$c.s$

Current study

$d$

Diameter (m)

$g$

Gravitational acceleration (m×s⁻²)

$P$

Average normal Pressure (kg×m⁻¹×s⁻²)

$p$

Pressure (kg×m⁻¹×s⁻²)

$u$

Velocity (m×s⁻¹)

$x$

Dimensionless voidage = $\left(\epsilon -{\epsilon }_{mf}\right)/\left(1-{\epsilon }_{mf}\right)$

$y$

Dimensionless drag coefficient = $1-\beta /{\beta }_{mf}$

$z$

Height (m)

Greek symbols

$\beta$

Drag coefficient (-)

$\epsilon$

Voidage (-)

$\lambda$

Lagrange multiplier (-)

$\mu$

Dynamic viscosity (kg×m⁻¹×s⁻¹)

$\rho$

Density (kg×m⁻³)

$\sigma$

Solid pressure (kg×m⁻¹×s⁻²)

$\tau$

Shear stress (kg×m⁻¹×s⁻²)

Subscript

$f$

Fluid

$s$

Solid

$t$

Terminal