Lubricating oil 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:

  1. PURPOSE OF THE EXERCISE:
    Demonstrate the application of pump similitude via the affinity laws to determine the operating speed required on a scaled pump model, ensuring that the nondimensional parameters remain consistent.

  2. ENGINEERING CONTEXT:
    This problem involves predicting the prototype pump performance using a scale model. Once mastered, you are able to design and test pumps at different scales and then extrapolate the results to full‐scale machines.

  3. PHYSICAL CONTEXT:
    The dominant effect is the matching of the characteristic velocity (or tip speed) so that the flow dynamics are geometrically and dynamically similar.

  4. ASSUMPTIONS:
    Assume that the flow remains dynamically similar between the model and prototype when the tip speeds are equated and that viscous effects or fluid property variations (beyond those due to the 60°F lubricating oil) are negligible; this is reasonable provided the Reynolds numbers are high enough.

  5. DRAWINGS:
    A schematic drawing showing the prototype pump with impeller diameter D and the scale model with impeller diameter D/3, with arrows indicating rotational speeds and tip velocities, would help visualize the similarity condition. However, the problem can be solved without an explicit drawing.

  6. SOLUTION TECHNIQUE:
    For geometrically similar centrifugal pumps to operate dynamically similarly, the tip speeds must be equal, i.e.,

\omega_{\text{prototype}}\,D = \omega_{\text{model}}\,\left(\frac{D}{3}\right)\,.

Rearrange to solve for the model speed:

\omega_{\text{model}} = 3\,\omega_{\text{prototype}}\,.

Substitute the prototype speed, where 1200\,\text{rpm} is given:

\omega_{\text{model}} = 3\times1200\,\text{rpm} = 3600\,\text{rpm}\,.

Thus, to maintain dynamic similitude, the scale model should run at 3600\,\text{rpm}.

  1. REFLECTION:
    Matching the tip speed ensures that the non-dimensional performance parameters, such as the flow coefficient and head coefficient, remain the same between the prototype and scale model. This approach is fundamental in pump scaling and helps predict full-scale performance accurately using model data.

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 2.1: Turbomachines Part 3 (HIGHLY RELEVANT)
  2. Chapter 6.6: Pump selection (HIGHLY RELEVANT)
  3. Chapter 2.3: Selecting a Turbomachine Class (HIGHLY RELEVANT)
  4. Chapter 2.5: Combining and Resizing Turbomachines Part 2 (HIGHLY RELEVANT)
  5. Chapter 9.6: Centrifugal Pump Design Part 5 (HIGHLY RELEVANT)

Disclaimer:

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