Velocity, absolute

The equation of motion as given in terms of angular momentum can be transformed into other forms that are more convenient to understanding some of the basic design components. To understand the flow in a turbomachine, the concepts of aboslute and relative velocity must be grasped. Absolute velocity (V) is gas velocity with respect to a stationary coordinate system. Relative velocity (IV) is the velocity relative to the rotor. In turbomachinery. 

Since the meridional velocity remains constant, the increase in relative velocity must be accompanied with a decrease in absolute velocity. 

Vane thickness. Because of manufacturing problems and physical necessity, impeller vanes are thick. When fluid exits the impeller, the vanes no longer contain the flow, and the velocity is immediately slowed. Because it is the meridional velocity that decreases, both the relative and absolute velocities decrease, changing the exit angle of the fluid. 

There are three state points within a turbine that are important when analyzing the flow. They are located at the nozzle entrance, the rotor entrance, and at the rotor exit. Fluid velocity is an important variable governing the flow and energy transfer within a turbine. The absolute velocity (F) is the fluid velocity relative to some stationary point. Absolute velocity is important when analyzing the flow across a stationary blade such as a nozzle. When considering the flow across a rotating element or rotor blade, the relative velocity IV is important. Vectorially, the relative velocity is defined... 

Vu2 = tangential component of the absolute velocity U2 = impeller tip velocity... 

U to the bottom of the bed. The absolute velocity of a bubble as seen by a stationary observer is then... 

In Eq. (9.90), C2 is the tangential component of the absolute velocity at the exit if the flow is exactly in the blade direction. Since the slip factor is ieSs than 1, the total pressure increase will decrease according to Eq. ( 9.72) for the same impeller and isentropic flow. 

In the following discussion, u is the average circumference speed. 1 he absolute velocity in the shaft direction is denoted by c. ... 

Equation (9.102) gives = C2a- The axial component does not change, but when C2 > then C2 > Cj. Thus, the axial fan increases the absolute velocity of airflow. 

The rotating of the impeller increases the absolute velocity of air. In order to increase the static pressure of the gas flow owing to the fan, the velocity relative to the blades should decrease according to Eq. (9.103). 

At the exit the absolute velocity has velocity component C2 on the large circumference parallel to the shaft of Example 3. Component is of no advantage if a duct is connected to the axial fan, since it disappears due to the friction between the walls of the duct and gas flow. 

The nitrate ion (N03) is one of the most electronegative ions and its absolute velocity... 

The absolute ionic mobility or the absolute velocity of an ion represents its velocity in centimeters per second under a potential gradient of one volt per centimeter (potential gradient = applied emf/distance between the electrodes). For example, if the velocity of the ion at infinite dilution is U cm per second when the distance between the electrodes is 25 cm and voltage is 125, the potential gradient is 125/25, i.e., 5 volts per cm and the absolute mobility is U/5 cm s 1. 

Another method for obtaining these values is to determine the mobilities of ions, from which the ratio A+ /A" can be calculated. This is based on the measurement of the absolute velocities of the cations and anions under the influence of a potential gradient, as originally suggested by Lodge (1886) and applied later by Masson and many others. For instance, Masson (1899)1 carried out experiments with 10% KC1 solution in gelatine gel, the principle of which is illustrated in Fig. 2.2. 

Further, in order to arrive at the absolute velocity, the so-called mobility of the ions, Vg and Vg, must be divided by the potential gradient, p so... 

To consider the control volume form of the conservation of mass for a species in a reacting mixture volume, we apply Equation (2.14) for the system and make the conversion from Equation (3.12). Here we select/ = pt, the species density. In applying Equation (3.13), v must be the velocity of the species. However, in a mixture, species can move by the process of diffusion even though the bulk of the mixture might be at rest. This requires a more careful distinction between the velocity of the bulk mixture and its individual components. Indeed, the velocity v given in Equation (3.13) is for the bulk mixture. Diffusion velocities, Vi, are defined as relative to this bulk mixture velocity v. Then, the absolute velocity of species i is given as... 

The rate of a generic reaction j is represented by its absolute velocity Vj, which may be obtained from experiments, provided that the mass of solvent is held constant throughout the experiment and no additional homogeneous or heterogeneous reactions concur to modify the molality of the ion in solution (Delany et al., 1986) ... 

Plummer et al. (1978) utilized, for instance, an equation in the form of equation 8.289 to describe the dissolution of calcite. According to the authors, the simultaneous reactions concurring to define the absolute velocity of dissolution are... 

Figure 12.4 The comparison of predicted mean temperature fields in long and short combustors at t = 14.9 ms (a), 22.1 (6), and 58.1 ms (c) after ignition behind a bluff body. Boundary condition at outlets is ABC of Eq. (12.19). Mean velocity at the inlet Uin = 10 m/s. Other conditions are po = 0.1 MPa, To = 293 K, fco = 0.06 J/kg, lo = 4 mm. A set of graphs below compares mean absolute velocity distributions in the different cross-sections (/ to VII) of both combustors (from left to right x = 0, 80, 100, 112, 135, 235, and 330 mm). Solid line — short combustor, dashed line — long combustor, j/max is the height of the corresponding cross-section of the combustor...

It may be mentioned that from dynamic measurements, nevertheless, some first information about the reaction order has been obtained by Schwab and Theophilidis (7), by determining the absolute velocity. 

A study of the relationship between the rates of catalyzed reactions and the concentrations of reactants may clear up the intermolecular mechanism and such studies may help in finding out which molecules are adsorbed, whether the adsorption is weak or strong, and which fraction of the surface is active. Every theory of the intermolecular mechanism can and must be checked by a calculation of the absolute velocity. 

The dotted lines in Fig. 1 show the stopping powers for the different ions at a constant velocity in units of MeV/amu. This unit of energy is very often used in heavy ion radiolysis and it is based on the classical formula for kinetic energy, E = V2 MV, where M is the heavy ion mass. As seen in Eq. (1), the ion velocity is a dominant parameter in energy loss processes and the MeV/amu energy unit is more convenient to use than converting to absolute velocity units. Remember that MeV/amu is actually proportional to the square of the velocity. 

Transport number Temp, coeff. Absolute velocity. ... 

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