Dynamic vs displacement

How Fluid Machines Work
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for what specific speed would I select a displacement pump over a centrifugal pump

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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:
A rule of thumb is that centrifugal pumps start having low efficiency below \omega_p\simeq 0.2 in SI units, so below 0.2 you either need a multistage radial flow pump or you need to move to a displacement pump.

  1. ENGINEERING CONTEXT:
    The problem asks you to use specific speed as a design parameter to decide when a displacement (i.e., positive‐displacement) pump is preferable to a centrifugal pump. When the operating condition requires the pump to provide a high pressure at a low flow rate—resulting in a very low specific speed—the centrifugal pump becomes inefficient and a displacement pump is the correct choice. In practice, you design a system knowing that when the specific speed falls far below the efficient range for dynamic pumps, you build a system with a displacement pump.

  2. PHYSICS:
    The problem doesn’t have any physics – it is just a known rule of thumb. However the rule of thumb comes from the observation that it is difficult to design an impeller with angles such that the fluid moving through it gains so much energy that the resulting head and capacity correspond to a specific speed below 0.2. A displacement pump’s capacity and losses are much much weaker functions of head, and the geometric constraints are simpler than that of an impeller in a dynamic pump.

  3. ASSUMPTIONS:
    Assume an incompressible, steady flow and negligible interstage losses so that the specific speed formulation is valid for comparing dynamic pump performance versus the inherent flowrate characteristics of displacement pumps.

  4. SOLUTION TECHNIQUE:
    For centrifugal (dynamic) pumps, high efficiency is maintained over a range of specific speeds given by

0.2\,\frac{\Delta p_0^{3/4}}{Q^{1/2}\rho^{3/4}} < \omega_{\mathrm{radial}} < 1.6\,\frac{\Delta p_0^{3/4}}{Q^{1/2}\rho^{3/4}}\ .

When the required operating condition leads to a calculated specific speed (using

\omega_p=\frac{\omega\,Q^{1/2}}{\Delta p_0^{3/4}\rho^{3/4}}

or an equivalent nondimensional form) that is well below the lower limit (i.e. substantially below 0.2 in these units), the centrifugal pump would operate far from its best efficiency range. Hence, you select a displacement pump because its flowrate is fixed by its mechanism, independent of the adverse effects that degrade centrifugal pump performance at low specific speeds. You can get high-efficiency low-specific-speed performance also from a multistage radial pump.

  1. REFLECTION:
    The analysis shows that if your design conditions yield a specific speed notably lower than 0.2 (in the formulation for dynamic pumps), the centrifugal pump will be inefficient; in this regime the engineering design calls for a displacement pump.

In formulating this response, I reviewed 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 2.1: Turbomachines Part 3 Part 1 (HIGHLY RELEVANT)
  2. Chapter 2.3: Selecting a Turbomachine Class (HIGHLY RELEVANT)
  3. Chapter 2.1: Turbomachines Part 4 (HIGHLY RELEVANT)
  4. Chapter 6.3: Pump types Part 2 (HIGHLY RELEVANT)
  5. Chapter 6.3: Pump types Part 1 (HIGHLY RELEVANT)

Disclaimer:

See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.

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PK Bot is using SI units and speed in rad/s, which is what I use in my textbook. Important to note that other sources often use US customary units which lead to very different values for the specific speed threshold (about 2500 times higher)