# GATE (TF) Textile 2007 Question Paper Solution | GATE/2007/TF/79

A 46 mm diameter rotor is spinning 60 tex yarn at 100 m/min. The trash level in feed sliver is 0.2%. The opening roller can clean the sliver to the extent of 70%. The self cleaning effect of the yarn arm within the rotor is 50%

###### Question 79 (Textile Engineering & Fibre Science)

If an interruption in spinning is expected once the deposition attains 0.2 mg/cm in the rotor groove, number of end breaks expected in 8 hours is

Option C is correct.

Rotor dia=46mm

Yarn count=60 tex

Rotor speed=100 m/min

Trash level in feed sliver=0.2%

Cleaning % of opening roller=70%

Self cleaning effect of the yarn within the rotor=50%

Deposition attains once=0.2 mg/cm in rotor groove

Number of ends breaks expected in 8 hrs=?

Calculation-

Rotor circumference=0.1444 m

Rotor circumference=14.44 cm

Now,

By definition of tex-

By unitary rule-

1000 meter length have..=60 gm weight

1 m have……………………………=60/1000

Similarily,

100 m length have…………….=60 x 100/1000

Weight of yarn=6 gm

Weight of output yarn=6 x (Trash level% in feed sliver) x (1-Cleaning % of opening roller) x (1-Self cleaning effect %of the yarn within the rotor)

Weight of output yarn=6 x (0.2%) x (1-70%) x (1-50%)

Weight of output yarn=6 x (0.002) x (1-0.70) x (1-0.50)

Weight of output yarn=6 x 0.002 x 0.30 x 0.50

Weight of output yarn=0.0018 gm

Weight of output yarn=1.8 mg

Trash deposition (mg/cm of rotor circumference) =Weight of output yarn/Rotor circumference

Trash deposition (mg/cm of rotor circumference) =1.8/14.44

Trash deposition (mg/cm of rotor circumference) =0.1245

Now,

Number of ends breaks expected in 8 hrs=Trash deposition (mg/cm of rotor circumference) x 60 x 8/Deposition attains once in rotor groove.

Number of ends breaks expected in 8 hrs=0.1245 x 60 x 8/0.2

Number of ends breaks expected in 8 hrs=59.76/0.2

Number of ends breaks expected in 8 hrs=298.8
=299 (Ans)