QUESTION $3-$ Classification and Performance

A cyclone's performance is being assessed, but the feed is inaccessible and so it is the underflow and overflow streams that are measured. The size distribution of each stream is measured by placing a representative sample into the top of a stack of sieves. The following table gives the mass retained on each of the sieve screens $($i$.$e$.$ the mass is the amount of material larger than the corresponding size and smaller than the size above$).$

$\backslash$table$[[,$Mass on sieve$],[$Sieve size,Underflow,Overflow,$],[$microns$,g,g,],[212,0,0,],[150,37,5,],[105,25,11,],[74,14,24,],[53,12,34,],[$Undersize$,16,56,]]$

The measure mass flowrate to the underflow is $24\frac{t}{h}r$ and the overflow is $35\frac{t}{h}r.$

a$)$ What is the mass recovery to the underflow?

b$)$ Calculate the cumulative size distributions of the underflow and overflow.

$(2)$

$(4)$

The performance can be assessed using partition numbers.

c$)$ Calculate all the partition numbers and their corresponding representative sizes.

d$)$ What is the d$50$ and bypass ratio?

$(5)$

$(2)$

You have enough information to calculate the size distribution of the feed.

e$)$ Calculate the cumulative size distribution of the feed.

$(4)$