The link between the flow rate Q and the total head H, at constant number of revolutions, is typical of each pump and is represented by a curve in the Cartesian plane Q, H which is called the characteristic curve of the pump.

The course of the characteristic curve essentially depends on the type of impeller. We can distinguish the three cases, represented in the previous figure, of a pump with radial impeller, semi-axial impeller and axial impeller. The characteristic curve of the radial impeller pump has a parabolic course. The pump is particularly suitable when the flow rate is considerably constant and the head is subject to limited variations. The semi-axial impeller pump has a characteristic curve with an always descending and tighter trend than that of a pump with a radial impeller. The axial impeller pump has an almost straight downward characteristic curve. It is generally used to lift significant capacities with heads of a few meters.

The trend of the characteristic curve H (Q) and of the complementary curves of the efficiency η (Q) and of the absorbed power W (Q) of a centrifugal pump are shown below.

### Characteristic curve H (Q)

The characteristic curve of a pump represents the variations of the head H as a function of the flow rate Q. The flow rate-head curve of the pump is plotted experimentally by points, at a constant number of revolutions, reporting the head H on the ordinate and the flow Q on the abscissa in a system of orthogonal Cartesian axes. Heads decrease with increasing flow (and vice versa).

It can therefore be deduced that: the centrifugal pump, at constant rotation speed n, conveys a flow rate Q which increases as the head H decreases. When the flow rate is zero, the head reaches the maximum value 2.

### Efficiency η (Q)

The efficiency η of a pump is the ratio between the useful power Wu and the absorbed power W, i.e. η = Wu / W. The yield curve first has an ascending and then a descending trend. At the point of maximum efficiency (or in a neighborhood of it) the pump operation is optimal.

### Absorbed power W (Q)

The power W is the product of the flow rate Q by the head H and by the density d of the fluid (W = Q ∙ d ∙ H). If the flow rate Q on the abscissa axis and the absorbed power W on the ordinate axis are represented in the diagram, the flow-power curve is obtained. This curve is generally ascending, that is, it rises as the flow rate increases.

### Optimal operating range of a pump

Although a pump can operate in such different conditions, there is a point on the curve on which (or around which) it would be appropriate to make it work. This point corresponds to the maximum efficiency value of the pump (see flow rate-efficiency curve).

### Clamshell diagram

The yields can also be represented in correspondence with the flow rate / head curves by means of equal yield curves. So called “hill diagram” also called “shell diagram”. The returns are gradually decreasing as we move from the point of maximum return to its periphery.

If the number of revolutions of the machine changes, the characteristic curve as well as that of the efficiency and that of the absorbed power also change. The figure shows the family of characteristic curves and of the absorbed powers at different speeds of the impeller, in which the constant efficiency curves having an oval shape are also marked. This diagram, which identifies the characteristic performance range of the machine, is generally referred to as the clamshell diagram.

The passage from one operating condition to another can be done very easily, bearing in mind that the flow rate Q, the head H and the power W measured at n revolutions and the flow rate Qx, the head Hx and the power Wx when the number of revolutions is nx, the following relations exist:

### Choice of pump

Manufacturers generally present the range of normal production pumps in the form of graphs consisting of many curvilinear quadrilaterals, each of which identifies the range, in the Cartesian flow-head plane, of use of a type of pump. The following figure shows an example of this type of chart called a mosaic diagram. Once the flow rate and the head are known, the diagram allows you to make a choice of first orientation of the pump.

### Characteristic curve of the pipe and duty point

As is known, the total head consists of two addends, the geodetic head and a term Y (Q) which expresses the pressure drops that occur in the delivery and suction pipes. Since the term Y (Q) is a quadratic function of the flow rate, it results: H = Hg + Y (Q) = Hg + kQ². This equation in the Q, H plane is represented by a parabola and is called the characteristic curve of the pipe.

The intersection in the Q, H plane between the characteristic curve of the pump and that of the pipeline, which is point B in the figure, is called the operating characteristic point. If the characteristic curve of the pipeline changes position, for example due to the variation of resistance to motion attributable to the degree of opening of a valve on the pipeline or due to an increase in the roughness of the pipeline, then the operating point varies.

The system characteristic curve can be modified:

- by varying the flow resistances (e.g. throttling a gate valve)
- by varying the static component of the head (e.g. by increasing or decreasing the pressure in the tank or the liquid level in the case of an open tank).

### Pressure drops in centrifugal pumps

This type of pressure drop occurs in the centrifugal pump in the section between the suction flange and the beginning of the impeller blading and is indicated by the manufacturers with the acronym NPSH. The term NPSH derives from the English and literally means “net positive suction head”, ie net positive height on the suction side.

The manufacturers provide in their catalogs the trend of the flow rate-NPSH curve which represents the variation of the pump NPSH (NPSHnec.) As a function of the flow rate variation.

The NPSH curve generally has a trend:

- gradually increasing starting from the minimum flow rate Qmin up to the best efficiency flow rate Qopt
- decidedly increasing upwards for flow rates higher than Qopt
- Below Qmin the NPSH curve (dashed in the figure) has a very steep upward, almost vertical trend.