55. Specific speed and its relation to impeller geometry

The similarity formulas obtained in the foregoing section can be used to develop a useful practical factor for calculating and design­ing centrifugal pumps which is commonly known as specific speed.

From Eq. (12.31)

Substitution into Eq. (12.32) yields

Rearranging and raising to the power of 3/4, we obtain

This expression is valid not only for two homologous pumps I and II but for аяу number of homologous pumps operating under similar conditions.

Suppose that among these homologous pumps we have a standard pump with a head delivery H_s = 1 m, and a water horsepower N_s = 1 h.p. at γ = 1,000 kg/m³.

Using the power equation (12.2) it is easy to determine the capac­ity of the standard pump:

Now let us relate the parameters Q_s, H_s, n_s of the standard pump to the corresponding parameters Q, H, n of any other homologous pump under similar operating conditions using Eq. (12.37):

Substituting the values of Q_s and H_s, we can determine the rota­tional speed of the standard pump:

The expression

is the specific speed.

The physical meaning of the quantity n₅ is apparent from the fore­going reasoning: it is the rpm of a standard pump homologous with a given pump and generating, under similar operating condi­tions, a head H_s = 1 m at a rate of discharge of Q_s = 0.075 m³/sec. The hydraulic and volumetric efficiencies of the two pumps are, naturally, the same.

The water horsepower of the standard pump is 1 h.p., provided that γ = 1,000 kg/m³. Pump capacity is less when the liquid is lighter and more when it is heavier. Therefore for general consid­erations capacity should not be introduced in defining n_s.

It is not difficult now to determine the impeller diameter of a standard pump. From Eq. (12.32)

whence

In using Eqs (12.38) and (12.39) the metric units of measure are metres for H, m³/sec for Q and revolutions per minute for n.

Under certain conditions the specific speed n_s characterises the ability of a pump to develop head and ensure a certain delivery. The higher the specific speed the less the head (for a given Q and n) and the greater the capacity (for a given H and n).

Specific speed depends on impeller design. Pumps with low spe­cific speed have impellers with small relative width () but ahigh value of , i. e., long vanes, which is necessary to obtain a higher head. Flow through such an impeller is in a plane perpen­dicular to the axis of rotation.

With n_s increasing the ratio (as well as ) decreases, I. e., the vanes are shorter and the relative width of the impeller is greater. Furthermore, the flow through the impeller departs from the plane of rotation and becomes increasingly three-dimensional. In the limit, at maximum values of n_s, the flow is along the axis of rotation and the impeller is of the axial-flow type.

The vane angle p₂ decreases from about 35° to 15° with n_s increasing from 40 to 200.

Centrifugal and other rotodynamic pumps may be classified ac­cording to the specific speed as follows:

1. low-speed radial-flow: ;

2. normal-speed radial-flow: ;

3. high-speed radial-flow: ;

4. mixed-flow: ;

5. axial-flow, or propeller: .

The impeller shapes corresponding to these five types are present­ed schematically in Fig. 146.

The first three belong to the true centrifugal pump, the mixed-and axial-flow designs actually representing other pump types. Obviously, no sharp boundaries can be drawn between the different types of pumps, and the centrifugal impeller turns gradually, through a mixed-flow impeller, into a true propeller as n_s increases.