Pump design

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A radial-flow pump needs to pump 300 gpm and generate a total-pressure change of 30 ft. What is a sensible rotation rate for the pump to have? Can this be achieved with an AC motor? and if so, how many poles would it have

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

PK Bot’s answer:
Below is one way to arrive at an answer using the design guidelines from Professor Kirby’s material. Note that we must make a few assumptions:

• We assume the working fluid is water (with density \rho\approx1000~\rm kg/m^3).
• We work in SI units when applying the design relations but then convert the answer back to rpm.
• We assume a 60‐Hz AC power supply, so typical AC motor speeds are 3600, 1800, 1200 rpm, etc.

In one section of the course material the following design bounds were given for a radial‐flow pump:

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

Here the idea is that the pump should run roughly within this range to have a good efficiency. Let’s show how one might use this relation.

  1. Convert the operating condition to SI units.
    • The required capacity is 300 gallons per minute (gpm). Since
    1 gallon ≈ 3.785×10⁻³ m³,
    300 gpm ≈ 300×(3.785×10⁻³) m³/min ≈ 1.1355 m³/min.
    Dividing by 60,
Q\approx0.01893~\rm m^3/s.

• The head is given as 30 ft. Since
1 ft = 0.3048 m,
30 ft ≈ 9.144 m,
the pressure change is approximately

\Delta p_0 \approx \rho g (9.144) \approx 1000\times9.81\times9.144\approx 90\,000~\rm Pa.

(We round a bit here.)

  1. Evaluate the nondimensional combination (using approximate numbers):
    • Compute \Delta p_0^{3/4}, Q^{1/2}, and \rho^{3/4}.
    Even if one does not compute these exactly, one finds that there is a range for \omega_{\rm radial} corresponding roughly to values between the lower bound (when using 0.2 in the expression) and the upper bound (multiplying by 1.6) that yield rotation rates on the order of several hundred rad/s. A detailed numerical evaluation (with our approximations) suggests that the acceptable range falls roughly between about 42 and 340 rad/s.

  2. Converting these rad/s values to rpm (recall 1~\rm rpm\approx 0.105~rad/s):
    • 42 rad/s corresponds to about $$42/0.105\approx 400~\rm rpm,$$
    • 340 rad/s corresponds to about $$340/0.105\approx 3238~\rm rpm.$$

From experience and design practice (as emphasized in the notes) pumps are not typically run at arbitrary speeds. In practice, pump design does not allow you to shift the motor speed by an order of magnitude. Instead, you choose a practical speed that naturally falls into one of the “preferred” AC motor speeds. In most cases for a radial-flow pump used in such a moderate head application (30 ft) the design is best served by picking an operating speed somewhere in the middle of the acceptable band. A common choice is around 1800 rpm, which falls well within the computed range and is a standard speed available from AC motors.

  1. Can this be achieved with an AC motor?
    Yes. For example, on a 60-Hz mains supply, a 4-pole AC motor runs at approximately 1800 rpm (while a 2-pole motor would run near 3600 rpm). Thus, a 4-pole motor is a sensible and practical choice.

So, in summary:

• A practical rotation rate for this radial-flow pump is about 1800 rpm.
• This is achievable with an AC motor – by selecting a motor with 4 poles.

Keep in mind that we assumed water as the working fluid and a 60-Hz supply, which are common in practice.

In crafting this response, I dedicated some time to reviewing the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I found these sections to be particularly helpful in formulating my answer. I encourage you to explore the pertinent ones directly:

Textbook sections:

  1. Chapter 2.3: Selecting a Turbomachine Class (HIGHLY RELEVANT)
  2. Chapter 6.3: Pump types (RELEVANT)
  3. Chapter 2.4: Selecting a Turbine Class (RELEVANT)
  4. Chapter 2.1: Turbomachines Part 2 (RELEVANT)
  5. Chapter 9.6: Centrifugal Pump Design Part 1 (RELEVANT)
  6. Chapter 2.5: Combining and Resizing Turbomachines (RELEVANT)
  7. Chapter 2.2: Nondimensional Turbomachine Parameters (RELEVANT)
  8. Chapter 2 How Stuff Works: How AC motors and generators work (RELEVANT)
  9. Chapter 9.6: Centrifugal Pump Design Part 2 (RELEVANT)
  10. Chapter 6.1: Pumps (MARGINALLY RELEVANT)

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