Exit velocity

Typically the exit velocity in a flow domain is unknown and hence the prescription of Dirichlet-type boundary conditions at the outlet is not possible. However, at the outlet of sufficiently long domains fully developed flow conditions may be imposed. In the example considered here these can be written as... 

Selecting the inlet and outlet surfaces 1 and 2 as shown, the continuity equation Eq. (6-9) can he used to find the exit velocity V2 = ViAi/A2. The mass flow rate is obtained by m = pViAi. 

Solution of Eq. (6-114) for G and differentiation with respect to p reveals a maximum mass flux = P2VMJ RT) and a corresponding exit velocity and exit Mach number Mo = L/. This... 

Note that under choked conditions, the exit velocity is V = V = c = V/cKTVM not V/cKT(/M, . Sonic velocity must be evaluated at the exit temperature. For air, with k = 1.4, the critical pressure ratio p /vo is 0.5285 and the critical temperature ratio T /Tq = 0.8333. Thus, for air discharging from 300 K, the temperature drops by 50 K (90 R). This large temperature decrease results from the conversion of internal energy into kinetic energy and is reversible. As the discharged jet decelerates in the external stagant gas, it recovers its initial enthalpy. 

The shape of the converging section is a smooth trumpet shape similar to the simple converging nozzle. However, special shapes of the diverging section are required to produce the maximum supersonic-exit velocity. Shocks result if the divergence is too rapid and excessive boundary layer friction occurs if the divergence is too shallow. See Liepmann and Roshko (Elements of Gas Dynamic.s, Wiley, New York, 1957, p. 284). If the nozzle is to be used as a thrust device, the diverg-... 

For return manifolds with K = 1.0 and 4fL/(3D) 1, 5 percent maldistribution is achieved when hole pressure drop is 20 times the pipe exit velocity head. 

Aerodynamic Downwash Should the stack exit velocity be too low as compared with the speed of the crosswind, some of the effluent can be pulled downward by the low pressure on the lee side of the stack. This phenomenon, known as stack-tip downwash, can be minimized by keeping the exit velocity greater than the mean wind speed (i.e., typically twice the mean wind speed). Another way to minimize stack-tip downwash is to fit the top of the stack with a flat disc that extends for at least one stack diameter outward from the stack. 

If it becomes necessary to increase the stack-gas exit velocity to avoid downwash, it may be necessary to remodel the stack exit. A venturi-nozzle design has been found to be the most effective. This design also keeps pressure losses to a minimum. 

From the velocity diagram in Fig. 29-13 it is apparent that an increase in wheel peripheral velocity [L permits an increase in nozzle exit velocity C] without increasing Co- Accordingly, a high-speed tur-... 

The lowering below the stack top of pieces of the plume by the vortices shed downwind of the stack is simulated by using a value h in place of the physical stack height h. This is somewhat less than the physical height when the stack gas exit velocity is less than 1.5 times the wind speed u,... 

Boundary-layer development. The boundary layer that develops within an impeller passage causes the flowing fluid to experience a smaller exit area as shown in Figure 6-23. This smaller exit is due to small flow (if any) within the boundary layer. For the fluid to exit this smaller area, its velocity must increase. This increase gives a higher relative exit velocity. 

Leakage. Fluid flow from one side of a blade to the other side is referred to as leakage. Leakage reduces the energy transfer from impeller to fluid and decreases the exit velocity angle. 

A backward-curved impeller blade combines all these effects. The exit velocity triangle for this impeller with the different slip phenomenon changes is shown in Figure 6-25. This triangle shows that actual operating conditions are far removed from the projected design condition. 

The 50% reaction turbine has been used widely and has special significance. The velocity diagram for a 50% reaction is symmetrical and, for the maximum utilization factor, the exit velocity (V4) must be axial. Figure 9-11 shows a velocity diagram of a 50% reaction turbine and the effect on the utilization factor. From the diagram IV = V4, the angles of both the stationary and rotating blades are identical. Therefore, for maximum utilization. 

Figure 4. HETP Curves for the Same Column and Solute Using the Average Mobile Phase Velocity and the Exit Velocity...

It is seen that the two curves are quite different and, if the results are fitted to the HETP equation, only the data obtained by using the exit velocity gives correct and realistic values for the individual dispersion processes. This point is emphasized by the graphs shown in Figure 5 where the HETP curve obtained by using average velocity data are deconvoluted into the individual contributions from the different dispersion processes. 

Figure 5 shows that using average velocity data the extracted value for the multi-path term is negative, which is physically impossible, and, furthermore, for a capillary column should be zero or close to zero. In contrast, the extracted values for the different dispersion processes obtained from data involving the exit velocity give small positive, but realistic values for the multi-path term. 

It should be noted that the velocity employed in equation (7) will be the exit velocity (uq) and not the mean velocity (umean)- Differentiating equation (3) and equating to zero, to obtain an expression for the optimum velocity (uopt). 

A particularly difficult aspect of the problem of diffusion of atmospheric pollution is the determination of the height to which a buoyant plume with an initial exit velocity will rise. Plume rise, which is defined as the distance between the top of the stack and the axis of the centroid of the pollutant distribution, has been found to depend on ... 

Holland Ah = (1.5V,d -H 0.04QJ/U where Ah — plume rise (m), Vj = stack exit velocity (m/s), d = stack diameter (m), = heat emission rate (kcal/s), U = stack top wind speed (m/s) Highly empirical. Requires stack testing confirmation on case-bycase basis... 

Stack gas exit velocity (m/s) or flow rate (ftVmin or m /s)... 

The SCREEN model uses free format to read the numerical input data, with the exception of the exit velocity/flow rate option. The default choice for this input is stack gas exit velocity, which SCREEN will read as free format. However, if the user precedes the input with the characters VF= in columns 1-3, then SCREEN will interpret the input as flow rate in actual cubic feet per minute (ACFM). Alternatively, if the user inputs the characters VM= in columns 1-3, then SCREEN will interpret the... 

Outlet Pipe Sizing - Outlet piping is sized according to minimum diameter and exit velocity considerations, as follows ... 

PR valve risers in flammable service should also be sized such that exit velocities are at least 30 m/s under all foreseable contingencies (except fire) which would cause the valve to release. On the basis of experimental work and plant experience, this minimum velocity, in conjunction with the riser elevation requirements, has been shown to ensure effective dispersion. Entrainment of air and dilution result in a limited flammable zone, with a negligible probability of this zone reaching any equipment which could constimte an ignition source. 

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