Shouldn't pressure loss quadruple if flow rate doubles?

[TSN79]

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...?

 

[russ_watters]

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?

 

[TSN79]

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 :)

 

[SteamKing]

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:

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[TSN79]

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.

 

[SteamKing]

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.