Shouldn't pressure loss quadruple if flow rate doubles?

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Discussion Overview

The discussion revolves around the relationship between flow rate and pressure loss in piping systems, specifically examining the Darcy-Weisbach equation. Participants explore the expected theoretical behavior versus observed results, considering factors such as friction factor, flow regime, and minor losses.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asserts that pressure loss should quadruple if the flow rate doubles, based on traditional teachings.
  • Another participant agrees with the quadrupling expectation but questions the application of the Darcy-Weisbach equation, suggesting that other variables might be changing simultaneously.
  • A participant mentions that maintaining a constant friction factor allows for the quadrupling of pressure loss, indicating a potential misunderstanding of the conditions affecting the equation.
  • It is noted that in fully turbulent flow, the friction factor should remain constant, referencing the Moody diagram.
  • One participant describes their typical flow rates having Reynolds numbers in the 10-20,000 range, which places them in the transition zone where the friction factor varies, impacting pressure loss calculations.
  • Concerns are raised about accounting for minor losses in flow regimes that are not fully turbulent, suggesting that K-factors may not be reliable in these scenarios.
  • A recommendation is made to consult a specific book on fluid mechanics for further insights into pressure drop predictions in different flow regimes.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between flow rate and pressure loss, with some supporting the quadrupling theory while others highlight conditions under which this may not hold true. The discussion remains unresolved regarding the exact influence of varying friction factors and flow regimes on pressure loss calculations.

Contextual Notes

Participants acknowledge limitations in their assumptions, particularly regarding the constancy of the friction factor and the impact of flow regime on pressure loss predictions. The discussion highlights the complexity of accurately applying the Darcy-Weisbach equation under varying conditions.

TSN79
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I've always been taught that in a piping system (only water), if the flow rate doubles, then pressure loss quadruples. But when using the Darcy-Weisbach equation I often find that it is closer to triple. Playing around with viscosity and temperature I've never been able to bring the ratio higher than 3,6. Am I missing something...?
 
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Generally, yes, if flow rate doubles, pressure loss should quadruple. I'm not sure how you are using the D-W equation because it looks pretty clear in the equation that head loss is a square function of velocity. Are you changing other things at the same time?
 
russ_watters said:
Are you changing other things at the same time?

If I pretend the friction factor stays the same with both flow rates, then I'm able to get the loss to quadruple, so I guess that's the issue. Thanks anyway :)
 
TSN79 said:
If I pretend the friction factor stays the same with both flow rates, then I'm able to get the loss to quadruple, so I guess that's the issue. Thanks anyway :)
In pipe flow, if the flow regime is fully turbulent at both flow rates, the friction factor should remain constant. That's what the Moody diagram shows:
screenshot.png

​
 
SteamKing said:
In pipe flow, if the flow regime is fully turbulent at both flow rates, the friction factor should remain constant. That's what the Moody diagram shows.
The flow rates I usually work with have Reynolds numbers in the 10-20 000 range, and so they are in the tranistion zone and the friction factor changes slightly - which makes quite a difference apparently.
 
TSN79 said:
The flow rates I usually work with have Reynolds numbers in the 10-20 000 range, and so they are in the tranistion zone and the friction factor changes slightly - which makes quite a difference apparently.
It's also not clear how you are accounting for minor losses in these flow regimes.

It has been shown that using K-factors, which are acceptable for fully turbulent flows, are not as accurate at predicting pressure drop when used in the laminar or transition regime. In these flow regimes which are not fully turbulent, the K-factors develop a component which depends on the Reynolds No. of the flow; hence, they do not remain constant.

For more information, you might want to check out a book called Chemical Engineering Fluid Mechanics, by Ron Darby. Darby discusses his own 3-K method as well as the 2-K method of Hooper.
 

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