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Reynolds number in slurry launder design

Reynolds number in slurry launder design

Reynolds number in slurry launder design

(OP)
Hi All,

I am looking into the design of launders transporting slurry within the minerals processing industry. Within my limited experience, the most commonly used method for performing slurry launder calculations is based upon a paper by H.R. Green, et al. titled "A new launder design procedure" published in the late 1970's.

I have noticed that in this paper the following equation is used to calculate Reynolds number for open channel flow:
 
Re = ro_slu[kg/m3] * Q[m3/s] / (Rh[m] * u[Pa.s] *pi)

Where: ro_slu is the density of the slurry mixture, Q is the volumetric flow rate of the slurry, Rh is the hydraulic radius (CSA/Wetted perimeter) and u is the absolute viscosity of the slurry.

The formula I am more familiar with is:

Re = 4* ro_slu[kg/m3] * V[m/s] * Rh[m] / u[Pa.s]

Where: V is the average or mass continuity velocity

The problem I have is that these two formulas produce very different results. I'd appreciate if anyone provide some insight on the matter. I'm not sure if I'm just chasing shadows.

RE: Reynolds number in slurry launder design

I'm actually travelling and do not have acces to my regular (good old) paper files, but the "4" in you second formula does not look familiar to me.  

RE: Reynolds number in slurry launder design

Reynolds number is dimensionless. All dimension must cancel out and they do not in at least one of your equations.

RE: Reynolds number in slurry launder design

(OP)
Thanks for the replies Micalbrch and Compositepro.

Upon further review I believe I have identified why the two equations return the same reynolds number for full pipe flow but not for open channel flow (e.g. rectangular launder, u-shaped launder or a partially filled pipe launder).

Setting both equations equal and erradicating common terms the only way I coul get the statement to be true is if the cross-sectional area of flow is equal to the area of a circle using the hydraulic diameter. This is correct for full pipe flow but not for other cross section geometries.

The begs the questions "Was this intentional by Green & co.?". I think it was. Secondly, "What difference does this make to the quality of the design?". The Reynolds number is used to determine the flow regime and as a factor in the darcy friction factor to determine losses. The Reynolds number calculated by the equation employed by Green and Co. seems to undershoot the actual Re therefore providing a safety factor when determining flow regime. I realise it isn't great to have unintentional safety factors everywhere but esentially it isn't detrimental to the design. Secondly it is used in the calculation of the friction factor, fD, for turbulent flow, but will it make a significant difference? I don't believe it does for small (relatively) applications. Getting this correct would be more approriate for large launder designs.

In conclusion I think I have convinced myself that I wasn't jumping at shadows but the results of the exercise were almost as futile.  

Micalbrch,

The second equation referenced above is the Reynolds number for open channel flow. Hence the Hydraulic diameter (DH) can be replaced by 4*RH (RH=Hydraulic radius).


CompositePro,

Both equations presented above are dimensionless. That is their dimensions cancel out. See below.

EQ1

Re = ro_slu{kg/m^3} * Q{m^3/s} / (Rh{m} * u{Pa*s} * pi )

Looking purely at dimensions,

Re = ({kg/m^3}*{m^3/s}) / ({m}*{Pa.s})
=({kg*m^3}/{m^3*s})/({m}*{Pa*s})
=(kg/s)/(m*Pa*s)
=kg/(m*s^2*Pa)
=kg/(m*s^2)*(1/Pa)
=Pa*(1/Pa)

EQ2

Re = 4 * ro_slu{kg/m^3} * V{m/s} * Rh{m} / u{Pa*s}

Looking purely at dimensions,

Re = (kg/m^3) * (m/s) * m / (Pa * s)
= (kg *m^2 / {m^3*s})/(Pa * s)
= (kg * m^2) / (m^3 * s^2 * Pa)
= kg / (m * s^2 * Pa)
= kg / (m * s^2) * (1/Pa)
= Pa*(1/Pa)

 

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