How to do hydrocyclone calculations in this assignment?

[Naicker2013]

I am a chemical engineering student and our lecturer gave us this assignment. I completed part two of the assignment but this is part one. Nobody in my class seems to know exactly what to do. It's hard to understand what exactly he is asking for. I can write the MATLAB code once I understand how to perform the calculations. I would like to know what how to do it in steps. If anyone could help with this then it would be greatly appreciated.

Hydrocyclone diagram was also given with the following information

Feed: fi , F
solids= 200 t/h
ps= 2.7 g/m^3

Overflow: o/fi , O/F

Underflow: u/fi , U/F
water=270 t/h

Assume the following:
• water fraction (short circuiting = water in underflow/water in feed) = 0.262
• Volume % solids in underflow = 40

1.1 Write a Matlab code to predict the performance, parameters, and product size distributions of the hydrocyclone. The user should input the desired d50 size, the relative densities of solids and pulp, and the volumetric flowrate of the pulp. The code should then outputs the cyclone size that is optimal for the imputed data, or all the cyclone sizes that will satisfy the imputed data at the user’s choice. As the size distribution of the feed is available, the code calculates the size distributions, mass and volume splits, and relative densities of the overflow and underflow pulp. The imperfection should also be calculated.
1.2 The code must also output the feed distribution together with the resulting semi-log graph of Mass % of feed material reporting to the underflow (U/F) versus the mean particle sizes (μm) on the sampling data shown in Table 1. Label all axes and include comments in your Matlab code to describe your method.

Table 1. Screening Analysis of the feed, underflow and overflow

Screen Size (mm)
0.3
0.212
0.15
0.106
0.075
0.053
0.038
-0.038

Feed mass%
6.11
7.49
11.08
17.62
14.11
9.20
6.76
27.64

Overflow mass%
0
0.01
0.44
4.21
9.67
11.67
12.24
61.76

Underflow mass%
9.12
11.18
16.30
7.97
4.05
10.81

I assume that the first step is to start with a material balance on the hydrocyclone.

 

[Valkarie]

From there, you can calculate the mass fractions of the feed, overflow, and underflow. Then, you can calculate the size distribution of the feed, overflow, and underflow from the data given in Table 1. Next, you can calculate the relative densities of the solids and pulp. Finally, you can use the data to calculate the optimal cyclone size for the imputed data. You can also use the data to calculate the size distributions, mass and volume splits, and relative densities of the overflow and underflow pulp.