Friction factor charts for

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

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

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 =...

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. 

In practice pipes are not smooth and for turbulent flow it is found that/also depends on surface roughness. Friction factor charts for rough pipes are available. ... 

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. 

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. 

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 ... 

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

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 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. 

Figure 5.10 is a friction-factor chart in which / is plotted against for the flow of power-law fluids in smooth pipes. A series of lines depending on the magnitude of n is needed for turbulent flow. For these lines the following equation, andogous to Eq. (5.43), for newtonian fluids, has been suggested ... 

For turbulent flow at > 10,000 with a smooth wall,/o is given by Eq. (13.15) or a Fanning friction factor chart can be used to obtain/. 

A large number of experimental data on friction factors of smooth pipe and pipes of varying degrees of equivalent roughness have been obtained and the data correlated. For design purposes to predict the friction factor/and, hence, the frictional pressure drop of round pipe, the friction factor chart in Fig. 2.10-3 can be used. It is a log-log plot of/... 

Looking at the friction factor chart (Fig. 48.6), we see how the experimental data further confirms Reynolds earlier work and helps us even today with our own field work. Once we have determined the friction factor (j) for the pipe flow we are studying, all that remains is to evaluate the frictional pressure loss, AP from... 

You will have noticed that there is just one line on the friction factor chart (Fig. 48.6) for < ) in terms of Re in the laminar flow region (Re less than 2 x 10 ) of slope < ) = 8/Re. This means that for Reynolds numbers of less than 2000 we can very simply calculate the frictional pressure loss by the relationship... 

There is also a friction factor chart drawn by Dodge and Metzner plotting the Fanning friction factor versus the Metzner-Reed Reynolds number (although this has been subsequently redrawn for convenience with (j), see ref. 4). This chart shows that the friction factor decreases with n in turbulent flow—that is, it decreases as shear-thinning character increases. If you are studying this chart, be aware that the only experimentally verified data for turbulent flow is that given for m = 1.0 to n = 0.4. 

In a simple cyclone diffuser performance test conducted by the writers, however, a much larger decrease in cyclone pressure loss was observed. The apparatus tested was a 6-inch (153 mm) cylindrical bodied cyclone shown in Fig. 15.1.15. The cyclone Reynolds number for these tests were in the 800 to 1000 range (per Eq. 4.2.8) which, for cyclones, makes the Eu value very insensitive to the Reynolds number. (See gas phase friction factor charts in Ch. 6, for example.)... 

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