Fig.G-32 Series connection of pumps or blowers leads to increased resultant specific energy difference (and, of course, pressure or height difference as well) - but this is not a simple addition of differences which would be generated by a single machine placed in the same position of the circuit. It is important to note that this connection should be used if the dissipance of the load is high.

Fig.G-33 Parallel connection of pumps or blowers leads to increased resultant flow rate - but this is not a simple addition of flows which would be generated by a single machine placed in the same position of the circuit. It is important to note that this connection should be used if the dissipance of the load is small.


Quite often, a situation may arise when a single available turbomachine (pump or ventilator) does not suffice for generation of required energetic difference or required flowrate and it is possible to use two or more machines to do the job (such multiplication might be also chosen to increase the reliability - some fluid circulation is retained even in the case of failure of one unit). If the machines are connected in series - Fig.G-32 - their individual values of parameters as well as simply add. Fig.G-33 presents the graphical construction of the resultant characteristic of the aggregate consiting of two identival pumps. In the parallel connection case, Fig.G-33, the expression is more complicated: if there are (as is the case in Fig.G-33) two identical pumps, the resultant aggregate behaves as a source with value equal to that of each pump, but with lower resultant dissipance.



As long as the simplified expression for the characteristic, derived in Fig.G-15, is applicable, power transferred from the pump into
Fig.G-34
the load is
= = -
In Fig.G-34 the hyperbolic curves as loci of constant output power are plotted into the common loading characteristic. It may be useful, however, to plot the power characteristics as a diagram = f (). In Fig.G-35 there is such a diagram in the relative co-ordinates
= /
= /
related to the maximum values
- where there is



If the load dissipance is high, it is possible to get a large specific-energy drop across the load,
but flowrates passing through it are small. The power transferred to the load, which is product of energetic drop and mass flowrate, will be small. On the other hand, also a load with dispropotionately small dissipance will receive only a small transferred power - this time despite the large flow this will be because of too small energetic drop. Obviously, between these two extremes there must exist an optimum load capable of receiving the largest power from a given source. For such a load, the power handed over to the pump by the driving motor will be optimally used. Conversely, using the optimum load expression, it is possible to select the best pump unit for a given loading. This is an actual problem nowadays where there is a strong criticism of excessive energetic demands of our industry - and, in contract to previous
Fig.G-35

regime, there is a wide choice of pumps available on the market.

Let us denote by = /
Note: There is, unfortunately no Greek equivalent of "Q", which should be used to denote a simple ratio. Lower case symbols are normally reserved for specific values - fortunately, dissipance is not an extensive quantity so that no confusion can arise from this departure from proper nomenclature.
Because in the intersection (Fig.G-34) both equations of characteristic, that of the pump as well as the one of the load, must hold, there is
= - ... and this means that in relative co-ordinates there is
Inserting this expression into the above equation of relative power characteristics leads to . Points evaluated from this formula for several values of are shown in Fig.G-35. It is seen that pump is optimally loaded if there is = 2.


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This is page Nr. G10 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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