Question

A blowroom line has three beaters, each having a trash removal efficiency (cleaning index) of 30%. The trash removal efficiency (%) of the blowroom line (rounded off to 1 decimal place) is _________

Hint:

For a blowroom line with multiple beaters, the combined efficiency can be found using the formula \( E_{total} = 1 - (1 - E_1)(1 - E_2)(1 - E_3) \).

Answer 1

Step 1: Formula for Combined Efficiency. The combined efficiency of the blowroom line with multiple beaters can be calculated using the formula for successive removal of trash. If the efficiency of each beater is \( E \), the combined efficiency \( E_{total} \) is given by: \[ E_{total} = 1 - (1 - E_1)(1 - E_2)(1 - E_3) \] Where \( E_1, E_2, E_3 \) are the efficiencies of the individual beaters. 
Step 2: Substituting Values. For each beater, \( E_1 = E_2 = E_3 = 0.30 \), so: \[ E_{total} = 1 - (1 - 0.30)(1 - 0.30)(1 - 0.30) = 1 - (0.70)(0.70)(0.70) = 1 - 0.343 = 0.657 \] Step 3: Final Calculation. The total trash removal efficiency is \( 0.657 \) or 65.7%. 
Answer: 65.7%