Following is a diagram of the shirt-cleaning process used by the Floods of Suds

Question

Following is a diagram of the shirt-cleaning process used by the Floods of Suds One-Day Laundry Services, Inc. The shirts are soaked in an agitated tub containing Whizzo, the Wonder Detergent, and are then wrung out and sent to a rinse stage. The dirty Whizzo is sent to a filter in which most of the dirt is removed, and the cleaned detergent is recycled back to join a stream of pure Whizzo, with the combined stream serving as the feed to the washtub. Whizzo Dirty Shirts Clean Shirts AGITATED TUB Whizzo 97.0% Whizzo Drain Waste FILTER Recycled Whizzo

Explanation / Answer

Part a

85% Dirt balance

Dirt in dirty shirts = 1lbm

Dirt removed = 1 x 0.85 = 0.85 lbm

Mass of dirt in clean shirts = Dirt in dirty shirts - Dirt removed

= 1 - 0.85 = 0.15 lbm

Overall dirt balance

In the wet dirt, Whizzo = 8%

In the wet dirt, dirt = 100 - 8 = 92%

Dirt in dirty shirts = Dirt in clean shirts + dirt in wet dirt (waste)

1 = 0.15 + mass of wet dirt x 0.92

Mass of wet dirt = (1 - 0.15)/0.92 = 0.924 lbm

Overall Whizzo balance

Mass of Whizzo in clean shirts = 33 - 22 = 11 lbm

Mass of pure Whizzo = Whizzo in clean shirts + Whizzo in waste

= 11 + 0.924*0.08

= 11.074 lbm

Part b

Dirt balance around the tub

Mass % of Whizzo leaves the tub (enter into filter) = 79%

Mass% of dirt leaves the tub (enter into filter) = 100 - 79 = 21%

Mass % of dirt enter into tub with Whizzo = 100 - 97 = 3%

Mass of Whizzo stream enters into tub = m1

Mass of Whizzo stream exit (that enter into filter) = m2

1 + m1*0.03 = m2*0.21 + 0.15

0.03*m1 - 0.21*m2 = - 0.85........eq1

Whizzo balance around the tub

0 + m1*0.97 = 0.79*m2 + 11

0.97*m1 - 0.79*m2 = 11.......eq2

Solve eq1 and eq2 simultaneously

m1 = 16.564 lbm

m2 = 6.414 lbm

Balance around mixing point

Mass of pure Whizzo + mass of recycled stream = m1

mass of recycled stream = 16.564 - 11.074 = 5.49 lbm

Whizzo balance at mixing point

Mass of pure Whizzo + Whizzo in recycled stream = Whizzo in m1

11.074 + 5.49*x = 16.564*0.97

x = 0.9095 = 90.95%

Whizzo in recycled stream = 90.95%

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