- #1
Rukt
- 2
- 0
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.
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.