Tue, 25 Aug 2015
Bingham plastic is a material that behaves as rigid body at low stresses but flows as a viscous fluid at high stress. This behaviour is exhibited by slurries, suspensions of solids in liquids, paints, emulsions, foams, etc.
Bingham model is described by following relation.
τ = τo + μp γ
where, τ is shear stress, γ is shear rate, τo is called minimum yield stress and μp is called plastic viscosity.
Reynolds number for Bingham plastic fluid is defined as
Re = D V ρ / μp
where, D is pipe inside diameter, V is fluid velocity and ρ is fluid density.
For Laminar flow, friction factor is provided by Buckingham Reiner equation.
where, He is Hedstrom number and is calculated as
He = D²ρτo / μp²
For turbulent flow, an empirical relationship was developed by Darby and Melson.
The friction factor for a Bingham plastic can be calculated for any Reynolds number from the equation.
f = ( fLm + fTm ) 1/m
where, fL is laminar flow friction factor and fT is turbulent flow friction factor. Factor m is calculated from following equation.
m = 1.7 + 40,000 / Re
Pressure drop is calculated as
ΔP = 2fρV² (L'/D)
L' = L + Le
where, L is the pipe length and Le is equivalent length due to loss in pipe fittings and is calculated as
Le = kD / 4f