Friction Correction Research Articles

Friction Correction Factors for Center-Pivots

Analytical equations for friction correction factors for center-pivot laterals without end guns are developed. This work illustrates a discrepancy when earlier equations are applied to center-pivots with small numbers of outlets. Earlier equations were also limited to center-pivots with constant outlet spacing. Equations presented in the current work are developed for center-pivots with constant outlet spacing and also for center-pivots with constant outlet discharge. When the equations developed in the current work are applied to center-pivots with a large number of outlets, the results are in good agreement with previous work for center-pivot laterals with an infinite number of outlets. When applied to a smaller number of outlets the equations presented here provide a more precise estimate of the friction correction factor. Using the current equations, the friction correction factor for center-pivots with constant outlet spacing was found to be very similar to the friction correction factor for center-pivots with constant outlet discharge. Useful simple equations are also presented for calculating the discharge of each outlet or for calculating the spacing between outlets.

The stability of osumilite in metapelitic granulites

Abstract A petrogenetic grid and related diagrams derived from KFMASH‐system experiments demonstrate that osumilite is stable in relatively magnesian bulk rock compositions (XMg > 0.6) at temperatures in excess of 875° C and pressures less than 11 kbar. The experiments, involving the dehydration melting of biotite in synthetic metapelites, were conducted in the range 850–1000° C. Both the mineral assemblages and phase compositions reported from well‐documented natural examples of osumilite‐bearing rocks are reproduced by the experiments at P‐T conditions similar to those previously estimated for these occurrences. Peak metamorphic P‐T conditions can be reliably inferred from distinctive osumilite‐bearing assemblages identified in the phase diagrams, thereby avoiding the problems of diffusional re‐equilibration that often prohibits conventional geothermobarometry from recovering peak conditions. Integration of the experimental data with recent independent experiments, after correcting the latter for an underestimated friction correction, allows extension of the petrogenetic grid to higher temperatures. The extended grid is applied to assess and refine the metamorphic history of the Napier Complex, East Antarctica: the high‐P stability limit for osumilite in the Napier Complex is 9–10 kbar, the prograde P‐T‐t path is not necessarily anticlockwise and isobaric cooling in the Scott and Tula mountains occurred, respectively, at pressures greater and less than reactions in the range 8–9 kbar. The stability range for osumilite predicted by the KFMASH‐system petrogenetic grid overlaps many more metamorphic terranes than osumilite is found in. Whilst osumilite is not distinctive in thin section and is prone to retrogression, it is possible that carbon dioxide present in the natural system stabilizes cordierite at the expense of osumilite.

A film model for free convection over a vertical porous plate with blowing or suction

A film model is described for free convective heat transfer and friction in the presence of wall suction or injection. The analysis yields a thermal correction factor, which appears to be the classical (Ackermann) expression, and a novel friction correction factor, derived here for the first time. Both correction factors are applied to free convection along a vertical flat porous plate for values of the Prandtl number of 0.73, 1 and 7. Subsequently, the film theory predictions are compared with the numerical and asymptotic results of a boundary layer analysis, performed by previous investigators. On the basis of this comparison, a modified correction factor is proposed which correlates excellently with the results of the boundary layer analyses.

Rotational diffusion kinetics of polar solutes in hexamethylphosphoramide–water systems

The rotational reorientation times (τr) of three kinds of dyes—cresyl violet (a monocation), nile red (neutral but polar), and resorufin (a monoanion) were measured in a series of binary mixtures of hexamethylphosphoramide (HMPA)–water at 298 K using the picosecond fluorescence depolarization spectroscopy. A hook-type profile of τr vs η was observed for all three dyes. The contribution due to the dielectric friction is minimal and is irrelevant in explaining the rotational dynamics of nile red. The dielectric friction correction is modest for cresyl violet and resorufin. The solvation effects in the binary mixture are dominant for understanding the rotational dynamics of cresyl violet. The microscopic structure features of the binary mixture are brought out by the study of resorufin.

An elasto-plastic finite element and experimental study of the ironing process

This paper applies the incremental finite-element method of elasto-plastic large deformation analysis to the ironing process. In addition, an experimental test of the ironing process has been performed to verify the theoretical formulation. The paper is divided into two parts. The first part involves deriving the load correction and friction correction matrices which are indispensable for surface traction rate equilibrium in the updated Lagrangian formulation, following which the preparation and procedure of the experimental work is described. The second part involves numerical simulation and a comparison of the results of the numerical model with those of the experiment. The finite-element calculations also predict the forming load, the stress distribution, the plastic enclave, and the deformation history. The comparison shows good agreement between the load-displacement relations of the experiment and the finite-element predictions.

Discussion of “ Friction Correction Factor for Center‐Pivot Irrigation Systems ” by J. Mohan Reddy and Horacio Apolayo (February, 1988, Vol. 114, No. 1)

Discussion of “ <i>Friction Correction Factor for Center‐Pivot Irrigation Systems</i> ” by J. Mohan Reddy and Horacio Apolayo (February, 1988, Vol. 114, No. 1)

Friction Correction Factor For Center‐Pivot Irrigation Systems

A friction correction factor (Fcp) for use in the estimation of friction loss in a center-pivot irrigation system lateral is derived. The results obtained using the Fcp are compared with the result...

Stress-strain properties of structural steel at strain rates of up to 10 5 per second at sub-zero, room and high temperatures

A testing technique and method of processing the displacement-time data have been developed following which the stress-strain characteristics of structural steel at strain rates between 10 3 to 10 5 per second over a strain of about 50% and at different temperatures have been determined. The steel under present test condition within this strain rate range showed a strong strain rate sensitivity. The material inertia and temperature rise during high speed deformation were found to have mutually cancelling effect on the deduced flow stress. In determining the results, appropriate friction correction was also made and the results presented in this paper are all converted to those under frictionless condition. Finally, a constitutive equation has been proposed for the steel incorporating the effects of work-hardening and strain rate sensitivity of the material.

Indentation processes in poly(methyl methacrylate). I. Ball indentation

The indentation of PMMA is shown to be highly dependent on indenter-PMMA friction and a correction for this effect is proposed. For penetrations greater than half a radius the pressure varies with penetration rate and ball size as predicted by the expanding cavity model of Puttick et al. (1977) provided the indentation diameter is determined under load and the friction correction is applied. This allows assignment of a value to the parameter plastic-zone radius/cavity radius, c/a. Observations of the growth and position of the region of anomalous refractive index beneath the indenter and the fracture surfaces shows the creation of a core of material beneath the indenter which can be identified with the cavity of the plastic-elastic model. This allows an alternative estimate of c/a and both methods give a value of 1.9.

Low-friction cell for piston-cylinder high-pressure apparatus

A high-temperature cell has been developed in which a weak salt such as NaCl is used as a pressure medium. This cell exhibits extremely low friction. The behavior of the cell was studied in detail by observing the melting temperature of metals by dta over the range 10–60 kbar and 300°–1400°C. Melting temperatures determined on compression and decompression strokes coincide. Friction corrections are eliminated. Transition pressures determined in this cell agree with those determined in gas apparatus over the range of overlap. Comparison with other cells indicates systematic overestimation of pressure in the other dta cells studied. Applicability to geologic phase studies is discussed. Over the range 10–60 kbar the precision of pressure determination in this cell is ±(0.3–0.5) kbar. Absolute accuracy is estimated to be ±(1% + 0.5) kbar.

Strength of solid pressure media and implications for high pressure apparatus

The stress-strain properties of talc, pyrophyllite, silver chloride, sodium chloride, boron nitride and graphite have been measured under confining pressures up to 8 or 10 kb at room temperature, and, in the case of talc, also at temperatures up to 900° C. The extrapolation and application of these results to solid medium high pressure apparatus of pistoncylinder type is discussed and a calculation made of the correction to nominal pressure (“friction correction”), taking into account the stress gradients in the medium and the shearing between the medium and the cylinder wall. Correction to the nominal differential stress measured in solid medium stress-strain apparatus is also discussed.

Note on wave run-up

A comparison is made of total run-up of breakers on beaches predicted by present theory and observed in channel experiments. The inviscid theory is shown to predict the observed dependence of run-up on bore strength, but not that on beach slope. A tentative, simple friction correction proposed by Le Mehaute brings theory and experiment into much better agreement, if abnormally large hydraulic friction be accepted. The evidence indicates that studies of the role of dissipation are most likely to lead to better run-up predictions.

The quartz-coesite transition measured in the presence of a silicate liquid and calibration of piston-cylinder apparatus

Hydrothermal melting reactions in the system NaAlSiO_4-SiO_2-H_2O have been extended into the coesite stability field using piston-cylinder apparatus, and the quartz-coesite transition has been bracketed at 735° (28.0±0.9 Kb) and at 800° C (28.15±0.9 Kb) in the presence of a silicate liquid phase; this provided favorable kinetic conditions. The results agree closely with previous piston-cylinder determinations employing a correction for pressure loss due to friction. Consideration of previous calibration and hysteresis experiments leads to the conclusion that despite its potential utility, the quartz-coesite transition can not be confidently used as a calibrant for piston-cylinder apparatus until the question of whether or not to apply a friction correction has been resolved.

Effect of pressure on the melting of diopside, CaMgSi2O6, and albite, NaAlSi3O8, in the range up to 50 kilobars

The melting curves of albite and diopside have been determined in the pressure range 5 to 50 kb by means of single-stage apparatus. Data are given for NaAlSi3O8 composition only at pressures below 33 kb, where albite is the phase stable at the liquidus. Simon equations have been calculated for both curves, and they fit the data well. The melting curves have a pronounced curvature, and the slopes at pressures above 25 kb are only about half the initial slopes. These results suggest that the effect of pressure on the melting of rocks in the mantle will decrease notably with depth. Extrapolation of the diopside curve to a pressure of 1400 kb, equivalent to that present at the core-mantle boundary, gives a melting temperature of 3750°C. Experience with single-stage apparatus has shown that the friction correction of −8 per cent that we previously applied is probably too large. Results of this study are given as load pressures and are believed to be accurate within ±5 per cent.

Some Model Experiments and Ship Correlation in respect to Manoeuvrability

The present paper relates to some model experiments and ship correlation in respect to manoeuvrability, carried out at the Osaka University Tank under cooperation of Kawasaki Dockyard Co. and Sasebo Heavy Industries Co. The standard zig-zag tests were carried out for a 12, 000 DW cargo liner and her model at various load condition, while the similar tests as well as turning and spiral tests were done for a 130, 000 DW super-tanker and her model at full load condition. These correlative studies show that model ships are much more stable on course, much quicker in response to helm and have less turning ability for slight helm, compared with actual ships. The difference between models and ships, however, decreases with increasing the intensity of turning motion, so that there is no significant discrepancy between the two in respect to turning diameter for hard over helm. In a word, there is a considerable model-ship disagreement upon stability on course, but not upon turning performance at hard over.It should seem that this discrepancy relate largely to difference in propeller race intensity through rudder effectiveness and possibly propeller fin effect. The difference depends upon the lack of friction correction for free-running models.