Pressure Drop in a Coil Argument

[mkenwort]

Please help me settle an argument in flow of turbulent water through a coil. I argue that one must account for an increase in the effective length of the coil due to the continuous bend of the pipe as it follows the helical path. In my opinion this effective length increase may be modeled as four 90 degree elbows with the appropriate r/D factor (in my case r/D ~ 4 -&gt Le/D ~ 13).

My colleague argues that I don't even need to account for this continuous bending. So his flow rate result is a factor of 4 higher than mine. His result meets the minimum specifications and mine says that it fails.

Thanks for your comments and insight.

-mtk

 

[mkenwort]

Actually I see that both methods are flawed. Required a pretty freaking extensive literature search though ;[. And the resulting equations aren't the prettiest ever.

I'd still like to hear some comments on the ideas though.

 

[TD2K]

I'm not sure what you mean by flow rate factor, he sure isn't going to get 4x your calculated flow rate.

It's an interesting question. I will admit if I was trying to calculate the pressure drop through a coil, I'd likely just estimate it using the length as if it was straight.

Crane has the L/D for an elbow where r/D = 4 as 14.

If I take a look at the elbow, the length = r*theta where theta is 90 deg in radians or pi/2. The length I travel through the elbow is then 2*D*pi. L/D for this (just looking at the length) is then 2pi or 6.28. So the pressure drop through an elbow with an r/D of 4 would be just over 2x the same length of straight pipe.

From the point of view of flow, I'd get about 1.5x difference in flow.

 

[25362]

Whatever the formula used for estimating the friction drop through a coil, one has to remember that the Fanning friction factor is about 1/4 of the Darcy friction factor. When estimating friction drops the Darcy f is the one to be used. If the Fanning f is used then the delta P_f should be multiplied by 4.

For example for smooth straight pipes or tubes and a Re=100,000, the Fanning f=0.0045, whilst the Darcy f=0.018.

The length of a coil L, with diameter D, made of a tube with diameter d, is simply

L= N*[(pi.D)²+p²]^0.5​

where p is the pitch, pi =3.1416, and N the number of turns.

Friction factors for coils can be found in Trans. Instn. Chem. Engrs., 48, T 156- T 161 (1970).

 

[quark]

Actually this topic is well discussed in Perry's handbook in Fluid and Particle Dynamics Chapter. In coils a secondary flow perpendicular to main flow occurs and this is called Dean Effect. This flow increases the friction and delays the transition Reynolds number. Laminar frictional coefficient can be calculated either by 64/Re or 16/Re as per the formula you use, and there is one correlation for turbulent flow (which I can't remember at the moment).

Regards,

 

[quark]

I got the old thread124-71405 which may be of use to you.

Regards,

 

[mkenwort]

yes you are right on quark

the transition from laminar to turbulent is not constant at Re ~2100, but must also account for the Dean Effect and geometry (d_pipe/D_helix)...this can result in vastly higher transition Re, 10k for d/D ~ 8 or so...

btw the estimate of just using a straight pipe ends up actually being a relatively good estimate...for my particular conditions, the resulting pressure drop was only about 3% from a 55 psi input pressure...input velocity was about 11 ft/sec iirc...

thanks all for comments and the reference you gave especially quark...

-mtk

 

[TD2K]

If you have access to a copy of Crane's flow of fluids paper, this is also discussed on pages 2-12 and 2-13 with a method to estimate the additional pressure drop over the equivalent length of straight of pipe/tubing.