1. A sludge containing 4% solid (by weight) needs to bethickened by centrifugation to ≥15% solid for disposal. Thecentrifuge has a high constant speed and produces a dewateredsludge containing 20% solid. To increase the processing capacitywhile still meeting the disposal requirement, you decide to bypass(i.e., not dewater) some of the feed sludge and blend the untreatedsludge with the dewatered (20% solid) sludge, so as to produce afinal sludge with a 15% solid content. Assume all sludge streamshave the density of water.
(a) Give the centrate production rate (in L/min) and the percentsolid (of the total coming in) discharged via the centrate?
(b) What % of the feed sludge is bypassed (i.e., notcentrifuged)?
2. Eutrophication is a natural aging process all lakes undergoas nutrients and organic matter accumulate from their drainagebasins. Over time the accumulated nutrients enable increasedaquatic growth and stimulate biological activities. The increase inphytoplankton causes the lake to become murky, while decayingorganic matter depletes the available dissolved O2. Furtheraccumulation of silt, nutrients, and organic matter causes theeutrophic (\"well-fed\") lake to become shallower and warmer withmore plants growing in the shallow edges. This process transformslakes into bogs and marshes over time. Natural eutrophication isusually quite slow, often measured in thousands of years beforemajor changes occur. What human activity has done is rapidlyaccelerate this process (called \"cultural eutrophication\") byintroducing large quantities of nutrients. Sources of nutrientsinclude municipal wastewater, industrial wastes, and runoff fromfertilized agricultural land. The introduction of superfluousnutrients disturbs the natural balance of the system, causingexcessive algae growth and water quality deterioration. Algalblooms are the unsightly and often malodorous clumps of rottingdebris along the shoreline and thick mats of dead organic matter inthe lake. A nutrient of major importance that enter fresh waterbodies such as lakes from the aforementioned sources isphosphorous. C = 20% C = 15% Q = 100 L/min C = 4% bypass centrifugeC = 0.1% (\"centrate\") 2 Consider a phosphorus-limited lake with asurface area equal to 8 x 107 m 2 that is being fed by a streamwith a flow rate of 15 m3 /s and a phosphorus concentration of 0.01mg/L. An outfall from a wastewater treatment plant also adds 1 g/sof phosphorus to the lake, but its volumetric flow rate is smalland can be ignored. The outflow rate from the lake is the same asthe inflow (15 m3 /s). Because phosphorus can attach to suspendedparticles in lake water, the phosphorus in the lake can also beremoved through particle settling (to sediment), which occurs at arate of 10 m/yr. For the questions below, assume the lake is acylindrical CSTR.
(a) Draw a diagram to represent the processes involved inphosphorus mass balance. List all sources and sinks. Estimate thesteady-state phosphorus concentration in the lake.
(b) An acceptable level of phosphorus in the lake is 0.01 mg/L,above which eutrophication is considered likely. By what percentmust the wastewater treatment plant reduce its phosphorousdischarge into the lake to achieve this concentration?
3. A textile finishing process involves drying fabric that hasbeen treated with a volatile solvent. The drying process involvesevaporation of solvent and removal of solvent vapor by air. The wetfabric entering the dryer contains 50% solvent by weight. Airenters the dryer at a rate of 8 kg per kg of solvent-free fabric.The drying process is 92% efficient; i.e., 92% of entering solventis removed from fabric and carried out by air. What is the weight %of solvent in the dried fabric? What is the mole % of solvent vaporin the exhaust? The molecular weight of the solvent is 46g/mol.(Note: Dried fabric still contains some solvent; i.e., driedfabric is not solvent-free).
4. A process heater burns 4.8 kg of natural gas per minute, andthe air supply rate is 20% higher than the stoichiometric rate.Exhaust from the heater is sent to a heat exchanger, where watervapor is condensed and removed from the exhaust. Assume natural gasis all methane (CH4), air contains 21% O2 and 79% N2, and thecombustion of CH4 is complete, what is the mole % of CO2 in thecooled exhaust?
