Friction factor charts

Determine friction factor, f, from Moody Friction Factor Charts, Figure 2-3. 

Note the friction factor used in equation 5.3 is related to the shear stress at the pipe wall, R, by the equation / = (R/pu2). Other workers use different relationships. Their charts for friction factor will give values that are multiples of those given by Figure 5.7. So, it is important to make sure that the pressure drop equation used matches the friction factor chart. 

Friction-factor chart. (From Unit Operations of Chemical Engineering by W. L. McCabe and J. C. Smith. Copyright (c) 1967. Used with permission of McGraw-Hill Book Company.)... 

This procedure based on the friction factor chart is too stringent for large-diameter vessels, which behave nearly like smooth pipe, requiring inordinately large values of Re. 

Values of the friction factor are traditionally presented on a friction factor chart such as that shown in Figure 2.1. It will be noted that the... 

Friction factor chart for Newtonian fluids. (See Friction Factor Charts on page 349.)... 

Use of the friction factor chart or a correlation such as equation 2.19 enables calculation of the frictional pressure drop for a specified flow rate from equation 2.13. 

Given a suitable algebraic correlation such as equation 2.19, the friction factor chart might be considered obsolete. Both / and fRe2 can be represented algebraically as functions of Re allowing both types of calculations to be done. In the case of the inverse problem, that is the calculation of the flow rate for a specified pressure drop, an alternative is to use an iterative calculation, a procedure that is particularly attractive with a pocket calculator or a spreadsheet. Using equation 2.19 for /, the procedure is as follows ... 

The changing character of the flow in the different regions of the turbulent boundary layer explains certain aspects of the friction factor chart. If the absolute roughness of the pipe wall is smaller than the thickness of the viscous sublayer, flow disturbances caused by the roughness will be damped out by viscosity. The wall is subject to a viscous shear stress. Under these conditions, the line on the friction factor chart... 

From the friction factor chart, Figure 2.1, for a smooth tube and this value of the Reynolds number, fLO = 0.0058. Therefore... 

Friction factor chart for laminar flow of Bingham plastic materials... 

At high Reynolds numbers (Re > 2500), the surface roughness is an important parameter and must be allowed for in the calculations. Friction factor charts [53] include curves relating to various values of the relative roughness, that is the ratio of the mean height of surface roughness to the tube diameter. 

The friction loss can also be estimated using the formula and friction factor chart given in Ref. P3 (p.143) ... 

Figure 7-22. Friction factor chart for various pipe sizes.

Figure 7 Fanning friction factor chart for pipe flow. (M) piping system example (see Section 3.10) Re = 363,000, e/d = 0.0005, cp =...

Determine the friction factor of this pipe. Enter Fig. 6.2 at the Reynolds number value of 61,900 and project to the curve 4 as indicated by Table 6.3. Read the friction factor as 0.0212 at the left. Alternatively, the Pipe Friction Manual friction-factor chart could be used, if desired. 

The reader will note that both the Karman-Nikuradse and the Colebrook equations are implicit in the friction factor and require a trial and error solution. For hand calculations, it is often simpler to use the friction factor chart. 

From the friction factor chart, the estimated friction factor is 0.0052. Finally the pressure drop per unit length is... 

Figure 8.16 Friction-factor chart. From Ref. 18 with permission. 

After the emulsion viscosity is estimated, friction factor charts may be used directly to determine the flow regime (laminar or turbulent) and the pressure gradient. Emulsion viscosity may be used as an input to a standard pipeline model. Nevertheless, it is strongly recommended that pilot-plant testing be completed on new crude oils before commercial application. 

Absolute roughness commercial steel pipe. Table 5.2 = 0.046 mm Relative roughness = 0.046/(25 x 10 3) = 0.0018, round to 0.002 From friction factor chart. Figure 5.11, f = 0.0032... 

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