Angular velocity of rotation

Let CO be the angular velocity of rotation this is equal to Inf where/is the disk frequency or number of revolutions per second. The distance r of any point from the center of the disk is identical with the distance from the flow stagnation point. The hnear velocity of any point on the electrode is cor. We see when substituting these quantities into Eq. (4.34) that the effects of the changes in distance and hnear vefocity mutuaUy cancel, so that the resulting diffusion-layer thickness is independent of distance. 

Just as the absorption of UV or visible light causes electrons to excite between different electronic quantum states, so absorption of infrared photons causes excitation between allowed vibrational states, and absorbing microwave radiation causes excitation between allowed rotational states in the absorbing molecule. As a crude physical representation, these quantum states correspond to different angular velocities of rotation, so absorption of two photons of microwave radiation by a molecule results in a rotation that is twice as rapid as following absorption of one photon. 

The rate of sedimentation is defined by the sedimentation constant 5, which is directly proportional to the polymer mass m, solution density p, and specific volume of the polymer V, and inversely proportional to the square of the angular velocity of rotation o), the distance from the center of rotation to the point of observation in the cell r, and the fractional coefficient /, which is inversely related to the diffusion coefficient D extrapolated to infinite dilution. These relationships are shown in the following equations in which (1 — Vp) is called the buoyancy factor since it determines the direction of macromolecular transport in the cell. 

In the case of a centrifugal separator (i.e., a centrifuge), the acceleration due to centrifugal force, which should be used in place ofg, is given as ra>, where r is the radial distance from the central rotating axis (m) and co is the angular velocity of rotation (radian s -). Thus, the terminal velocity Vj (ms ) is given as... 

F = intensity of the centrifugal force m = effective mass of the sedimenting particle w = angular velocity of rotation in rad/sec... 

The next figures give curves of dependency of M upon angular velocity of rotation n (Fig, 3), the strictly increasing functions dependencies of bulk velocity of the flow Q( l) (Fig. 4) for different values of f = p/1 (continuous lines correspond to calculations of Eqs. (13)—(16) and dotted lines correspond to similar calculations with... 

Solid angle, (4.92) angle between the electric vector and the transition dipole moment, (5.3) angular velocity of rotational modulation (section 8.3.1). 

Equation 7.2-22 indicates that the separating force is proportional to the local shear stress (fiy) in the liquid, it is a sensitive function of the Euler angles of orientation, and is proportional to the projection of the cross-sectional are (S = nc2). The angular velocities of rotation of the freely suspended spheroid particle were given by Zia, Cox, and Mason (46)... 

Because of the strong effects of plate rotations on the rector performance for both RE and PC electrolyzers, the critical design parameters for these reactors are the Taylor number (a2w/4v)0 5 and the Reynolds number (aVf/v). Here a is the gap width between the plate, w the angular velocity of rotation (in radians per second), v the kinematic viscosity of the fluid, and V the velocity in the feed pipe. Since no asymptotic velocity profile is reached for PC, the length of the cell will be an important design parameter in a pump-cell electrolyzer. Detailed mathematical models for RE and PC electrolyzers are given by Thomas et al. (1988), Jansson (1978), Jansson et al. (1978) and Simek and Rousar (1984). 

Fig. 6.19 presents part of the results on the electrical resistance measured in foam layers of thickness AZ = 0.5 and 1.5 cm, in a foam from NaDoS solution (103 mol dm3 and 0.5 mol dm 3 NaCl) at different angular velocity of rotation. 

In both foams, from Triton-X-100 and NaDoS solutions, the bubble sizes during 5 min of centrifugation did not exceed avL = 2 to 2.5-1 O 2 cm. The dispersity of a NaDoS foam at the 15 to 20th minute of centrifugation was avL = 310"2 cm. For small angular velocity of rotation co = 52.3 s 1 and A1= 1.5 cm, the highest expansion ratio exceeded the lowest by a factor of 5 times and by a factor of 1.5 its harmonic mean value (Table 6.2). The destruction of a foam layer with A/ = 1.5 cm from NaDoS begins at capillary pressure 8.95 kPa which corresponds as well to a harmonic mean value of 10.9 kPa. 

It is interesting to note that as neither y p nor depend on g, these velocities do not depend on the selected angular velocity of rotation. This is because the field intensity influences in the same way the size of the capillary wavelength and the sedimentation velocity of the droplet. 

Let the axes be fixed in the Earth, with the x axis horizontal and extending to the east, the y axis horizontal and extending to the north, and the z axis normal to the Earth s surface. As before, Q is the angular velocity of rotation of the Earth and < ) is the latitude. The components of the Coriolis force in the x, y, and z directions on an air parcel are the... 

Total mechanical energy per unit mass of fluid Angular velocity of rotation... 

Q For a rotating object, rotational kinetic energy is Alor, where oi is the angular velocity of rotation and I is the moment of inertia. What is the r.m.s. speed of thermal rotation at 37 C for a spherical protein molecule of RMM 25,000 and radius 1.0 nm ... 

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