Coriolis force principle

A mass flowmeter based on the Coriolis force principle has been developed by Micro Motion. Example 7-3 describes some of its details. 

As was pointed out earlier, when we have considered the physical principles of the ballistic gravimeter and the pendulum an influence of the Coriolis force was ignored. Now we will try to take into account this factor and consider the motion of a particle near the earth s surface. With this purpose in mind let us choose a non-inertial frame of reference, shown in Fig. 3.5a its origin 0 is located near the earth s surface and it rotates together with the earth with angular velocity a>. The unit vectors i, j, and k of this system are fixed relative to the earth and directed as follows i is horizontal, that is, tangential to the earth s surface and points south, j is also horizontal and points east, k is vertical and points upward. As is shown in Fig. 3.5a SN is the earth s axis, drawn from south to north, I is the unit vector along OiO, and K is a unit vector parallel to SN. 

Viewing the structure in the direction of the sensitive axis, one can recognize a principle similar to Fig. 7.2.1. Owing to the paddle structure, the Coriolis forces... 

Fig. 7.2.6 Functional principle of a silicon micromachined tuning fork, the tines are excited by piezoelectric actuators, the Coriolis forces bend the suspensions and are detected by piezoresistive resistors in the suspension bars. Source Conti Temic, Produktlinie Sensorsysteme...

Fig. 7.2.14 Principle of the micromachined rotational yaw-rate sensor 1, comb structure for drive and drive detection 2, rotating mass 3, sensitive direction Fc, Coriolis force ...

Modern sensors are remarkable in many ways. Their small dimensions open up new areas of mechanics, flow control, friction, and oscillation. Force measurements are just one example. The once somewhat obscure classical Coriolis force is now the principle means of sensing rotation. And the even more obscure miniscale quantum-mechanical Casimir force, arising between two close interfaces, is now also accessible to sensor structures. Sensitivities are astonishing even now, but will most probably continue to be enhanced. Very many external parameters, such as temperature, pressure, and electromagnetic fields, can be accurately and quickly measured. What a wonderful area of activity for physicists, chemists, engineers - and salespeople alike The prospect of protecting humankind as well as the environment is gratifying. 

In today s industrial applications, Coriolis mass flowmeters are widely used by process engineers to monitor mass flow rate. This meter measures the Coriolis force that depends on the mass momentum of the flow, and, in principle, it can be applied to both single- and mixed-phase flows. Magnetic or optical detectors are generally used to detect mass-flow-related Coriolis acceleration. A brief description of the Coriolis flowmeter will be presented because it is widely used in industrial processes. 

Flows are of fundamental importance for controlling a plant and for balancing and metering liquids. A large number of measurement principles are available here. Apart from the Coriolis-force meter, which directly measures the mass flux, all of them measure the volume flow. 

A sound wave is manifested as one kind of the atmospheric normal modes, known as the acoustic mode, and is caused by the compressibility of air. There are two more kinds One is called the gravity-inertia mode, which is caused by a combinations of the restitutive force of gravity against thermally stable atmospheric stratification and the Coriolis force due to the earth s rotation. The other kind is called the rotational or planetary mode, which is caused by the meridional variation of the Coriolis force. The importance of the latter kind of normal mode as a prototype of upper tropospheric large-scale disturbances was clarified by C. -G. Rossby and his collaborators a little over one decade prior to the dawn of the numerical prediction era (see Section I). In retrospect, the very natrrre of this discovery was hidden in complicated calcnlations for the normal modes of the global atmospheric model. The mathematical analysis was initiated by the French mathematician Marquis de Laplace (1749-1827), and the complete solntions became clear only with the aid of electronic compnters. It is remarkable that Rossby was able to capture the essence of this important type of wave motion, now referred to as the Rossby wave, from a simple hydrodynamic principle of the conservation of the absolute vorticity that is expressed by the sum of the vertical component of the relative vorticity and the planetary vorticify /. 

Due to the similarity of the flow profiles, most of these passive, continuous-flow schemes can, in principle, also be adopted for centrifugally driven flows. In addition, the availability of the Coriolis pseudo force/c (4) offers an intrinsic means for the generation transversal flow components, even in straight radial channels exhibiting a constant cross section (Fig. 8). Due to the scaling of forces //c (13), the Coriolis-force induced mixing is... 

Down the Drain. How often have you heard that that toilets in the northern hemisphere drain counterclockwise, but those in the southern hemisphere drain clockwise... or was it that in the northern hemisphere they drain clockwise and in the southern hemisphere they go counterclockwise No one seems to remember which way it is, and, of course, no one seems to check this accepted scientific "fact." As in many other "scientific myths," there is some real science here, but very few people have the initiative to check out this commonly believed principle by looking at real drains. If you start filling up wash basins and watching how they drain, and keep track of whether the vortex formed in the drains is clockwise or counterclockwise, after examining a fair number of drains you will see that it is 50 50. The physics of this phenomenon is actually pretty easy to understand, if you can comprehend the Coriolis force or the Coriolis effect. The earth rotates from west to east, and the sueed of a suot on the earth is faster, the closer you get to the equator. So if you think... 

The scheme we employ uses a Cartesian laboratory system of coordinates which avoids the spurious small kinetic and Coriolis energy terms that arise when center of mass coordinates are used. However, the overall translational and rotational degrees of freedom are still present. The unconstrained coupled dynamics of all participating electrons and atomic nuclei is considered explicitly. The particles move under the influence of the instantaneous forces derived from the Coulombic potentials of the system Hamiltonian and the time-dependent system wave function. The time-dependent variational principle is used to derive the dynamical equations for a given form of time-dependent system wave function. The choice of wave function ansatz and of sets of atomic basis functions are the limiting approximations of the method. Wave function parameters, such as molecular orbital coefficients, z,(f), average nuclear positions and momenta, and Pfe(0, etc., carry the time dependence and serve as the dynamical variables of the method. Therefore, the parameterization of the system wave function is important, and we have found that wave functions expressed as generalized coherent states are particularly useful. A minimal implementation of the method [16,17] employs a wave function of the form ... 

As far as mean amplitudes are concerned, interplay between spectroscopy and electron diffraction may come about in two ways. Firstly, even for comparatively simple polyatomic molecules e.g. the methyl halides ) the general harmonic force field is not well determined from all the spectroscopic data available, i.e. vibration frequencies, isotopic frequency shifts, Coriolis zfita constants, and centrifugal distortion constants. In principle, experimental mean amplitudes from electron diffraction studies should provide valuable additional data. In practice, however, the experimental amplitudes have as yet rarely been of sufficient precision to be helpful. Secondly, for more complex molecules, mean amplitudes calculated from spectroscopic data (by way of what are inevitably very approximate force fields in many cases) are sometimes used as fixed parameters in the electron diffraction analysis in order to reduce the total number of parameters refined. 

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