C r c J X 1780 a2500 1780 Vo1577 Specific Speed Qs 1 NS 2733 nq 529

TABLE 7 Impeller inlet (design example)

TABLE 7 Impeller inlet (design example)

including the effect of the blading. Moreover, the value of k1 should be more than adequate for this value of V1sh.

The Q,ss and t-fe relationships yield the eye flow coefficient f e, which in turn sizes the eye. fe = 0.29 implies a t-value of 0.253, which is typical. However, lower fe- and t-values are common, especially for the case of a shaft through the eye, because this tends to maintain the level of físs in the face of the ^.-effect in Eq. 50. The nominal velocity diagram at the eye—substantially the shroud-end or tip of the blade leading edge—shows Ve rather than V1sh for the meridional component of velocity and so is not the actual velocity diagram at that location. Rather, this triangle serves to identify the geometry through the basic ratio fe = Ve/Ue—without having to deal with the uncertain choice of V1sh /Ve. Moreover, fe is the tangent of the tip relative flow angle b¡¡1 as it would be for a uniform axial velocity profile in the eye.

With the eye radius re established, the local shroud radius of curvature Rsh follows from the guidelines associated with Figure 13. The geometry established so far is illustrated in Figure 25. Before the full picture shown there can be established, the outlet must be sized.

impeller outlet The computations in Table 8 for the impeller exit begin with the choice of the typical value of 22g degrees for the outlet blade angle This enables the head coefficient C to be chosen under the guidance of the upper curve in Figure 12. The value 0.385 is selected, and this yields the impeller diameter of 12 in. (304.8 mm). The other curve in Figure 12 is for outlet flow coefficient fi 2, which conveniently equals 0.1715 for

FIGURE 25 Impeller hub and shroud profiles (design example)

Q,s = 1. This leads to the exit width b2 after adding in the leakage and the blockage of blades and boundary layers per the computations of Tables 9 and 10.

However, Anderson6 points out that what matters for centrifugal pump performance is neither the blade angle nor the exit width individually, but the impeller outlet relative area 2pr2b2 sin bb2. Choosing a higher blade angle is possible if b2 is correspondingly reduced (and fi2 increased) so as to maintain this area and therefore the relative velocity W. Figure 15 shows that Vu2 is thereby essentially unchanged; this in turn preserves the impeller head.

efficiencies Anderson's overall pump efficiency correlation (Figure 10 and Eq. 44) and the component efficiency expressions of Table 3 lead to the results of Table 9. These give an indication of the relative magnitudes of the losses and are as follows:

Overall efficiency hp = 0.8550

Mechanical efficiency hm = 0.9814

Volumetric efficiency hv = 0.9833 (leakage across front and back rings)

Hydraulic efficiency hm = 0.8860

hm is at this point simply deduced from the others, beginning with Anderson's correlation. Although it is confirmed by Jekat's correlation in the table, it can be found in a

2.1 CENTRIFUGAL PUMP THEORY TABLE 8 Impeller outlet (design example)

2.1 CENTRIFUGAL PUMP THEORY TABLE 8 Impeller outlet (design example)

detailed computation of the hydraulic losses via one-dimensional methods. This will be carried out further on to obtain the performance characteristic curves. Meanwhile, this initial computation enables the determination of Vu2 at the end of Table 9, which, along with Vm 2 from Table 8, is a major element of the outlet velocity diagram of Figure 26.

blockage and width AT impeller exit With the leakage and exit blade angle information, Table 10 contains the computations of the blockage and the exit width b2. This entails the choice of the number of blades, the blade thickness t (2% of the impeller diameter and typically assumed to exist at the exit and elsewhere on the blades except near the leading edges where typically half that value is chosen), and the approximate blade length / (assuming the mean-streamline blade angle to be constant at 22^ deg). The boundary layer blockage is computed from the following approximations:

• Adverse pressure gradients on the blades lead to a boundary layer displacement thickness 8* of twice the zero-pressure gradient value 80* on each blade surface.

• Secondary flows scrub the boundary layers from the hub and shroud surfaces; so, 8* is assumed to be equal to 80* on those surfaces.

• 80* = 0.0462 /08 n02/W02 for flat-plate, turbulent flow56, and is approximated in this example for low viscosity by a linear growth with length along the blade.

The resulting thickness of the boundary blockage is 0.0732 in (1.86 mm) on the blades, which themselves have a thickness of 0.24 in (6.1 mm). Because these thicknesses are inclined at the 222-deg outlet angle, the actual circumferential blockage is (1 — e2b) = (1 - 0.870) or 13 percent of 2pr2. In particular, (0.24 + 0.0732)/sin (22^ deg) = 0.82 in or (6.1

TABLE 9 Component efficiencies (design example)

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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