In most average plant situations, the Process design will require that a specific rate of solids be transported, to a point at a level and distance away from the pump site. The transport medium is water at near ambient temperature. The process will most probably dictate that the slurry must be pumped at a certain pulp density. Thus, the required input data is:
TPH of dry solids to be pumped = M (tph)
Pulp Density of slurry (% solids by weight) = Cw (%)
S.G. Solids = S (t/m ³)
S.G. Liquid = SL (t/m³)
Liquid Viscosity = Cp (Centipoise)
Solids size = d50 (microns)
Vertical height separation from pump to discharge point = Hs (m)
Head loss through equipment Cyclone = Hequip (kPa)
Pipe Material internal roughness = k (m)
Pipe diameter = D (m)
Mass flow rate of water
Volume flow Rate of Water
Slurry specific gravity (density)
Percentage of solid by Volume
Durand factor
The Durand factor is an empirically derived factor based on tests of various particle sizes to enable the limiting settling velocity of flow in a pipe to be determined. The factor is used in the next equation.
Limiting settling velocity
This is the theoretical minimum velocity at which the slurry must be pumped to prevent any settlement in the pipeline. (Note that g is the acceleration due to gravity and is 9.8 m/sec²., which is acceptable for this calculation.
Reynolds Number
Reynolds number is a dimensionless parameter which relates fluid viscosity, flow velocity, solids mass and pipe dimension. For most slurry work, the Reynolds number will be quite high. It is used in the next formula to calculate the friction factor, which is then used to calculate the head loss due to friction between the slurry and the pipe wall.
Swamee Jain friction factor
The Swamee Jain formula approximates the Colebrook White formula but is mathematically simpler.
The friction head loss
The above formula is the well-known Darcy Weisbach formula for pipe friction, in metres of head lost.
The head ratio is calculated as
The above formula calculates a number called the Head Ratio. The HR is a factor which allows for the reduction of pump performance due to the difference in rheology of the slurry as compared with water. Pump performance curves are produced from tests on water, so it is necessary to correct for the effect of slurry. This same parameter is also called the Efficiency Ratio, ER.
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