View source for 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, <math>M_{\rm SU}</math> (m<sup>3</sup>/h), exceeds a solids capacity limit:{{Dubey et al. 2017}}

:<math>M_{\rm SU} > 0.35 {D_{\rm u}}^{2.35}</math>

'''Plitt''' further proposed a limit to the volume fraction of solids in cyclone underflow, <math>\Phi_{\rm L}</math> (% v/v), of:

:<math>\Phi_{\rm L} = 62.3 \left [ 1 - \exp \left ( - \dfrac{d_{\rm u}}{60} \right ) \right ]</math>

where <math>d_{\rm u}</math> is the mass median particle size of the underflow, computed here as the ''P<sub>50</sub>'' (μm).

The '''SPOC''' criterion indicates roping may occur when:{{Napier-Munn et al. (1996)}}

:<math>C_{\rm VU} > 56 + 0.2 (C_{\rm V} - 20)</math>

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

Investigations by '''Bustamante''' (1991) and '''Concha''' et al. (1996) led to the limiting values of cyclone geometry in Table 1:{{Gupta and Yan (2016)}}

:{| class=wikitable style="width: 30%;"
|+ Table 1. Transition from spray to roping discharge (after Gupta and Yan, 2016).{{Gupta and Yan (2016)}}
! Source
! <math>D_{\rm u}/D_{\rm o}</math>
! Condition
|-
|rowspan="3" | Bustamante
| <0.34
| Roping discharge
|-
| 0.34 - 0.5
| Roping or spray
|-
| >0.5
| Spray discharge
|-
|rowspan="3" | Concha et al.
| <0.45
| Roping discharge
|-
| 0.45 - 0.56
| Roping or spray
|-
| >0.56
| Spray discharge
|}