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. Each 100.0 lb_m of dirty shirts contains 2.00 lb_m of dirt. The washing removes 85.0% of the dirt in the dirty shirts. For each 100.0 lb_m of dirty shirts, 33.0 lb_m of Whizzo leaves with the clean shirts, of which 22.0 lb_m is wrung back into the tub. The detergent that enters the tub contains 97.0% Whizzo, and that which enters the filter contains 83.0%. The wet dirt that leaves the filter contains 8.00% Whizzo. Questions: How much pure Whizzo must be supplied per 100.0 lb_m of dirty shirts? Ib_m What is the composition of the recycled Whizzo stream from the filter? %Whizzo

Answer 1

a. 85% dirt removal: m_1 = 0.15 times 2 = 0.3 lbm dirt overall dirt balance: 2 = 0.3 + (0.92)m_5 = > m_5 = 1.848 lnm dirt overall whiyyo balance: m_2 = [11 + (0.08)(1.848)]lbm whiyyo = 11.15 lbm whiyyo \r\n b. tub dirt balance: 2 + 0.03 m_3 = 0.3 + 0.17 m_4 tub whiyyo balance: 0.97 m_3 = 11 + 0.83 m_4 solve (1) and (2) simultaneouly. m_3 = 23.436 lbm: m_4 = 14.136 lbm mixing pt.mass balance: 11.15 + m_6 = 23.436 lbm m_6 = 12.286 lbm mixing pt. whiyyo balance 11.15 + times (12.286) = (0.97) (23.436) x = 0.943 lbm whiyyo/lbm = > 94% whiyyo 6% dirt