Centrifugal Pump Control: Methods and Q/H Curves

Adjusting centrifugal pumps means modifying the actual operating point of a system by adjusting either the pump curve or the system curve. The practical goal is to adapt the flow rate (Q) and head (H) to the system’s requirements, minimizing waste whenever possible.

Q/H Curve and Operating Point: The Basics

The hydraulic performance of a centrifugal pump is represented by a Q/H curve (flow rate/Head): at a fixed rotational speed, each flow rate Q corresponds to a specific Head H. All points on the curve are, in theory, points at which the pump can operate.

The actual operating point is not determined “on paper” simply by looking at the pump: it is givenby the intersection of the pump’s characteristic curve and that of the system.

System characteristic curve: What does it really describe?

The system characteristic describes how the required head H depends on the flow rate Q.

For a non-branched pipeline, the required head is calculated by applyingBernoulli’s equation between two cross-sections (1 and 2), taking into account factors such as:

• pressures in the upstream and downstream tanks ($p_1$, $p_2$)
• density of the liquid ($\rho$)
• gravitational acceleration ($g=\mathrm{9,81}m/s^2$)
• static head ($H_{g\mathrm{and}o}$)
• total friction losses ($\mathrm{\Delta }{H}_{tot}$)

When the surface areas of the tanks are large compared to the pipes, the average velocities in the tanks are often negligible; this leads to a simplified form of the relationship.

Static and dynamic parts: $H_s$ and $H_d$

The system curve can be viewed as the sum of:

• a static part $H_s$, which does not depend on the flow rate
• a dynamic part $H_d$, related to pressure drops that increase with flow rate

In closed systems, the static value is zero.

Total pressure drops $\mathrm{\Delta }{H}_{tot}$ include inlet and outlet. For sufficiently high Reynolds numbers, they are proportional to the square of the flow rate. In simplified form, this results in a parabolic system characteristic curve, often expressed as: $$H_{i\mathrm{p.m.}p}=H_s+H_d\text{with}{H}_d\propto Q^2$$

Therefore, as Q increases, the head required by the system increases quadratically.

The key principle: To change the working point, you must change a curve

The point where the pump curve intersects with the piping curve (system curve) is the characteristic operating point.

To “truly” change it, it’s not enough to simply want a different flow rate: you have to modify one of the two curves:

• the system curve (by adjusting $H_s$, on $H_d$, or on both)
• the pump curve (by adjusting speed, configuration, and impeller)

Below you will find the methods mentioned and how they relate to this principle.

Outlet flow control with valve: adjust $H_d$ by “throttling”

This is the simplest and most cost-effective method: it involves adjusting the opening of a control valve installed immediately downstream of the pump’s outlet flange.

This introduces a variable localized pressure drop, which increases the slope of the system’s characteristic curve and shifts its intersection with the pump curve: at a constant speed, the flow rate can be reduced.

Be aware of the energy impact: the pump may generate a head greater than that required by the system, and the excess is “consumed” by the valve. This energy is dissipated as heat and is lost. This loss is acceptable if the control range is small or adjustments are infrequent.

Bypass Control: Modify $H_d$ by recirculating the excess flow rate

In this diagram, a valve is installed downstream of the pump to divert excess flow rate into the inlet tank.

This method is also energy-wasting: the pump delivers a flow rate greater than that required by the system. The text explicitly states that bypass losses are greater than those resulting from regulation using an outlet flow control valve.

When using the bypass, to identify the operating points, we move from the concept of:

• equivalent circuit (system and bypass in parallel)
• equivalent pump, determined using graphical constructions based on points on the characteristic curves
  , leading to the graphical determination of the operating points of the pump and the system.

Varying the rotational speed: shifting the pump curve (laws of similarity)

Another method is to change the operating point by varying the machine’s rotational speed. First, we introduce the laws of similarity, which are based on the idea that machines that are geometrically and kinematically similar will have the same hydraulic efficiency, and which allow us to establish relationships between head H, flow rate Q, and rotational speed n.

In practical terms, changing the speed results in a different pump characteristic curve for each speed. The system curve will intersect each pump curve at a different point; this allows the machine to adapt its performance to changes in demand.

The text cites the classic example of pressurizing a drinking water distribution pipeline, where hourly fluctuations in demand are managed using electronic control systems (sensors and inverters), resulting in significant energy savings because energy loss is avoided.

Changing the impeller diameter: different curve, but stiffer response

At a fixed speed, the performance curve can be adjusted by changing the impeller diameter (in pumps with radial impellers).

Compared to adjusting the speed, this procedure is described as much more involved, because it requires a mechanical adjustment: reducing the diameter or replacing the original impeller with one of a larger or smaller diameter.

Here, too, the principle remains the same: changing the pump curve alters its intersection with the system curve and, consequently, the operating point.

Pumps in Parallel or in Series: Modifying the “Pump System” Curve

The operating point can also be adjusted by connecting pumps:

• In parallel: multiple pumps each draw water independently and discharge into the same Outlet manifold; for any given head, the resulting flow rate is the sum of the flow rates of the individual pumps
• In series: The same flow rate passes through all the pumps, while the system’s head is the sum of the heads of the individual pumps (at the same Q)

These are two different configurations, but both affect the “resulting curve” as seen by the system.

Conclusion

Adjustment is not an “abstract” operation: it means choosing how to shift the intersection between the pump curve and the system curve. You can do this by adjusting for leaks and resistance (valve or bypass) or by adjusting the pump (speed, impeller, series/parallel configuration), keeping in mind that some methods result in energy loss while others better match the demand.