Friction factors for smooth pipe flow

Friction factor data from two recent pipe flow experiments are combined to provide a comprehensive picture of the friction factor variation for Reynolds numbers from 10 to 36,000,000

A new friction factor relationship for fully developed pipe flow

The friction factor relationship for high-Reynolds-number fully developed turbulent pipe flow is investigated using two sets of data from the Princeton Superpipe in the range 31×10^3 ≤ ReD ≤ 35×10^6. The constants of Prandtl’s ‘universal’ friction factor relationship are shown to be accurate over only a limited Reynolds-number range and unsuitable for extrapolation to high Reynolds numbers. New constants, based on a logarithmic overlap in the mean velocity, are found to represent the high-Reynolds-number data to within 0.5%, and yield a value for the von Kármán constant that is consistent with the mean velocity profiles themselves. The use of a generalized logarithmic law in the mean velocity is also examined. A general friction factor relationship is proposed that predicts all the data to within 1.4% and agrees with the Blasius relationship for low Reynolds numbers to within 2.0%

Comparison of Hirs' equation of Moody's equation for determining rotordynamic coefficients of annular pressure seals

The rotordynamic coefficients of an incompressible-flow annular pressure seal were determined using a bulk-flow model in conjunction with two different friction factor relationships. The first, Hirs' equation, assumes the friction factor is a function of Reynolds number only. The second, Moody's equation, approximates Moody's diagram and assumes the friction factor is a function of both Reynolds number and relative roughness. For each value of relative roughness, Hirs' constants were determined so that both equations gave the same magnitude and slope of the friction factor. For smooth seals, both relationships give the same results. For rough seals (e/2 H sub 0 = 0.05) Moody's equation predicts 44% greater direct stiffness, 35% greater cross-coupled stiffness, 19% smaller cross-coupled damping, 59% smaller cross-coupled inertia, and nominally the same direct damping and direct inertia

Friction anisotropy at Ni(100)/(100) interfaces: Molecular dynamics studies

The friction of surfaces moving relative to each other must derive from the atomic interaction at interfaces. However, recent experiments bring into question the fundamental understanding of this phenomenon. The analytic theories predict that most perfect clean incommensurate interfaces would produce no static friction, whereas commensurate aligned surfaces would have very high friction. In contrast recent experiments show that the static friction coefficient between clean but 45° misoriented Ni(001) surfaces is only a factor of 4 smaller than for the aligned surfaces (θ∼0°) and clearly does not vanish (θ is defined as the rotation angle between the relative crystallographic orientations of two parallel surfaces). To understand this friction anisotropy and the difference between analytic theory and experiment, we carried out a series of nonequilibrium molecular dynamics simulations at 300 K for sliding of Ni(001)/Ni(001) interfaces under a constant shear force. Our molecular dynamics calculations on interfaces with the top layer roughed (and rms roughness of 0.8 Å) lead to the static frictional coefficients in good agreement with the corresponding experimental data. On the other hand, perfect smooth surfaces (rms roughness of 0 Å) lead to a factor of 34–330 decreasing of static friction coefficients for misaligned surfaces, a result more consistent with the analytic theories. This shows that the major source of the discrepancy is that small amounts of roughness dramatically increase the friction on incommensurate surfaces, so that misaligned directions are comparable to aligned directions

One-body energy dissipation in fusion reaction from mean-field theory

Information on dissipation in the entrance channel of heavy-ion collisions is extracted by macroscopic reduction procedure of Time-Dependent Hartree-Fock theory. The method gives access to a fully microscopic description of the friction coefficient associated with transfer of energy from the relative motion towards intrinsic degrees of freedom. The reduced friction coefficient exhibits a universal behavior, i.e. almost independent of systems investigated, whose order of magnitude is comparable with the calculations based on linear response theory. Similarly to nucleus-nucleus potential, especially close to the Coulomb barrier, there are sizable dynamical effects on the magnitude and form factor of friction coefficient.Comment: 7 pages, 10 figure

The Puzzling Collapse of Electronic Sliding Friction on a Superconductor Surface

In a recent paper [Phys. Rev. Lett. 80 (1998) 1690], Krim and coworkers have observed that the friction force, acting on a thin physisorbed layer of N_2 sliding on a lead film, abruptly decreases by a factor of ~2 when the lead film is cooled below its superconductivity transition temperature. We discuss the possible mechanisms for the abruptness of the sliding friction drop, and also discuss the relevance of these results to the problem of electronic friction.Comment: 5 pages, no figure

Interfacial friction between semiflexible polymers and crystalline surfaces

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities the decay of the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.Comment: 31 pages, 12 figure

Fission widths of hot nuclei from Langevin dynamics

Fission dynamics of excited nuclei is studied in the framework of Langevin equation. The one body wall-and-window friction is used as the dissipative force in the Langevin equation. In addition to the usual wall formula friction, the chaos weighted wall formula developed earlier to account for nonintegrability of single-particle motion within the nuclear volume is also considered here. The fission rate calculated with the chaos weighted wall formula is found to be faster by about a factor of two than that obtained with the usual wall friction. The systematic dependence of fission width on temperature and spin of the fissioning nucleus is investigated and a simple parametric form of fission width is obtained.Comment: RevTex, 12 pages including 9 Postscript figure

Relativistic Dynamical Friction in the Weak Scattering Limit

A test mass, $M$, moving through an ambient medium of light particles with lower average kinetic energy than itself suffers a deceleration caused by its scattering of the light particles. The phenomenon is usually referred to as dynamical friction. The velocity, \v, of the test mass decays on a timescale independent of \v in the non-relativistic case. We derive expressions for dynamical friction in the case that the test mass and the light particles are relativistic, and that the scattering is weak (with impact parameter, $b\gg M$). In the case that the light particles are ultra-relativistic, and isotropic in the frame in which $M$ moves with velocity $v$, we find an explicit expression for the dynamical friction. The well known factor of 2 correcting the Newtonian scattering of photons to give the Einstein angle, $4M/b$, has the largest effect on the resulting friction, which is modified by a factor of roughly $16 / 3\gamma_v$ over the simple non-relativistic case. In the non-relativistic case, the largest contribution to the friction comes from light particles moving slower than $v$. We find that this is not the case for ultra-relativistic scattering, essentially because the scattering angle is independent of \v. Some astrophysical implications are discussed. (Accepted for publication in Monthly Notices.)Comment: 10 pages (no figures), self-unpacking uuencoded PostScript (uufiles), RDF#