Question

In a two-stage wire drawing operation, the fractional reduction (ratio of change in cross- sectional area to initial cross-sectional area) in the first stage is 0.4. The fractional reduction in the second stage is 0.3. The overall fractional reduction is

• A. 0.24
• B. 0.58
• C. 0.60
• D. 1.00

Answer 1

The correct option is B 0.58

Fractional reduction in first stage $=\frac{\text{Change in area in first stage}}{\text{Original area (A) before reduction}}$

$0.4=\frac{\text{Change in area in first stage}}{A}$

Change in area in first stage
$=0.4A$

Area after first redirection
$=A-0.4A=0.6A$

Fraction reduction in second stage
$=\frac{\text{Change in area in second stage}}{\text{Original area (A) before second stage}}$

$0.3=\frac{\text{Change in area in second stage}}{0.6A}$

Change in after 2nd stage
$=0.18A$

Remaining area after 2nd reduction
$=0.6A-0.18A=0.42A$

Overall reduction in area
$=A-0.42A=0.58A$

Overall fractional reduction

$=\frac{\text{Overall reduction in area}}{\text{Original area}}=\frac{0.58A}{A}=0.58$