Siphon performance

Homework Help
1

what are the design parameters that would maximize the rate at which a siphon could be used to extract fluid from a reseroir

2

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 volumetric flow rate at which a siphon extracts fluid from a reservoir is

Q=C_dA\sqrt{2gh\frac{1}{1+\frac{f_D L}{d}}}

So you want as high a reservoir as possible and a large-diameter pipe of the minimum length possible. It is less important, but you want the pipe to have a smooth interior and a smooth end.

The dependences are:

  • the flowrate is proportional to the cross-sectional area A=\frac{\pi d^2}{4} of the tube used in the siphon
  • the flowrate is proportional to the discharge coefficient C_d of the tube. Unless the end of the tube has a weird geometry, this is just 1.
  • the flowrate is proportional to the square root of the height difference h between the top of the reservoir of fluid and the exhaust of the siphon.
  • the flowrate is slowed down by viscous dissipation in the tube, proportional to \sqrt{\frac{1}{1+\frac{f_D L}{d}}}. f_D is the viscous dissipation coefficient, which is a weak function of surface roughness and Reynolds number, but which is often approximately 1/30. L is the siphon length and d is its diameter. So, the flowrate is slowed down a bit if the siphon tube/pipe is very long comparted to its diameter. There is a 10% slowdown if L/d is about 6, a 40% slowdown if L/d is about 30.

An inviscid analysis would be the same as above but just assuming that f_D=0. A fully ideal analysis would assume that C_d=1 and f_D=0.

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 6.4: Bernoulli constant drop in pipes Part 3 (HIGHLY RELEVANT)
  2. Chapter 6.2: Modified Bernoulli equation Part 2 (RELEVANT)
  3. Appendix C.5: Viscous Dissipation Factor (RELEVANT)
  4. Appendix C.2: Dimensional Analysis to Generalize Experiments (RELEVANT)
  5. Chapter 6.4: Bernoulli constant drop in pipes Part 1 (RELEVANT)

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