Coriolis principle

R 18] [A 1] Each module is equipped with a heater (H3-H8) and a fluidic cooling (C03-C06). Temperature sensors integrated in the modules deliver the sensor signals for the heater control. Fluidic data such as flow and pressure are measured integrally outside the micro structured devices by laboratory-made flow sensors manufactured by silicon machining. The micro structured pressure sensor can tolerate up to 10 bar at 200 °C with a small dead volume of only 0.5 pi. The micro structured mass flow sensor relies on the Coriolis principle and is positioned behind the pumps in Figure 4.59 (FIC). For more detailed information about the product quality it was recommended to use optical flow cells inline with the chemical process combined with an NIR analytic or a Raman spectrometer. 

The feeding of the liquid components can be done with various pumps of different outputs and pressures. As a standard a peristaltic pump is used, controlled by a flow meter based on the Coriolis principle. With respect to the requirements of the formulation and process, different types of pumps can be used. 

Flow measurements using nonintrusive or low mechanical ac tion principles are desired, such as magnetic, vortex-shedding, or Coriolis-type flowmeters. Orifice plates are easy to use and reliable but have a limited range and may not be suitable for streams which are not totally clean. Rotameters with glass tubes should not be used. 

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. 

In this chapter we will illustrate and analyze some of the more common methods for measuring flow rate in conduits, including the pitot tube, venturi, nozzle, and orifice meters. This is by no means intended to be a comprehensive or exhaustive treatment, however, as there are a great many other devices in use for measuring flow rate, such as turbine, vane, Coriolis, ultrasonic, and magnetic flow meters, just to name a few. The examples considered here demonstrate the application of the fundamental conservation principles to the analysis of several of the most common devices. We also consider control valves in this chapter, because they are frequently employed in conjunction with the measurement of flow rate to provide a means of controlling flow. 

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 ... 

Figure 6.123 Functional principle of a Coriolis mass flowmeter.

The principle of operation of transducers is based on the conservation of either linear (i.e., Coriolis effect) or angular momentum, making a transducer well suited for micromachined rate-sensing gyros. One or more linearly or rotationally vibrating probe masses are required, for which the input motion stimulus and the output signal can be accomplished by various physical effects (electrostatic, electromagnetic, piezoresistive, etc.). Usually the drive motion is resonant, so the detection motion can also be resonant or the two natural frequencies are separated by a certain frequency shift. Drive and detection motion can be excited by inplane motions or by a mixture of in-plane and out-of-plane motions. 

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. 

A second rotational effect comes into play when rotations are strongly coupled to the vibrations, via, for instance, coriolis interactions. In that case, the projection of the principle rotational quantum number, the K quantum number in symmetric top molecules, is no longer conserved. The energy associated with this quantum number then gets mixed in with the molecule s vibrational energy, thereby increasing the density and sums of states. When this happens we say that the A -rotor is active. If the T-rotor does not couple with the vibrations, it is inactive. We first discuss what happens when a diatom dissociates and follow that with the dissociation of polyatomic molecules. 

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 /. 

The Rabi technique of radio frequency or microwave spectroscopy in atomic or molecular beams [10.14-10.17] has made outstanding contributions to the accurate determination of ground state parameters, such as the hfs splittings in atoms and molecules, small Coriolis splitting in rotating and vibrating molecules, or the narrow rotational structures of weakly bound van der Waals complexes [10.18]. Its basic principle is illustrated in Fig. 10.9. A collimated beam of molecules with a permanent dipole moment is deflected in a static... 

Floating Archimedes principle, as for pressure, cylinder pistons, spring-loaded plug, diaphragm, Doppler, Coriolis... 

Equipment Type Code (specific measurement principle within that measurement family (e.g., vortex, differential pressure, Coriolis)... 

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. 

We have kept the vibrational energy equation for a polyatomic molecule in simple form by assuming that motions along different modes are completely separable. The real world, of course, is more interesting. One commonly observed breakdown in the separation between vibrational modes occurs by means of the Coriolis interaction, and the principle can be crudely illustrated as follows. Draw the three nuclei of GO2, and draw the displacement arrows for the in-plane bend these will correspond to position vectors... 

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... 

---