A New Model for Predicting the Marsh Funnel Test

Acknowledgments

Notation

C

consistency index;

F (τ₀, α, z)

function representing the upward pressure induced by the sidewall in the conical section;

g

acceleration of gravity;

H_F

maximum filling height of the conical section of the funnel;

L

length of the capillary tube;

n

flow index;

p_d

pressure drop due to the dynamic force;

Q

discharge;

R

radius of the tube;

R_F

maximum radius of the fluid in the conical section of the funnel;

r

local radius of the fluid in the conical section of the funnel;

v

mean velocity of the fluid;

z

height from the top of the capillary tube to the liquid surface;

α

angle between the funnel wall and the vertical direction;

β

underrelaxation factor;

γ

shear rate;

ΔP_cone

pressure loss due to yield stress in the conical section of the funnel;

ΔP_tot

hydrostatic pressure minus the pressure loss due in the conical section of the funnel;

ρ

density of fluid;

ρ₀

density of water;

τ

shear stress;

τ₀

yield stress;

τ_{w new}

new value in calculation;

τ_{w old}

previous value in calculation; and

τ_w

wall shear stress.

References