Mechanical Operation: Particle Size

A particle can have any shape, which can be grouped into two regular shape like sphere, cubic, cylinder and irregular share like shape of stone or gravel. The size of any particle other than spherical is found based on some characteristic property like
Surface area: reaction in packed bed
Surface area per unit volume i.e. Sauter Diameter: Fluidization, Filteration
Volume: settling  of particle,
The effective diameter of a mixture of different size particles is calculated depending on different apllications. 

Mechanical Operation: Screen Efficiency Calculation

In a screening operation of feed size from mesh 4 to 45, the fraction of material retained on screen 8 and 14 as follows

Screen	Feed	Coarse fraction (Screen 8)	Middle fraction (Screen 14)	Fine fraction
4/6	18.5	64	4.2	0
6/8	27.5	24	35.8	0
8/14	39.5	12	49.1	46.7
14/20	9.1	0	10.1	20.2
20/28	3.4	0	0.8	19.6
28/35	2.0	0	0	13.5

To find the screen efficiency we have to calculate recovery and rejection
Recovery is the ratio of desired material in product to desired material in feed and rejection is undesired material in reject to undesired material in reject.
For an 8 mesh screen desired material is +8 fraction i.e. 4/6 and 6/8 (0.88) and undesired material is -8 fraction i.e. 8/14 (0.12).
for 14 mesh screen, desired material is +14 fraction i.e. 4/6, 6/8,8/14 (0.891) and undesired material is -14 fraction i.e. 14/20, 20/28 (0.109).

for basis of 100 gm of feed:
material bal of 4/6 and 6/8 fraction: coarse fraction=25
material bal of 14/20 and 20/28 fraction: middle fraction=60
material bal of 28/35 fraction: fine fraction=15

Efficiency of 1st screen:
Recovery of 1st screen: (0.88*25)/46=0.478
Rejection of 1st screen: [1-(0.12*25)/54]=0.944

Efficiency of 2nd screen:
Desired material in product (retained on 2nd screen): 4.2+35.8+49.1=0.891
Desired material in feed (2nd screen)= 18.5+27.5+39.5-25(retained on 1st screen)=60.5
Recovery of 2nd screen= (0.891*60)/60.5=0.88
Undesired material in product:0.101*60=6.54
Desired material in feed (2nd screen)=9.1+3.4+2=14.5
Rejection of 2nd screen= 6.54/14.5=0.451