Friction data

For extended surfaces, which include fins mounted perpendicularly to the tubes or spiral-wound fins, pin fins, plate fins, and so on, friction data for the specific surface involved should be used. For details, see Kays and London (Compact Heat Exchangers, 2d ed., McGraw-HiU, New York, 1964). If specific data are unavailable, the correlation by Gunter and Shaw (Trans. ASME, 67, 643-660 [1945]) may be used as an approximation. 

Pipe Friction Data for Clean Commercial Steel Pipe with Flow in Zone of Complete Turbulence... 

Brine Pipe Friction Multiples For Use With Water Friction Data, Figure 2-24... 

In this equation the negative sign is introduced in order to maintain a consistency of sign convention when shear stress is related to momentum transfer as in Chapter 11. Since (du,/dy)v=o must be positive (velocity increases towards the pipe centre), R0 is negative. It is therefore more convenient to work in terms of / , the shear stress exerted by the fluid on the surface (= —Rq) when calculating friction data. 

FIGURE 26.1 Experimental friction data (left) as function log speed at different temperatures and master curve (right) of an acrylate-butadiene rubber (ABR) gum compound on a clean dry silicon carbide 180 track surface referred to room temperature. (From Grosch, K.A., Sliding Friction and Abbrasion of Rubbers, PhD thesis. University of London, London, 1963.)... 

Like the original Darnell-Mol model, the Tadmor-Kleln model was developed with only very limited rate data because solids conveying measuring devices were not available at that time. Moreover, dynamic coefficient of friction data were also unavailable during their model developments. Complete plastlcatlng extrusion simulations, however, were developed with the Tadmor-Kleln model using engineering friction coefficients to estimate the characteristics in the process. 

The modified Campbell-Dontula model was developed using the LDPE resin friction data as applied to an empirical model. The empirical model is shown by Eq. 5.31 for the temperature range of 25 to 110 °C. The coefficients of dynamic friction using Eq. 5.31 is shown in Eig. 5.31. 

Here, V is the sliding velocity in cm/s, P is the pressure in MPa, and T is the interface temperature in degrees Celsius. The constants in the equation have units and these units have been omitted for clarity. At temperatures less than about 110 °C, the stress at the interface is due to a frictional force mechanism. At temperatures higher than 110 °C, the forces are from a viscous mechanism. The friction coefficients provided by Eq. 5.31 have the proper trends. Coefficients derived from the equation, however, need to be used with care because of its empirical nature and the difficulties in measuring frictional data. 

A number of issues relative to the prediction of solids conveying in smooth bore single-screw extruders are exposed from the theoretical fits to the data in Fig. 5.32. First, the data needed to carry out an effective simulation is difficult to take and is very time consuming, and only a few labs have the proper equipment that is, bulk density measurement, dynamic friction data, lateral stress, and solids conveying data. Moreover, care must be taken to develop an accurate representation of the surface temperature for the barrel and screw as a function of the axial position. This would be quite difficult in a traditional extruder with only a control thermocouple to measure the temperature at the midpoint of the barrel thickness. Second... 

For extended surfaces, which include fins mounted perpendicularly to the tubes or spiral-wound fins, pin fins, plate fins, and so on, friction data for the specific surface involved should be used. For... 

The Crane Company, Flow of Fluids Through Valves, Fittings, and Pipe, Pipe Friction Data Table, Crane Technical Paper No. 410, King of Prussia, PA, 1988, p. A-26. 

In view of these complexities, it is remarkable that Eq. 4.1-4 represents numerous metal-metal, dry frictional data rather well, for both the static and sliding cases. Polymers, on the other hand, exhibit an even more complex frictional behavior on metal. This is, perhaps, not surprising, since the physical situation involves a relatively soft, viscoelastic, and temperature-dependent material in contact with a hard, elastic, and much less temperature- and rate-dependent material. Empirical evidence of these complexities is the nonlinear relationship between the frictional force and the normal load... 

Kays, W. M., and R. K. Lo Basic Heat Transfer and Flow Friction Data for Gas Flow Normal to Banks of Staggered Tubes Use of a Transient Technique, Stanford Univ. Tech. Rep. 15, Navy Contract N6-ONR251 T.O. 6. 1952. 

PadProbe allows either continuous or periodic in situ, in-process control of two crucial CMP parameters pad life (dynamics of pad wear) and pad condition (dynamics and level of pad friction). Data obtained from such a... 

Thus, in practice we record friction data (images or loops) for both trace and retrace for different setpoints. We also acquire and capture for each setpoint the entire f-d curve to calculate the mean pull-off force (= adhesion A) and the load L. The analysis of the friction data provides the half width of friction loop W = (Mu-Md)/2) and the friction loop offsets (A (Mu + Md)/2) for sloped and flat surfaces for each load, i.e., we measured and calculate the following ... 

Friction data in the form of friction loops are captured at a constant load for various scan rates (that are converted to velocity taking the scan size into consideration) and sizes at room temperature and at 5°C. The friction force as half width of the friction loop is calculated and then plotted against velocity. 

Lateral force microscopy (LFM) is performed simultaneously with topographical imaging in contact mode using V-shaped Si3N4 cantilevers with a nominal spring constant of 0.06 N/m. All lateral force data are acquired under Milli-Q water. We use the open cell configuration (see Sect. 3.3 in Chap. 3). To ensure meaningful comparisons of friction data acquired on different films, the same tip must be used for all the films tested. 

These improvements have been achieved without sacrificing the antistiction characteristics of the film, in that water and hexadecane contact angles, apparent work of adhesion, and coefficient of static friction data are found to be similar to those of OTS, (see Table... 

A.32 [32] W. M. Kays and R. K. Lo. Basic heat transfer and friction data for gas flow normal to banks of staggered tubes Use of a transient technique. Stanford University, TR-1S, Navy Contract N6-ONR2SI, T.O. 6,1952. 

TABLE 19-12. FRICTION DATA FOR LAYER-LATTICE SOLIDS... 

Table 3.52. Results of Wear and Friction Data for a PFA Thrust Bearing...

Eq. 6.149 provides poor values of the slope du ldy. For flat plates with uniform free-stream velocities, Coles found agreement with the data when ft = 0.62. On the other hand, if experimental skin friction data obtained at very high Reynolds numbers are used to define ft, a value of 0.55 is favored. The use of these different values of ft produces differences of only a few percent in the skin friction and boundary layer integral parameters, such as the displacement thickness... 

The recommended design method for Mach numbers up to supersonic (Ma < 4) and adiabatic wall conditions (Tw = Taw) is arbitrary since all the methods yield essentially the same results The design methods for hypersonic Mach numbers (Ma, > 4) and cold wall conditions (Tw< T w) should be based on conservatism. Comparison of the available skin friction data reveals differences of 20 percent on surfaces near adiabatic wall temperature and as much as a factor of 2 for highly cooled walls (T 0.2Taw). If only the most recent skin friction data for... 

Tw/Taw < 1.0 are considered, particularly those where Rea was obtained from boundary-layer surveys, a recent evaluation [108] favors the Coles and van Driest methods. The Sommer and Short method and the Spalding and Chi method may underpredict the skin friction as much as 30 percent. For very cold walls (Tw < 03Taw), none of the methods predict the effect of wall temperature ratio in the available skin friction data. The van Driest skin friction predictions are shown in Fig. 6.42 for Te = 400 R (222 K), 0 < Ma, < 10, and TwITe = 1,2, 3, 5, TJTe. 

A later study by Hancock [142] revealed a significant dependence of the boundary layer momentum thickness on the free-stream turbulence level. Consequently, significant effects were observed when skin friction data were compared at the same momentum-thickness... 

Earlier investigators studying the drag-reducing phenomenon in viscoelastic fluids often used Re and Reeff. The former is generally valid only for dilute polymer solutions, in which case the solution viscosity is quite close to that of the solvent. The use of Reeff seems inappropriate in the study of the drag coefficient because it does not represent any physical property of nonnewtonian fluids, although it produces a unique reference line for experimental friction data in laminar pipe flow ... 

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