Is a Heterogeneous Slurry Still Governed by the Darcy-Weisbach Equation?

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Discussion Overview

The discussion revolves around the application of the Darcy-Weisbach equation to a hypothetical heterogeneous slurry pipeline. Participants explore the assumptions and calculations related to fluid dynamics, including pipeline length, diameter, roughness, density, viscosity, and resulting pressure and power requirements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant assumes that a heterogeneous slurry behaves according to the Darcy-Weisbach equation, questioning the validity of this assumption.
  • The pipeline specifications include a length of 15 km, a diameter of 0.9 m, and a roughness of 0.025 mm, leading to a calculated relative roughness of 2.78E-5.
  • The solid phase density is taken as 2000 kg/m3, and with a mixture ratio of 1 part solid to 0.8 parts water, the slurry density is calculated to be 1555.56 kg/m3.
  • There is uncertainty regarding the viscosity of the slurry, with an initial assumption of using water's viscosity (8.9E-4 Pa.s), leading to an extremely high Reynolds number of over 5E10.
  • The friction factor is estimated at 0.01 based on extrapolation from the Moody Diagram, which raises concerns about the accuracy of the calculations.
  • Initial calculations suggested an excessive head requirement of over 500 km, later corrected to 500 kPa of pressure, with a pump power requirement estimated at 600 kW based on volumetric flow rate.
  • Another participant suggests considering multiple pumps for the 15 km span if the numbers are indeed too large.

Areas of Agreement / Disagreement

Participants express uncertainty about the calculations and assumptions, with no consensus reached on the validity of the Darcy-Weisbach equation for heterogeneous slurries or the accuracy of the derived values.

Contextual Notes

Limitations include potential inaccuracies in viscosity assumptions, the dependence on the definition of heterogeneous slurries, and unresolved calculations regarding pressure and pump power requirements.

Rukt
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Hey folks,

I'm trying to do a bit of back-of-the-envelope stuff for a hypothetical slurry pipeline, but it's been a while since I've done any fluid mech./dyn., and I have no confidence in my numbers -- please jump in wherever you catch an error.

First of all, I'm making the assumption that a heterogeneous slurry still behaves according to the Darcy-Weisbach equation, and all of the associated paraphernalia. This might be shaky ground already, but bear with me..

The pipeline is to be in the order of 15 km long, with an internal diameter of, say, 0.9 m. I'm assuming a roughness of 0.025 mm (steel, right?), giving a relative roughness of 2.78E-5 (first sanity check: relative roughness has the 'units' of m/m, not mm/m, right?).

Continuing, I've taken the density of solid phase as 2000 kg/m3. With 1 part solid to 0.8 parts water, I get a slurry density of (1*2000 + 0.8*1000) / 1.8 = 1555.56 kg/m3.

Here's where things start to go really bad, because I've got no idea what the viscosity of the slurry is. As a sanity check I've started with that of water: 8.9E-4 Pa.s. All of this gives me a Reynolds number in excess of 5E10 -- way off the end of Wikipedia's Moody Diagram. Assuming those lines just go horizontal, drawing a line across to the left gives a friction factor of -- for the sake of nicety -- 0.01.

Finally, putting it all back into D-W, I get ... over 500 km of head. Well then.

Please help!
Rukt.
 
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(Sorry for the double-post; couldn't see an 'Edit' option -- must've expired)

Rukt said:
... over 500 km of head.

Strike that; I forgot the gravity term. 50 km or 500 km -- they're both excessive.

Additionally, given P = q.rho.g.h, I figure the pump has to supply 920 MW. That's got to be out by at least two orders of magnitude..

--

EDIT: I should really keep my mouth shut in the echo chamber. That wasn't 500 km of head, it was 500 kPa of pressure (requiring a pump power approaching 600 kW, given the volumetric flow rate of one-and-a-bit m3/s.
 
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so complicated! is this question so important to you?l try to find something that will help. one of my friends is busy now writing his diploma on the gravity maybe he'll find the answer)
 
I have no idea, either, whether your numbers are too huge or not, but if they are, maybe you should think about using more than one pump for the entire 15km span