Pumps/pumping scaling laws

Pumping is a unit operation that is used to move fluid from one point to another. This chapter discusses various topics of this important unit operation relevant to the physical treatment of water and wastewater. These topics include pumping stations and various types of pumps total developed head pump scaling laws pump characteristics best operating efficiency pump specific speed pumping station heads net positive suction head and deep-well pumps and pumping station head analysis. 

When designing a pumping station or specifying sizes of pumps, the engineer refers to a pnmp characteristic cnrve that defines the performance of a pump. Several different sizes of pumps are used, so theoretically, there should also be a number of these curves to correspond to each pnmp. In practice, however, this is not done. The characteristic performance of any other pnmp can be obtained from the curves of any one pnmp by the use of pump scaling laws, provided the pumps are similar. The word similar will become clear later. 

The pump performance with He II at 1.8 K is compared in Fig. 7.30 with the pump performance obtained by Sundstrand with He I at 4.2 K. The study has shown that He II obeys the pump scaling laws in spite of the unique characteristics of the superfluid component. One major concern in using centrifugal pumps for transfer of He II in space applications is that a net positive suction head (NPSH) is required. The fountain effect pump described by DiPirro and Castlesfor this application appears to be simpler and more reliable than the centrifugal pump because it has no moving parts. 

Figures 32.12 and 32.13, and Figure 32.14 shows how the effect of changing speed or diameter of a pump impeller may be predicted, using the scaling laws ...

Pumps that follow the above relations are called similar or homologous pumps. In particular, when the n variable C, which involves force are equal in the series of pumps, the pumps are said to be dynamically similar. When the 11 variable Cq, which relates only to the motion of the fluid are equal in the series of pumps, the pumps are said to be kinematically similar. Finally, when corresponding parts of the pumps are proportional, the pumps are said to be geometrically similar. The relationships of Eqs. (4.30) and (4.31) are called similarity, affinity, or scaling laws. 

From the equations derived, the following simplified scaling laws for a given pump operated at different speeds, o), are obtained ... 

For pumps of constant rotational or stroking speed, co, but of different diameter or stroke, D, the following simplified scaling laws are also obtained ... 

Scaling laws— Mathematical equations that establish the similarity of homologous pumps. 

Similarity, affinity, or scaling laws—The equations that state that the head, flow, and power coefficients of a series of pumps are equal. 

By stepping a over the duration of the pulse and collecting a pump-probe spectrum for each time value of a, the vibrational population transfer over the course of the pulse is assessed. To quantitatively extract relative vibrational populations from these pump-probe spectra, we fit peak intensities assuming a harmonic scaling law for the transition dipoles [e.g., (n + l) /xn n+i 2 = (n + 2)... 

Ohwa, M., and Obara, M. (1986). Theoretical analysis of efficiency scaling laws for a self-sustained discharge-pumped XeCl laser. J. Appl Phys. 59(1), 32-34. 

This scaling law explains why large pumps are designed with particular attention being paid to the forces exerted on the structures. 

When trying to manipulate fluids on the micron scale, formidable problems have to be overcome [301], Miniature pumps, valves, switches, and new analytical tools have to be developed. To illustrate this we discuss the fundamental problem of transporting a liquid through a capillary tube. In the macroscopic world we would apply a pressure AP between the two ends. According to the law of Hagen-Poiseuille the volume of liquid V transported per time t is (assuming laminar flow)... 

Thus, the similarity laws enable us to make experiments with a convenient fluid—such as water, for example—and then apply the results to a fluid which is less convenient to work with, such as air, gas, steam, or oil. Also, in both hydraulics and aeronautics valuable results can be obtained at a minimum cost by tests made with small-scale models of the full-size apparatus. The laws of similitude make it possible to determine the performance of the full-size prototype, from tests made with the model. It is not necessary that the same fluid be used for the model and its prototype. Neither is the model necessarily smaller than its prototype. Thus, the flow in a carburetor might be studied in a very large model. And the flow of water at the entrance to a small centrifugal-pump runner might be investigated by the flow of air at the entrance to a large model of the runner. 

The power (P is the power given to the fluid. In plots of characteristic curves such as Figure 4.8, however, the brake power is the one plotted. Becanse bears a ratio to that of the brake power in the form of the efficiency t], the similarity laws that we have developed also apply to the brake power, and figures such Figure 4.8 may be used for scaling brake powers of pumps. 

Below about 80 mW of incident power (842 Wcm" ) with sample at lOK, emission spectra for the Iiv2 —transition are as shown in fig. 7 above this threshold observed spectra peaked only at 2.72 pm, showing clearly a spectral narrowing. Output intensity vs. incident pump power is shown in fig. 8 on a l<%-log scale. There is a marked threshold, then emission follows a square law vs. pump power. When the temperature... 

Both A and B are dimensionless quantities that characterize the geometry of the pump. In accordance with the dimensional laws, it is observed that the specific speed depends neither on the size D of the pump nor on its rotational speed co. It characterizes the geometrical design of the pump, as it depends only on angles a and scale ratios e/Z), (S>slD given in [5.2]. Centrifugal pumps are typically characterized by specific speed values between 30 and 50. 

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