Slurry pipeline and pump head

[Rukt]

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.

 

[Rukt]

(Sorry for the double-post; couldn't see an 'Edit' option -- must've expired)

... 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.

 

[Johny8]

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)

 

[gsal]

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

 

[alphy]

Hi Rukt,

Thank you for sharing your calculations and assumptions regarding the slurry pipeline and pump head. I can offer some insights and suggestions to help improve your calculations.

Firstly, your assumption that a heterogeneous slurry behaves according to the Darcy-Weisbach equation may not be entirely accurate. While this equation is commonly used for fluid flow in pipes, it may not be suitable for slurry flow due to the presence of solid particles. The presence of solid particles can significantly alter the behavior and characteristics of the slurry, making it more complex to model. It is important to consider the rheology of the slurry, which takes into account the interactions between the solid particles and the fluid.

In terms of the relative roughness, it is correct that it should be in units of m/m. However, the value of 2.78E-5 seems quite low for a steel pipeline. It would be helpful to verify this value with the manufacturer or through experimental data.

Moving on to the slurry density, it is important to note that the density of the slurry may vary depending on the size and concentration of the solid particles. It would be best to obtain this information from the supplier or through experimental measurements.

Regarding the viscosity of the slurry, it is important to note that it will not be the same as that of water. The presence of solid particles can significantly increase the viscosity of the slurry. It would be best to obtain this information from the supplier or through experimental measurements.

In summary, to improve the accuracy of your calculations, it would be helpful to obtain more specific information about the slurry, such as the size and concentration of the solid particles, as well as the rheological properties. Additionally, it may be beneficial to consult with experts in the field of slurry flow to obtain more accurate and reliable calculations.

I hope this helps. Good luck with your calculations!

Best,