**Related Resources: calculators**

### 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} ) R^{4} 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*= Output Pressure (psi)

_{L }*R =*Radius or tube (ft)

*ρ =*Density of Fluid (ppg)

*µ =*Viscosity of Fluid (cP)

*L*= Length (ft)

*τ*= Torsion Stress (psi)

_{o }*τ*= Shear Stress at the Tube Wall (psi)

_{R }*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.

Related

- A Practical Utilization of the Theory of Bingham Plastic Flow in Stationary Pipes and Annuli Basic membership minimum Required to download
- Brinkman Number Equation and Calculator
- Archimedes Number Calculator
- Einstein Equation Effective Viscosity
- Critical Pressure and Temperature Cavett Correlation Calculation
- Harris Formula for Pressure Change at Standard Conditions Equation and Calculator
- Pressure Losses for Fluid Flow in 90Â° Pipe Bends
- Volumetric Flow Rate volumetric flow rate (V ) of a system is a measure of the volume of fluid passing a point in the system per unit time.
- Swamee-Jain Friction Factor Equation and Calculator This is another explicit equation for calculating the friction factor typically used in the Darcy-Weisbach.
- Weir Flow Rectangular Open Channel Water Flow Calculator and Formula