Template:Model theory (Text, Hydrocyclone, Roping)

Several methods are available to identify the potential for roping discharge from a hydrocyclone underflow.

Plitt proposed that roping may occur when when the volumetric feed rate to the cyclone, $M_{SU}$ (m³/h), exceeds a solids capacity limit:

$M_{SU}>0.35{D_{u}}^{2.35}$

Plitt further proposed a limit to the volume fraction of solids in cyclone underflow, $\Phi _{L}$ (% v/v), of:

$\Phi _{L}=62.3\left[1-\exp \left(-{\dfrac {d_{u}}{60}}\right)\right]$

where $d_{u}$ is the mass median particle size of the underflow, computed here as the P₅₀ (μm).

The SPOC criterion indicates roping may occur when:

$C_{VU}>56+0.2(C_{V}-20)$

where $C_{VU}$ is the percentage volume fraction of solids in the underflow stream (% v/v). The SPOC criterion is only valid when $C_{VU}<35{\text{ }}\%{\text{ v/v}}$.

Investigations by Bustamante (1991) and Concha et al. (1996) led to the limiting values of cyclone geometry in Table 1:

Table 1. Transition from spray to roping discharge (after Gupta and Yan, 2016).

Source	$D_{u}/D_{o}$	Condition
Bustamante	<0.34	Roping discharge
	0.34 - 0.5	Roping or spray
	>0.5	Spray discharge
Concha et al.	<0.45	Roping discharge
	0.45 - 0.56	Roping or spray
	>0.56	Spray discharge