration term, Co in Eq. (4.2.9), would have increased 10-fold, and fdust by a factor of a/Io. a comparison with the variation in the friction factor for flow in a reasonably rough pipe at the same two pressures (and comparable values of Re) shows that Eq. (4.2.9) predicts an unrealistically large increase in / because of this increase in fdust- Equation (6.1.11) represents an improvement over Eq. (4.2.9) in this respect. In Eq. (6.1.11) the increase in Co is compensated due to the inclusion of the factor p (the gas density). 

The radiator pipe is the structure through which heat is rejected to space. Wall friction is turned off in favor of representing the desired friction factor with the Reynolds number dependent form loss coefficient option in RELAP5-3D. Idel chik (Reference 12-23) Section 8-2, paragraph 15, provides an empirical relation to determine the friction factor for flow past a bundle of vertically arranged tubes uniformly distributed over conduit cross sections. For a duct that is 3.8 cm wide with heat pipes in one row that have 12.5 cm between heat pipe centers and 2.2 cm outside diameters the equation for friction factor is ... 

Flow Along Smooth Surfaces. When the flow is entirely parallel to a smooth surface, eg, in a pipe far from the entrance, only the shear stresses contribute to the drag the normal stresses are directed perpendicular to the flow (see Piping systems). The shear stress is usually expressed in terms of a dimensionless friction factor ... 

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) ... 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

In laminar flow, the friction factor for curved pipe/ may be expressed in terms of the straight pipe friction factor/= 16/Re as (Hart, Chem. Eng. ScL, 43, 775-783 [1988])... 

For commercial steel pipe, with a roughness of 0.046 mm, the friction factor for fully rough flow is about 0.0047, from Eq. (6-38) or Fig. 6-9. It remains to be verified that the Reynolds number is sufficiently large to assume fully rough flow. Assuming an abrupt entrance with 0.5 velocity heads lost,... 

FIG. 6-31 Friction factors for condensing liqiiid/gas flow downward in vertical pipe. In this correlation F/pL is in fr/h. To convert fr/h to mvs, multiply by 0.00155. (From Bergelin, et al., Proc. Heat Transfer Fluid Mech. Inst., ASMF, 1949, p. 19. )... 

For commercial pipe with roughness e = 0.046 mm, the friction factor is about 0.0043. Approaching the last hole, the flow rate, velocity and Reynolds number are about one-tenth their inlet values. At Re = 16,400 the friction factor/is about 0.0070. Using an average value of/ = 0.0057 over the length of the pipe, 4/Z73D is 0.068 and may reasonably be neglected so that Eq. (6-151) may be used. With C, = 0.62,... 

Figure 6-40 shows power number vs. impeller Reynolds number for a typical configuration. The similarity to the friction factor vs. Reynolds number behavior for pipe flow is significant. In laminar flow, the power number is inversely proportional to Reynolds number, reflecting the dominance of viscous forces over inertial forces. In turbulent flow, where inertial forces dominate, the power number is nearly constant. 

The Lapple charts for compressible fluid flow are a good example for this operation. Assumptions of the gas obeying the ideal gas law, a horizontal pipe, and constant friction factor over the pipe length were used. Compressible flow analysis is normally used where pressure drop produces a change in density of more than 10%. 

Pressure drop calculations for shnple geometries like pipe flows are straightforward. The Farming friction factor is given by ... 

The following analysis enables one to calculate the diameter of a pipeline transporting any compressible fluid. The required inputs are volumetric flow rate, the specific gravity of the gas relative to air, flow conditions, compressibility factor Z where Z is defined by nZRT = PV, the pressure at the point of origin and the destination, the pipe length, and pipe constants such as effective roughness. The working equations have been obtained from the literature. Since the friction factor... 

Figure 2-3. Moody or regular Fanning friction factors for any kind and size of pipe. Note the friction factor read from this chart is four times the value of the f factor read from Perry s Handbook, 6th Ed. [5]. Reprinted by permission, Pipe Friction Manual, 1954 by The Hydraulic Institute. Also see Engineering DataBook, 1st Ed., The Hydraulic Institute, 1979 [2]. Data from L. F, Moody, Friction Factors for Pipe Flow by ASME [1].

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]. 

VTien the Reynolds number is below a value of 2000, the flow region is considered laminar. The pipe friction factor is defined as ... 

Flow is <2000, therefore, flow of viscous or laminar system consists of friction factor, fp, for 4-in. pipe = 0.017 (Table 2-2). 

Figure 2-24. Friction loss for flow of water in steel pipes. Note C = pipe roughness factor. See Tables 2-9 and 2-22. Courtesy of Carrier Corp.

Figure 2-31 is useful in sohing the usual steam or any vapor flow problem for turbulent flow based on the modified Darcy relation with fixed friction factors. At low vapor velocities the results may be low then use Figure 2-30. For steel pipe the limitations listed in (A) above apply.

Note Friction Factors F] and F2 are based on rale of flow, while Factors and C 2 based on actual pipe diameter. 

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

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