Fig.F-8
Rotating pipe does not represent any important application in itself. As we shall see, however, it is a starting point for understanding processes that take place inside radial turbomachines such as centrifugal pumps (- for liquids) or blowers (- for low-pressure gas). In the upper part of Fig.F-8 there is a case of liquid at rest, corresponding to what we have already learned in Fig.F-6 on the previous page. If the rotation speed is increased (lower part of Fig.F-8), fluid starts to flow. In principle, such a simple bent pipe might be used as a functioning pump - or a blower, according to Fig.F-9. Actual layout of real turbomachines is different: instead of a single rotating pipe, there is a rotor provided with blades. The real flow between the blades is an extremely complex three-dimensional one. In the simplest, one-dimensional study, each of the spaces between
Fig.F-9 The simplest blower consisting of just a single rotating duct
... and derivation of its characteristic: the dependence between generated
specific-energy increase and the generated mass flow rate (which may be
decreased by turning down the valve at vessel exit).

neighbouring blades may be treated as a rotating pipe and although this is just a rough approximation, it may provide many interesting explanations of the basic dependences between the variables. In Fig.F-9, the study of the rotating pipe flow provides a basis for investigating the characteristic of a turbomachine. The characteristic (as we have already learned on page D10 in the case of a passive element - note that pumps are active elements) is a dependence between mass flow rate (plotted on the horizontal co-ordinate) and generated specific energy difference (on the vertical co-ordinate). The characteristic curve (which is graphical presentation of the characteristic) provides the basic information any user needs for designing hydraulic system containing the pump (or pneumatic system with a blower). Although characteristics of real turbomachines might be sometimes
Fig.F-10
more complex, most of them usually more or less correspond to the simple quadratic model derived in Fig.F-9. An important fact that follows from Fig.F-9 is emphasised in Fig.F-10: because rotational speed is represented only in the term of the expression of the characteristic - this is the term which determines the vertical position of the horizontal line corresponding to an ideal source - changing speed of a pump causes the characteristic to be shifted vertically, without any change of its shape. Note in Fig.F-9 that depends upon second power of speed so that the vertical shift increases quadratically with increasing shaft speed.


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This is page Nr. F04 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
Any comments and suggestions concerning this text may be mailed to the author to his address tesar@fsid.cvut.cz

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