Pump efficiency

Theory and Concepts
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why is the most efficient performance for a pump in the middle of the pump curve

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This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:
The most efficient performance for a pump occurs in the middle of the pump curve due to the balance between flow rate and pressure head, which is optimized at this point. This optimal region is often referred to as the Best Efficiency Point (BEP).

The kinematics of an impeller blade, as described by the Euler turbomachine equations, tells us how the \Delta p vs Q curve could look in the absence of losses. Then by pointing out loss mechanisms we can see how the efficiency curve looks in practice.

A backward-curved impeller blade, for purely kinematic reasons (conservation of mass plus the assumption that flow is parallel to the blade surface) , leads to the prediction that if the impeller is lossless, the \Delta p vs Q curve is a negatively sloped line. The pump power transferred to the fluid is the product of \Delta p and Q, and that is a downward-facing parabola as a function of Q. At zero flow rate, no power is transferred to the fluid. At max flow rate, no power is transferred to the fluid. In the center of the curve, the power transferred to the fluid is maximum.

The efficiency of the motor is a function of the power. The losses of the motor are not a strong function of the load, so when the motor is transferring maximum power, it is at max efficiency. When transferring zero power, it is all losses in the windings and shaft bearings.

So, if the impeller is lossless, the pump efficiency is max in the center of the curve because the impeller is transferring alot of power and the pump losses are not that big in comparison. At the max-\Delta p and max-Q ends of the performance curve, the motor is transferring little or no power, and all you see is losses at the motor windings and shaft bearings.

The impeller, of course, is not lossless. But the impeller geometry is designed to minimize losses (e.g. separation at leading and trailing edge) in the middle of the curve, because that is where the motor is relatively efficient. There is no reason to design an impeller that avoids leading or trailing edge separation in the zero-Q flow condition, or the zero-\Delta p flow condition, because those flow conditions are not what you will use the pump for. So the impeller design also peaks in efficiency in the center of the curve.

In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections according to their relevance. If they are marked as relevant, I encourage you to explore them:

Textbook sections:

  1. Chapter 6.2: Pump types Part 2 (HIGHLY RELEVANT)
  2. Chapter 2.1: Turbomachines Part 3 (HIGHLY RELEVANT)
  3. Chapter 9.6: Centrifugal Pump Design Part 2 (HIGHLY RELEVANT)
  4. Chapter 2.1: Turbomachines Part 4 (HIGHLY RELEVANT)
  5. Chapter 9.6: Centrifugal Pump Design Part 5 (HIGHLY RELEVANT)

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