Hydrocyclones- Calculation steps and separation results

[MMImpel]

TL;DR

Help understanding hydrocyclones and a simple calculation using an empirical equation by Bradley

Hello,

I want to see if hydrocyclones can be used in a application, where we have small metall particles that we want to extract from a closed loop water system. I found a book "Chemical Engineering Design" written by Richardson, where there are some equations given that makes it possible to calculate the effectiveness of the hydrocyclone dependent on the hydrocyclones and the water flow properties. I have used eq (10.3)

The following in-data are used

This gives me a value for the d_50 = 7,3 micrometer.
Firstly; what does this actually mean, will the hydrocyclone capture 50 % of the particles of the d_50 size what about if they are larger or smaller? Is it possible to determine how effective the hydrocyclone will be if the particles for instance have a d = 200 micrometers ?

 

[BvU]

Firstly; what does this actually mean, will the hydrocyclone capture 50 % of the particles of the d_50 size what about if they are larger or smaller?

If I turn the page after equation 10.3, I read: $d_{50} =$ the particle diameter for which the cyclone is 50 per cent efficient, $\mu$m

Meaning half go over the top and the remainder over the bottom.

The diagram Fig. 10.22 just above allows you to estimate the efficiency for 200 $\mu$m particles for a cyclone with $d_{50} = 10$ (that's the lowest value on the left). WIth 200 $\mu$m the highest value on the middle axis, the estimated efficiency on the rightmost axis is way off scale, so over 99.8 %.

Read carefully, work out the example 10.2 to understand what's what.

$\$

 

[MMImpel]

Thank you, I came to the same conclusion but was worried that I missunderstood that the effectiveness might get lower with larger particles?
Since this is really out of my comfort-zone I felt the need to double-check.

Best regards!