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Buckingham Reiner Equation and Calculator

Fluids Flow Design and Engineering
Heat Transfer Engineering

Buckingham Reiner Equation and Calculator 

Laminar flow of Bingham plastic fluids friction factor is given by the Buckingham-Reiner equation

Eq. 1

τ_R = [ ( P_o - P_L ) R ] / 2 L

Eq. 2

Q = [ ( π ( P_o - P_L ) R⁴ ρ )  / ( 8 µ L ) ] [ 1 - ( 4 τ_o ) / ( 3 τ_R ) + 0.333 ( τ_o / τ_R )⁴ ]

Where:

P_o = Input Pressure (psi)
P_L = Output Pressure (psi)
R = Radius or tube (ft)
ρ = Density of Fluid (ppg)
µ = Viscosity of Fluid (cP)
L = Length (ft)
τ_o = Torsion Stress (psi)
τ_R = Shear Stress at the Tube Wall (psi)
Q = Mass Flow Rate (lb/s)

ppg = pounds per gallon
cP = Poise

Note: When τ_o  is zero, the Bingham model reduces to the Newtonian model and the final equation presented above reduces appropriately to the Hagen-Poiseuille equation.

Reference:

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons,Chapter: 8, Page: 260.

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