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Fig.F-11
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Of paramount importance is the fact that apart from the work
written on the right-hand side of the Bernoullis' Theorem
equation, some additional work must be done to increase the fluid absolute velocity. This "outer" (or "external") work (Fig.F-11) does not appear in the equation, yet it must be performed if the pipe is to be rotated at the given speed. As a result, the power for driving the simple pump or blower
shown in Fig.F-9 is actually higher than might be expected ... if the pipe exit is at right angle to the rotation axis, as is the case in Fig.F-9 , the power is actually twice as high. Moreover, in the layout of Fig.F-9 the additional input power is lost: it is used to increase the
fluid velocity at the pipe exit - but the increased kinetic energy corresponding to this velocity is uselessly
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Fig.F-12
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dissipated in the space (the vessel in Fig. F-9) into which fluid passes from the tube.
It is, however, possible to make use of this kinetic energy by adapting the pump layout as shown in Fig.F-13: there is a system of stationary blades (suitably shaped to make for fluid entering the passages between them easy) between which fluid is slowed down
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Fig.F-13
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and its increased kinetic energy is converted into ustilisable pressure energy. This approach is quite common in real pumps and blowers. Another possibility, also in common use in real machines, is decreasing the required "outer" work. This is possible to achieve by additional curvature of the duct, out of the meridional plane - as shown for the bent-pipe case in Fig.F-14. An important fact is that the expression for the work imparted to fluid in a rotating duct, as derived in Fig. F-14, retains its validity also in real machines - which use a multi-duct rotor in place of the simple bent pipe, used here in Figs.F-9 to F-14 as an instructive model.
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Fig.F-14
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This is page Nr. F05 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
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