Reynolds number Chart

Figure 3.10 shows a friction factor - Reynolds number chart for Bingham plastics at various values of the Hedstrom number. The turbulent flow line is that for Newtonian behaviour and is followed by some Bingham plastics with low values of the yield stress [Thomas (1962)]. 

Substitution of the generalized Reynolds number (Section IIB) for the simple Newtonian Reynolds number has been shown (06) to enable approximate prediction of agitator power consumption for non-Newtonian fluids at low Reynolds numbers. The conventional Newtonian power number-Reynolds number charts which have been drawn up by Rushton et al. (R9) were shown to be applicable in the laminar region. This laminar region, however, appeared to extend to Reynolds numbers of 20 to 25, as compared with critical values of 8 to 10 for Newtonian liquids. Above Reynolds numbers of about 70 the conventional Newtonian curve again appeared to be followed. 

In summary, two of the principal approaches which were found useful for the calculation of pipe-line pressure drops have been extended to the problem of predicting power consumption for the agitation of non-Newtonian fluids. Extension of this work is required, but until further data become available, use of the standard power number-Reynolds number charts (with the generalized Reynolds number) is recommended. Between Reynolds numbers of 10 and 70 these charts will provide con-... 

Determine the kinematic viscosity of the oil Use Fig. 6.1 and Table 6.2 or the Hydraulic Institute—Pipe Friction Manual kinematic viscosity and Reynolds number chart to determine the kinematic viscosity of the liquid. Enter Table 6.2 at kerosene and find the coordinates as X = 10.2, Y = 16.9. Using these coordinates, enter Fig. 6.1 and find the absolute viscosity of kerosene at 65°F as 2.4 cP. Using the method of Example 6.2, the kinematic viscosity, in cSt, equals absolute viscosity, cP/specific gravity of the liquid = 2.4/0.813 = 2.95 cSt. This value agrees closely with that given in the Pipe Friction Manual. 

Determination of friction factors for some fluid flow applications can involves a trial-and-error procedure because the friction factor is not a simple function of the Reynolds number. Process engineers, therefore, refer to a Moody chart that has been developed using the following relationships ... 

The chart given in Figure 16 can be used in the following manner in order to size a relief valve for liquid service. First, determine the area required, A, without any viscosity correction (i.e., for K = 1). Then select the next larger standard orifice size from manufacturer s literature. Determine the Reynolds number, based on the following definition ... 

Resistance factors are taken from the Moody chart, when the Reynolds number and roughness are known. 

Equations 2-60 and 2-61 are illustrated graphically in Figure 2-21. This chart is called a Moody diagram, and it may be used to find the friction factor, given the Reynolds number and the surface roughness. 

In subcritical flow the discharge coefficient is affected by the velocity of approach as well as the type of choke and the ratio of choke diameter to pipe diameter. Discharge coefficients for subcritical flow are given in Figure 2-24 as a function of the diameter ratio and the upstream Reynolds number. Since the flow rate is not initially known, it is expedient to assume C = 1, calculate Q, use this Q to calculate the Reynold s number, and then use the charts to find a better value of C. This cycle should be repeated until the value of C no longer changes. 

The friction factor depends on the Reynolds number and the surface conditions of the pipe. There are numerous charts and equations for determining the relationship between the friction factor and Reynolds number. The friction factor can be calculated by [63]... 

Resistance, equivalent feet, design, 86-89 Chart, 87, 88 Reynolds number, 55, 67 Calculations, 68 Chart, 110 Rotary pumps, 206 Selection, 214 Type, 213... 

For a Newtonian fluid, the data for pressure drop may be represented on a pipe friction chart as a friction factor = (R/pu2) expressed as a function of Reynolds number Re = (udp/n). The friction factor is independent of the rheological properties of the fluid, but the Reynolds number involves the viscosity which, for a non-Newtonian fluid, is... 

As indicated earlier, non-Newtonian characteristics have a much stronger influence on flow in the streamline flow region where viscous effects dominate than in turbulent flow where inertial forces are of prime importance. Furthermore, there is substantial evidence to the effect that for shear-thinning fluids, the standard friction chart tends to over-predict pressure drop if the Metzner and Reed Reynolds number Re R is used. Furthermore, laminar flow can persist for slightly higher Reynolds numbers than for Newtonian fluids. Overall, therefore, there is a factor of safety involved in treating the fluid as Newtonian when flow is expected to be turbulent. 

The friction factor may be calculated from a knowledge of the fluid Reynolds number using the chart shown as Figure 13.2. Table 13.1 indicates the friction factors that correspond to zero and 80% conversion for the three pipe sizes of interest at two temperature levels. Examination... 

The Fanning friction factor may be determined either from a chart for both rough and smooth tubes or from a variety of correlations (Knudsen and Katz, 1958, pp. 173,176). The following correlation applies for turbulent flow in smooth tubes and for Reynolds numbers between 3,000 and 3,000,000 ... 

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. 

Alternatively, the friction loss can be estimated using the formula and friction factor (Fp) chart presented in Ref. P3 (p. 143). In this case the friction factor is a function of Reynolds number (NRe). Friction loss per metre = 4 FDp u2/D... 

For the Reynolds number range typical of drag reduction (Re 105), / is about 0.02 from the Moody chart (see Fig. 11.7). The typical turbulent intensity of gas in a pipe flow is about 5 percent. Using the Hinze-Tchen model (see 5.3.4.1), the ratio of the velocity fluctuation of the particles to that of the gas may be given by Eq. (5.196) as... 

Charts and equations describing the variation of the friction factor, /, with the Reynolds number, Rep, and wall roughness ratio, elD, where e is a measure of the roughness of the walls, are available [18],[19], [20]. A Moody chart that gives the friction factor variation is shown in Fig. 7.4. 

Determine the Reynolds number of the liquid. The Reynolds number can be found from the Pipe Friction Manual chart mentioned in step 1 or computed from Re =2214 B/dk = 2214(500)/[(6.065)(2.95)] = 61,900. 

To use the Pipe Friction Manual chart, compute the velocity of the liquid in the pipe by converting the flow rate to cubic feet per second. Since there are 42 gal/bbl and 1 gal = 0.13368 ft3, 1 bbl = (42)(0.13368) = 5.6 ft3. With a flow rate of 500 bbl/h, the equivalent flow in ft3 = (500)(5.6) = 2800 ft3/h, or 2800/3600 s/h = 0.778 ft3/s. Since 6-in schedule 40 pipe has a cross-sectional area of 0.2006 ft2 internally, the liquid velocity, in ft/s, equals 0.778/0.2006 = 3.88 ft/s. Then, the product (velocity, ft/s)(internal diameter, in) = (3.88)(6.065) = 23.75. In the Pipe Friction Manual, project horizontally from the kerosene specific-gravity curve to the vd product of 23.75 and read the Reynolds number as 61,900, as before. In general, the Reynolds number can be found faster by computing it using the appropriate relation given in Table 6.1, unless the flow velocity is already known. 

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. 

Chemical engineers are familiar with the Fanning (or Darcy) friction factor,/, the Moody chart of/vs. Reynolds number, Rg, and how all of this fits together to calculate pressure drop for a given fluid flow in a given sized pipe. The friction factor is calculated from the Colebrook equation ... 

The friction factor corresponding to this relative roughness and the Reynolds number can simply be determined from the Moody chart. To avoid the reading error, we determine it from the Colebrook equation ... 

---