1. Lecture 5 Centrifugal Pumps: Performance and Characteristic Curves
MEP 4120 – Hydraulic Machines (A)
Lecture 5 Centrifugal Pumps: Performance and Characteristic Curves

2. Centrifugal Pumps Performance
Previously, we learned that the main parameters involved in all hydraulic turbomachines and that influence their performance are: the fluid quantities (represented in the flowrate (Q) and the head (H)) and the mechanical (associated with the machine itself) quantities (represented in the power (P), speed (N), size (D) and efficiency (h)).
Although they are all of equal importance, the emphasis placed on certain of these quantities is different for pumps and turbines.
The output of a pump running at a given speed is the flow rate delivered by it and the head developed. Thus, a plot of a head against flowrate at constant speed forms the fundamental performance characteristic of a pump.
In order to achieve this performance, a power input is required which involves efficiency of energy transfer. Thus, it is useful to plot also the power and the efficiency against the flowrate.

3. Centrifugal Pumps Performance
A typical complete set of performance characteristics of a centrifugal pump, for example, is shown in the following figures.

4. Centrifugal Pumps Performance

5. Centrifugal Pumps Performance
The performance characteristics, then , represent in a graphical form the relationships between variables relevant to a specific pump machine. Each and every machine has its own set of characteristics curves which represent its performance.
In real practice, because of the complexity of concluding these characteristics curves theoretically, all of them are experimentally deduced by carrying out the required set of experiments on each individual machine at a given constant value of speed against the flowrate as the independent variable.
Several important notes may be extracted from the above argument and should be declared before we continue to analyze the performance data.

6. Centrifugal Pumps Performance
Let’s firstly recall the theoretical Euler’s pump equation:
From this equation, we can inferring the following:
1- for the same pump rotating at constant speed, the pump will generate a head dependent upon the quantity of fluid it is handling
2- for the same machine, i.e. the geometrical parameters (b, r, and b) will be fixed, increasing the impeller speed will considerably improve the theoretical head gained. Thus, for every speed value, it is expected to have a completely different set of characteristics performance curves, i.e. we have another pump.
3- since for machines of different design features and different sizes the values of a and b will be different, their characteristics will also be totally different, i.e. each machine will have its typical performance curves.

7. Centrifugal Pumps Performance
A- Losses in Rotodynamic Machines
In the preceding lecture, we showed how the actual head developed by the pump as a function of the flowrate was reducibly derived from the theoretical Euler’s pump head equation. We attributed this reduction to a multiple of prementioned reasons.
However, as we all know well that for all machines which are deserving for converting the energy from one form to another, the efficiency parameter is the fundamental factor used to indicate and measure at the same time how/how much this conversion process was fulfilled.
Losses must inherently accompanying any energy conversion process and the main reason for reducing the efficiency. And how small these losses are or how good a machine is in converting energy is indicated by its efficiency.

8. Centrifugal Pumps Performance
Efficiency of a machine is always defined as the ratio of power output of the machine (what is gained) to the power input into it (what is paid).
However, rotodynamic machines are complex, consisting of a number of parts through which the fluid moves and, thus, it is convenient for analytical and design purposes to consider component losses as well as their sum total and to express each component loss in the efficiency form.
Let’s now consider these component losses one by one. First, the actual energy transfer in a rotodynamic machine occurs in its impeller. Here the fluid passes through the blade passages and either receives energy from the moving blades or imparts energy to them.

9. Centrifugal Pumps Performance
In any case, there are two major sources of energy loss within the impeller. The expected contact between the fluid moving over solid surfaces gives rise to boundary layer development and, hence, to frictional losses, whereas the need for the fluid to change direction often results in separation and, hence, leads to separation (or shock) losses.
Both these losses may be augmented by secondary flows which may occur within the impeller due to pressure distribution across it, as we showed before, and are usually prominent at off-design points of operation.
Thus if hi is the head loss in the impeller and Qi is the discharge through the impeller, then the impeller power loss is:

10. Centrifugal Pumps Performance
Now, the discharge through the impeller Qi is usually not the same as that flowing through the machine, simply because some fluid passes through clearances between the impeller and the casing. In a pump, of all the fluid passing through the impeller most flows into the discharge end but some passes through the inlet clearance and finds itself passing through the impeller again as shown in the Figures. Thus, the impeller always handles a greater volume than that discharged by the pump.

11. Centrifugal Pumps Performance
If we denote by q the discharge leaking past the impeller and if Hi is the total head across the impeller, then the power loss due to the leakage may be expressed as:

12. Centrifugal Pumps Performance
In most machines the impeller is surrounded by a stationary casing so that the fluid passes through parts of the casing before it enters the impeller and after leaving it. Thus, losses due to friction and separation occur in the casing as well. If the flow rate through the casing and , thus, through the machine is Q (greater or smaller than Qi depending whether it is a turbine or a pump, respectively, the difference being q) and the loss of head in the casing is hc, then the power loss in the casing is:
Finally, there are mechanical losses of energy such as in the bearings and sealing glands which must be accounted for. It is normal practice in hydraulic machines to include within this category losses due to disc friction “called windage loss”. This is the power required to spin the impeller at the required velocity without any work being done by the impeller or on the impeller by the fluid. This would be possible only if the impeller did not have any blades. Thus, windage loss accounts for the friction between the outer surfaces of the impeller rotating in the fluid surrounding to it within the casing.

13. Centrifugal Pumps Performance
It is now possible to consider the energy balance for the whole machine, but here we must begin to distinguish between pumps and turbines because what represents the output of one is the input of the other and vice versa. Thus for a pump:
Shaft power
input
Mechanical loss
Impeller loss
Leakage loss
Casing loss
Useful fluid power
Hydraulic losses

14. Centrifugal Pumps Performance
In the following Figures the energy conservation diagram for a pump is shown.

15. Centrifugal Pumps Performance

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B- Efficiencies of Rotodynamic Machines
After discussing all the losses sources in a hydraulic machines and the completely energy conservation diagram, it is now possible to define efficiencies for every part, for intermediate related categories and for the most important overall efficiency.
The overall efficiency refers to the machine as a whole and is, therefore, always plotted as one of the performance characteristics. It is defined as:
Where H is the actual total head difference measured between the inlet and outlet flanges of the machine or as defined in previous lecture as the manometric head delivered by the machine and is given by:

17. Centrifugal Pumps Performance
If the mechanical power loss Pm, then the power input o the impeller is (P-Pm) and the mechanical efficiency may be defined as:
The impeller efficiency takes care of the losses in the impeller, and, defined as:
If we express the denominator in terms of the fluid loss in the impeller, we will have:

18. Centrifugal Pumps Performance
The volumetric efficiency is not always appropriate, for example, in axial-flow machines, but is important in the case of centrifugal pumps and especially fans. In general,
Thus, the volumetric efficiency is defined as:
The casing efficiency accounts for the power loss in the casing, and defined as:

19. Centrifugal Pumps Performance
It is now possible to show that the overall efficiency is equal to the product of all the components efficiencies:
Which defines the overall efficiency as already predefined before.

20. Centrifugal Pumps Performance
Now, the internal losses of the machine, i.e. those occurring in the impeller and in the casing due to friction and separation are sometimes called hydraulic losses, which gives rise to the hydraulic efficiency, and defined as:
Where EN and Hth , n is the theoretical head calculated from the net power input to the impeller and defined as prementioned before from:
Sometimes we neglect the effect of slip factor and taken as one. Thus, the theoretical Euler’s head will equal the theoretical net head and the hydraulic efficiency may be defined as:

21. Centrifugal Pumps Performance
Finally, the overall efficiency may also be defined as:
C- Remarks on the Centrifugal Pumps and Fans Performance
1- Now, the actual form of the characteristics performance curves for a given centrifugal pump running at constant value of rotational speed are clear. As we discussed before, varying the pump speed will provide a new set of performance curves. There is an individual set corresponding to each speed value. The (Q, H) curve of each set has a particular point called the design point (BEP) which is normally corresponding to the best efficiency value on the efficiency curve.

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As expected, the position of (BEP) moves to the right or, hence, the design discharge increases with increasing the speed. Normally, this point is located at no-shock condition where the fluid meets the impeller entry tangentially, i.e. with the same inlet blade angle of b1. Increasing the speed will increase the tangential velocity at the entry section (U1). Satisfying the no-shock condition means increasing the flow velocity component (Cr1) which for the same pump geometry is corresponding to increasing the discharge.
Thus, it is recommended to operate the pump at or close the BEP, i.e. the design discharge corresponding to each speed value in case of using variable speed primeover.

25. Centrifugal Pumps Performance
2- However, it is not always the case in real practice that the operating point lies at the design point. This may be due to:
A pipeline being partially blocked;
A valve jammed partially closed;
Poor matching of the pump to the piping system.

26. Centrifugal Pumps Performance
3- Thus, operating mono-speed pump at decreased or increased discharge with respect to the design discharge may release the following conditions:
At the inlet to the impeller blades eddies due to shock formation will be released on either the suction side for reduced discharge or on the pressure side for increased discharge. Remembering the following Figure:

27. Centrifugal Pumps Performance
At the outlet to the impeller blades as shown in the Figure, when the discharge changes, Cr2 changes, and since U2 is constant and β2 is constant (assume no slip, i.e. β'2 = β2), the magnitudes of W2 and C2 must change along with α2. Since E depends on Cx2, then E will change accordingly. Thus, a reduction in Q gives an increase in Cx2, while an increase in Q gives a reduction in Cx2. If head against which pump operates increased, E and therefore Cx2 increase and Q decreases to give the new operating point at the increased head. Conversely, reduction in the operating head gives an increase in Q .

28. Centrifugal Pumps Performance
4- For constant speed (N), pump size (D) and discharge (Q) , let’s now examine the effect of the outlet blade angle b2. As shown in Figure, three different blade angles referred to as backward facing blades (b2 < 90°), forward facing blades (b2 > 90°) and radial blades (b2 = 90° ).
It is clear that as b2 increases, the absolute velocity C2 (and hence the whirl component Cx2) also increases. Thus, the head developed depends upon b2 and is larger for the forward blades.

29. Centrifugal Pumps Performance
Referring to the figure, one can notice that the large head developed by the forward blades impellers includes a large proportion of velocity head since C2 is very large. This presents practical difficulties in converting some of this kinetic energy into pressure energy, due to the substantial uncontrolled losses.
The effect of outlet blade angle on the real characteristics performance curves is shown in the following Figure.

30. Centrifugal Pumps Performance
It is clear that the forward bladed impeller generates greater head at a given discharge, but remembering that a substantial part of this total head is in fact the velocity head.
However, the power characteristics performance show important differences of considerable practical importance.
For backward bladed impeller, the maximum power occurs near the maximum efficiency point and any increase of the discharge beyond this point results in a decrease of power. Thus, an electric motor used to drive such a pump or fan may be safely rated at the maximum power. This type of power characteristic is called self-limiting.

31. Centrifugal Pumps Performance
However, this is not the case for the radial and forward bladed impellers, for which the power is continuously rising with discharge. Choosing an appropriate motor, therefore, poses problems, because to have one rated for maximum power would mean over-rating and an unnecessary expenditure (cost), if the pump will operate only near the maximum efficiency point. On the other hand, a smaller motor rated just for the operating point may be in great danger of being overloaded should the pump be operated by mistake at a discharge greater than the design value corresponding to the maximum efficiency point.
The most common blade outlet angles for centrifugal pumps are from 15° to 90°, but, for fans, the range extends into forward inclined blades (well-known multi-vane fans) with b2 as large as 140°.

32. Centrifugal Pumps Performance
5- Now, another implication to operating the pump at off-design discharge, i.e. away in both directions from the BEP point. Thus, any deviation from the design point will arise a radial thrust distribution around the impeller and causing a bending moment on the impeller shaft. This thrust changes in its magnitude and direction as a function of the discharge.
This radial thrust can be calculated from the following formulae:
where P = Radial Force (N),
H = Head (m),
D2 = Peripheral Diameter (m),
B2 = Impeller Width (m) and
K = Constant, K = 0.36[1 – (Q/QD)2]

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34. Centrifugal Pumps Performance
Radial thrust at off-design reduced discharge
Radial thrust at design discharge

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36. Centrifugal Pumps Performance
Centrifugal Pump Component Damage and Caused as a Function of Operating Point

37. Centrifugal Pumps Performance

38. Centrifugal Pumps Performance
6- Finally, the discharge in the casing can be arranged in one of the following forms due to the overall design requirements:
1- simple volute or scroll casing
2- vaneless diffuser
3- vaned diffuser
The contribution of each component within the centrifugal pump into the total output head developed by the pump is shown in the Figure.