Velocity triangles

Figure 4-128. Typical velocity triangles for different size particles.

Outlet (RMS) Velocity Triangle Figure 7-10. One-dimensional turbine model and turbine velocity triangles. 

Supposing constant rotational speeds, no slip, and an axial inlet, the velocity triangles are as shown in Figure 6-10. For the radial vane, the absolute tangential fluid velocity at the impeller exit is constant—even if the flow rate is increased or decreased. 

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. 

It should be noted that the illustrations of the flow paths in Figures 6-37 through 6-39 are somewhat simplistic. Each flow path is indicated by a single streamline. The actual flow field is far more complex, with flow separation and recalculation present. Nevertheless, these figures should help with a practical understanding of the effects of changes in velocity triangles. 

Figure 9-4. Turbine velocity triangles showing the effect of various degrees of reaction.

Figure 5-21 includes an outlet velocity vector triangle for the various vane shapes. Figure 5-20 shows a backward curved impeller that includes the inlet and outlet velocity vector triangle. Because most of the compressors used in process applications are either backward curved or radial, only these two types will be covered in detail. 

Figure 5-22. Discharge velocity vector triangle showing the effect of slip.

The velocity triangles of the incoming and leaving flow at the blade edges of a centrifugal fan are shown in Fig. 9.34. The flow to the blade is in a radial direction. 

FIGURE 9.34 Velocity triangles at the blade edges of a backward-blade centrifugal hn. ... 

The velocity triangle at the entrance, taking into consideration that Ci = 0, is shown in Fig. 9.39a. 

From the exit velocity triangle, it can be seen that the gas flow has a tangential velocity component. The gas rotates when it leaves the fan. Normally, the tangential velocity component is of no benefit if a duct is attached to the fan, since it disappears due to friction. 

In this section, the rotational velocity is directly proportional to the rotational velocity n according to the equation u — irDn. The impeller blade angles remain the same regardless of the rotational velocity of the impeller. Hence, the inlet and exit velocity triangles have the same form. The axial velocity of an axial fan changes directly proportionally to the circumference velocity u. This is also valid for the radial velocity at the outer circumference of a radial impeller fan. These velocities are directly proportional to the fan flow volume hence. 

The regulation of axial fan blade angle also influences the inlet and exit velocity triangles in such a way that the axial velocity and thus the volume flow change. When the relative velocity remains parallel to the blade, the efficiency remains high (Fig. 9.52). 

FIGURE 9.S2 Influence of axial Ian blade angle on volume flow and velocity triangles. 

Recently, the regulation of impeller rotational velocity has become a popular regulation mode for volume flow. Electric-motor rotational velocity is regulated by a frequency changer, and its price has dropped lately. Changing the rotational speed also affects the circumference velocity of the impeller. The volume flow can be changed by the same ratio as rotational speed. The form of the velocity triangles and the efficiency remain the same. 

Figure 32.16 presents on the basis of the characteristic number the typical impeller profiles, velocity triangle shapes, and characteristic curves to be expected from the machine flow paths shown. This indicates the use of the number as a design tool for the pump engineer. 

Figure 2 Velocity field triangulation at the inlet using 64 triangles. The dotted line indicates the polymer-metal interface, and the dimensions are in centimeters.

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