Pump Characteristic Curves,Affinity Laws,System Curves

Pump Characteristic Curves

Section A -- Centrifugal Pump Fundamentals

A-7 Pump Characteristic Curves
The performance of a centrifugal pump can be shown graphically on a characteristic curve. A typical characteristic curve shows the total dynamic head, brake horsepower, efficiency, and net positive Suction head all plotted over the capacity range of the pump.

Figures 5, 6, & 7 are non-dimensional curves which indicate the general shape of the characteristic curves for the various types of pumps. They show the head, brake horsepower, and efficiency plotted as a percent of their values at the design or best efficiency point of the pump.

Fig. 5 below shows that the head curve for a radial flow pump is relatively flat and that the head decreases gradually as the flow increases. Note that the brake horsepower increases gradually over the flow range with the maximum normally at the point of maximum flow.

Fig. 5 Radial Flow Pump

Mixed flow centrifugal pumps and axial flow or propeller pumps have considerably different characteristics as shown in Figs. 6 and 7 below. The head curve for a mixed flow pump is steeper than for a radial flow pump. The shut-off head is usually 150% to 200% of the design head, The brake horsepower remains fairly constant over the flow range. For a typical axial flow pump, the head and brake horsepower both increase drastically near shutoff as shown in Fig. 7.

Fig. 6 Mixed Flow Pump

Fig. 7 Axial Flow Pump

The distinction between the above three classes is not absolute, and there are many pumps with characteristics falling somewhere between the three. For instance, the Francis vane impeller would have a characteristic between the radial and mixed flow classes. Most turbine pumps are also in this same range depending upon their specific speeds.

Fig. 8 below shows a typical pump curve as furnished by a manufacturer. It is a composite curve which tells at a glance what the pump will do at a given speed with various impeller diameters from maximum to minimum. Constant horsepower, efficiency, and NPSHR lines are superimposed over the various head curves. It is made up from individual test curves at various diameters.

Fig. 8 Composite Performance Curve

Affinity Laws

Section A -- Centrifugal Pump Fundamentals

A-8 Affinity Laws
The affinity laws express the mathematical relationship between the several variables involved in pump performance. They apply to all types of centrifugal and axial flow pumps. They are as follows:

1.      With impeller diameter D held constant:

Where:

Q = Capacity, GPM
H = Total Head, Feet
BHP = Brake Horsepower
N = Pump Speed, RPM

2.      With speed N held constant:

When the performance (Q₁, H₁, & BHP₁) is known at some particular speed (N₁) or diameter (D₁), the formulas can be used to estimate the performance (Q₂, H₂, & BHP₂) at some other speed (N₂) or diameter (D₂). The efficiency remains nearly constant for speed changes and for small changes in impeller diameter.

Example:
To illustrate the use of these laws, refer to Fig. 8 below. It shows the performance of a particular pump at 1750 RPM with various impeller diameters. This performance data has been determined by actual tests by the manufacturer. Now assume that you have a 13" maximum diameter impeller, but you want to belt drive the pump at 2000 RPM.

Fig. 8 Composite Performance Curve

The affinity laws listed under 1 above will be used to determine the new performance, with N1 1750 RPM and N2 = 2000 RPM. The first step is to read the capacity, head, and horsepower at several points on the 13" dia. curve in Fig. 9 below. For example, one point may be near the best efficiency point where the capacity is 300 GPM, the head is 160 ft, and the BHP is approx. 20 hp.

This will then be the best efficiency point on the new 2000 RPM curve. By performing the same calculations for several other points on the 1750 RPM curve, a new curve can be drawn which will approximate the pump's performance at 2000 RPM, Fig. 9.

Trial and error would be required to solve this problem in reverse. In other words, assume you want to determine the speed required to make a rating of 343 GPM at a head of 209 ft. You would begin by selecting a trial speed and applying the affinity laws to convert the desired rating to the corresponding rating at 1750 RPM. When you arrive at the correct speed, 2000 RPM in this case, the corresponding 1750 RPM rating will fall on the 13" diameter curve.

Fig. 9

System Curves

Section A -- Centrifugal Pump Fundamentals

A-9 System Curves
For a specified impeller diameter and speed, a centrifugal pump has a fixed and predictable performance curve. The point where the pump operates on its curve is dependent upon the characteristics of the system In which it is operating, commonly called the System Head Curve. ..or, the relationship between flow and hydraulic losses* in a system. This representation is in a graphic form and, since friction losses vary as a square of the flow rate, the system curve is parabolic in shape.

By plotting the system head curve and pump curve together, it can be determined:

1.      Where the pump will operate on its curve.

2.      What changes will occur if the system head curve or the pump performance curve changes.

NO STATIC HEAD - ALL FRICTION
As the levels in the suction and discharge are the same (Fig. 1), there is no static head and, therefore, the system curve starts at zero flow and zero head and its shape is determined solely from pipeline losses. The point of operation is at the intersection of the system head curve and the pump curve. The flow rate may be reduced by throttling valve.

Fig.1 No Static Head All Friction