Friction, generalised

Yooi24) has proposed a simple modification to the Blasius equation for turbulent flow in a pipe, which gives values of the friction factor accurate to within about 10 per cent. The friction factor is expressed in terms of the Metzner and Reed(I8) generalised Reynolds number ReMR and the power-law index n. 

Another frictional coefficient formalism is that represented by the generalised Stefan-Maxwell equation s>... 

D only assumes a constant value over times long compared with rc( 10rc), such that (u(O)u(f)), the velocity autocorrelation function, is nearly zero. The diffusion equation is not valid over times < 10rc(i.e. a few picoseconds at least). A better approach would be to use a generalised Langevin equation with a friction coefficient which has a memory and such that the velocity autocorrelation takes 0.5ps to decay to insignificant levels (see Chap. 11) [453]. 

Xi = generalised force 0j = flux of species i Llk = phenomenological coefficient E = electrical potential difference A P= pressure difference Le = electrical conductivity of one square cm of membrane n = number of components of a system ut = velocity of component i i3j j = friction coefficients 7, - = electrical transport number lt = reduced transport number or transference number z( = charge of ion i vt = partial volume of ion i per gmol vD — partial volume of the solvent per gmol... 

The linear approximation (7.9) is insufficient to describe the variation of the friction coefficient at large velocity gradients. In this case, approximation (7.9) can be generalised (Pokrovskii and Pyshnograi 1990, 1991) to become... 

Some useful generalisations can be made about friction and wear behaviour. The coefficient of friction decreases with increasing contact pressure although the relationship will vary with the type of coating and other test conditions. The effects of contact load and speed on wear rate or wear life are less easily defined, although the general patterns are as shown in Figures 11.3 and 11.4. However, as has been... 

It may be mentioned here that a recent study (Vasconcelos 1996) of a simple noncooperative (one-block) model of stick-slip motion (described by eqn (4.2) with / o = 0 or eqn (4.4) with k = 0) shows discontinuous velocity-dependent transition in the block displacement, for generic velocity-dependent friction forces. Naive generalisation of this observation for the coupled Burridge-Knopoff model would indicate a possible absence of criticality in the model. 

We assume for the purposes of the present description that the generalised forces Q may depend on (t,q,u), but not directly on X, This rules out friction forces see [3,4] for their inclusion in the considerations. 

Gibilaro, L.G., Di Felice, R., Waldram, S.P. and Foscolo, P.U. (1985). Generalised friction factor and drag coefficient correlations for fluid-particle interactions. Chem. Eng. Sci., 40, 1817. 

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