Inertial error

The time difference (delay) between the measured quantity and the measurement result is called the inertial error. A definition- is the error due to iner tia (mechanical, thermal, etc.) of the parts of a measuring instrument. In ventilation equipment the critical component in the measuring chain, from the dynamic point of view, is often the sensor or the measuring transducer (probe). 

Depending on the sensor/probe construction, there may be from one to several capacities, each increasing the inertial error. The inertial error depends not only on the features of the instrument, but also on the character of the... 

Continuing the above example, the inertial error obviously is the difference between the final temperature and the sensor temperature. From Eq. (12.15), the inertial error of a first-order system is... 

The error has its maximum value E, — IT - Tj at t = 0 and decreases toward , =0 when the time approaches infinity. Fntm Eq. (12.16), the desired time for the inertial error to reach a certain value can be solved for. 

For determination of the aerodynamic diameters of particles, the most commonly apphcable methods for particle-size analysis are those based on inertia aerosol centrifuges, cyclones, and inertial impactors (Lundgren et al.. Aerosol Measurement, University of Florida, Gainesville, 1979 and Liu, Fine Paiiicles—Aerosol Generation, Measurement, Sampling, and Analysis, Academic, New York, 1976). Impactors are the most commonly used. Nevertheless, impactor measurements are subject to numerous errors [Rao and Whitby, Am. Ind. Hyg. A.s.soc.]., 38, 174 (1977) Marple and WiUeke, "Inertial Impactors, in Lundgren et al.. Aerosol Measurement and Fuchs, "Aerosol Impactors, in Shaw, Fundamentals of Aerosol Sci-... 

These inertial effects become less important for particles with diameters less than 5 /rm and for low wind velocities, but for samplers attempting to collect particles above 5 p.m, the inlet design and flow rates become important parameters. In addition, the wind speed has a much greater impact on sampling errors associated with particles more than 5 fim in diameter (4). 

Extensive comparisons of predictions and experimental results for drag on spheres suggest that the influence of non-Newtonian characteristics progressively diminishes as the value of the Reynolds number increases, with inertial effects then becoming dominant, and the standard curve for Newtonian fluids may be used with little error. Experimentally determined values of the drag coefficient for power-law fluids (1 < Re n < 1000 0.4 < n < 1) are within 30 per cent of those given by the standard drag curve 37 38. ... 

With these data and Darcy s law, the in-plane viscous permeabilihes were determined. Only the viscous permeability coefficient was determined because it was claimed that the inertial component was undetectable within the error limits of measuremenf for fhese fesfs. If is imporfanf to mention fhaf fhis technique could also be used to measure fhe permeabilify of diffusion layers wifh different fluids, such as liquid wafer. 

Equation (11-11) depends on neglect of inertial terms in the Navier-Stokes equation. Neglect of inertia terms is often less serious for unsteady motion than for steady flow since the convective acceleration term is small both for Re 0 (Chapters 3 and 4), and for small amplitude motion or initial motion from rest. The second case explains why the error in Eq. (11-11) can remain small up to high Re, and why an empirical extension to Eq. (11-11) (see below) describes some kinds of high Re motion. Note also that the limited diffusion of vorticity from the particle at high cd or small t implies that the effects of a containing wall are less critical for accelerated motion than for steady flow at low Re. 

This discrepancy is rather disturbing because the creep recovery experiments were obviously designed and tested with considerable care (186). Furthermore, as pointed out earlier, creep recovery is the most direct method for measuring J°. Most of the likely errors (such as inertial effects in the instrument or nonattainment of steady state) would tend to give values which are too small rather than too large. Similar but smaller effects have been observed by other methods in solutions of polyisoprene (167) and poly (a-methyl styrene) (187). In the latter... 

However, progress has recently been made in the ab initio calculation of rovib contributions to the inertial moments for small molecules [2,3], which appears to be a promising way of combining computer power and practical spectroscopy towards the goal of greatly improved accuracy of molecular structure determinations. Meanwhile, efforts must continue to at least estimate the resulting errors of the molecular structures obtained by the available methods or to develop variants which are less error prone due to a (partial) compensation of the rovib contributions or to devise methods to include them in some way in the model used. 

However, there is also a drawback. Small coordinates (< 15 pm) cannot be reliably determined because a small coordinate with its even smaller square is the result of a very small inertial moment difference which, due the experimental errors of the moments and the less than perfect compensation of the rovib contributions, may no longer be significant. The rs-method does not use the first or second moment equations (which would hold strictly only for the equilibrium configuration). The... 

While the relations between the inertial and planar moments are strictly linear and constant, the relation between the increments of the rotational constants Bg and the moments, say Ig, is a truncated series expression and only approximately linear, Alg = ( f/B2g)ABg. Also, the transformation coefficients f/B2g are not strictly constant (nonrandom), although usually afflicted with only a very small relative error. The approximations are, in general, good enough to satisfy the requirements for Eq. 22, and for the above statement rt = rp = rB to be true for all practical purposes. 

The 2+/3+ transition in the Marcus model or its successors involves only small Inner Sphere changes in solvation molecule coordinates in the radial direction to and from the ion. Electron transfer under FC or Born-Oppenheimer conditions demands that an activation energy in the outer Continuum should resist one-electron transfer via a continuum inertial term X = (e2/2r )(l/n2 - l/e0) where r is an effective intermediate reactant-product radius. To avoid error, X can be... 

This important result requires some comment. The expressions for the error (27) and (28) are derived under the assumption that metadynamics can be modelled with a stochastic differential equation of the form (19). In this equation the noise is independent on the position in the CV space, there are no inertial effects, and the relaxation to equilibrium is described by a simple diffusion coefficient. These approximations might sound severe, but the... 

Here, we assume that the gaseous phase hydrostatic pressure is negligible. We note that the approximations made in the evaluations of K,e and pc cause more errors in the determination of u( and ve than the exclusion of the inertial terms. Furthermore, we expect dptJdx to be small. Then, we can write Eqs. 9.114 and 9.115 as... 

Stokes law has been derived for Re 1, neglecting the inertial terms in the equation of motion. If Re = I, the drag predicted by Stokes law is 13% low, due to the errors introduced by the assumption that inertial terms are negligible. To account for these terms, the drag force is usually expressed in terms of an empirical drag coefficient Co as... 

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