Liquid escape velocity

Liquid escape velocity from the downcomer onto the tray below. 

Here again an equation is established (2) to describe the trajectory of a particle under the combined effect of the liquid transport velocity acting in the. v-direction and the centrifugal settling velocity in they-direction. Equation 13 determines the minimum particle size which originates from a position on the outer radius, r2, and the midpoint of the space,, between two adjacent disks, and just reaches the upper disk at the inner radius, q. Particles of this size initially located above the midpoint of space a are all collected on the underside of the upper disk those particles initially located below the midpoint escape capture. This condition defines the throughput, for which a 50% recovery of the entering particles is achieved. That is,... 

The impeller is the working part of a centrifugal pump. The function of the impeller is to increase the velocity or kinetic energy of the liquid. The liquid flows into the impeller, and leaves the impeller, at the same pressure. The black dot shown at the top of the impeller in Fig. 23.6 is called the vane tip. The pressure at the vane tip is the same as the pump s suction pressure. However, as the high-velocity liquid escapes from the impeller and flows into the volute, its velocity decreases. The volute (which is also called the diffuser) is shaped like a cone. It widens out in the manner illustrated in Fig. 23.7. As the liquid flows into the wider section of the volute, its velocity is reduced, and the lost velocity is converted—well, not into pressure, but into feet of head. 

There s a problem with my design criteria for downcomer clearances. That is, at low liquid rates, how can I keep a reasonable downcomer escape velocity without reducing the downcomer velocity below my 1-inch clearance The conventional answer is an inlet weir, as shown in Fig. 5.5. 

Size distribution Rate of change in Velocity required for the liquid to escape the... 

Consider a process unit that develops a small hole, as shown in Figure 4-4. The pressure of the liquid contained within the process unit is converted to kinetic energy as the fluid escapes through the leak. Frictional forces between the moving liquid and the wall of the leak convert some of the kinetic energy of the liquid into thermal energy, resulting in a reduced velocity. 

Whether the rocket is solid or liquid, its motion is governed by the escaping jet of hot gases. At sea level, the gases may escape with a velocity of 1800 to 4500 ms . 

Sherwood and Pigford (S9) have discussed the problem of the absorption of a solute A by a solvent S upon solution, A may be converted into B according to the reaction A = B (k/ and krf being the forward and reverse reaction-rate constants, and K = k//k/). The concentration of A is maintained at cAo at the surface of the liquid S, and it is assumed that S is semiinfinite in extent. It is further assumed that B is nonvolatile that is, it cannot escape from solvent S. Equation (51) is then used to explain the diffusion of A and B, with DAg and DBs taken as concentration independent, and the term containing the molar average velocity w is neglected. Hence the mathematical statement of the problem is (for very dilute solutions of A and B)... 

It was pointed out in Chap. 8, Sect. 2.1 that there are primarily two reasons for the failure of the diffusion equation to describe molecular motion on short times. They are connected with each other. A molecule moving in a solvent does not forget entirely the direction it was travelling prior to a collision [271, 502]. The velocity after the collision is, to some degree, correlated with its velocity before the collision. In essence, the Boltzmann assumption of molecular chaos is unsatisfactory in liquids [453, 490, 511—513]. The second consideration relates to the structure of the solvent (discussed in Chap. 8, Sects. 2.5 and 2.6). Because the solvent molecules interact with each other, despite the motion of solvent molecules, some structure develops and persists over several molecular diameters [451,452a]. Furthermore, as two reactants approach each other, the solvent molecules between them have to be squeezed-out of the way before the reactants can collide [70, 456]. These effects have been considered in a rather heuristic fashion earlier. While the potential of mean force has little overall effect on the rate of reaction, its effect on the probability of recombination or escape is rather more significant (Chap. 8, Sect. 2.6). Hydrodynamic repulsion can lead to a reduction in the rate of reaction by as much as 30-40% under the most favourable circumstances (see Chap. 8, Sect. 2.5 and Chap. 9, Sect. 3) [70, 71]. 

In the second part, flow in the vapor space of the separator, where the gas phase is a continuous phase, was modeled. An Eulerian-Lagrangian approach was used to simulate trajectories of the liquid droplets since the volume fraction of the dispersed liquid phase is quite small. The grid used for the vapor space is shown in Fig. 9.20. The simulated gas volume fraction distribution near the gas-liquid interface and corresponding gas flow in the vapor space are shown in Fig. 9.22. The gas volume fraction distribution and the gas velocity obtained from the model of the bottom portion of the loop reactor were used to specify boundary conditions for the vapor space model. In addition to the gas escaping from the gas-liquid interface, it is necessary to estimate the amount of liquid thrown into the vapor space by the vapor bubbles erupting at the... 

In the first alternative, if the terminal rise velocity of gas bubbles is known (or can be estimated with confidence), the top surface of the dispersion may be defined as an inlet . Normal liquid velocity may be set to zero while normal gas velocity may be set to terminal rise velocity. The implicit assumption here is that gas bubbles escape the dispersion with terminal rise velocity. It should be noted that even after defining the top surface as an inlet, gas volume fraction at the top surface is a free variable. There is no implicit forcing of gas volume fraction distribution. Alternatively, the top surface of the dispersion can be modeled as a no shear wall. This will automatically set normal liquid velocity to zero. It will also set normal gas velocity to zero. In order to represent escaping gas bubbles, an appropriate sink may be defined for all the computational cells attached to the top surface (Figure 11.7) ... 

The rate of evaporation is also dependent on the liquid s temperature. Increased temperature increases the average velocity and momentum of the particles. As a result, a greater percentage of particles will have the minimum momentum necessary to escape, so the liquid will evaporate more quickly (Figure 14.4). This explains why rainwater on a city street evaporates much more rapidly when the sun comes out. 

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