Question

1. In 1970, the total phosphorus (TP) load to Lake Erie was 18.150 tonnes/year (where tonnes or metric ton = 1,000 kg). The surface area, volume, and outflow from Lake Erie are given as 25.2 x 10 m² 468 x 10 m, and 182 x 10 m yr, respectively. Based on previous evaluations, the total phosphorus is removed from the lake with an apparent settling rate of 16 m/yr. a. Draw a diagram and write the mass balance equation for total phosphorus in the lake. b. Calculate the steady-state concentration of TP in the lake. c. Develop a mass budget for the lake and present as a diagram. d. Which mechanism removes more TP from the lake, settling or outflow? Ans. b) 31.0 ug/L; c) 18,150 tonnes/yr (load). 5,640 tonnes/yr (outflow). 12,500 tonnes/yr (settling) 2. An industrial contaminant is being discharged into a lake at the rate of 80 kg/day. The lake has a surface area of 10 m?, an average depth of 4 m, and an average flow through the lake of 10° m /day. Based on previous studies, the contaminant is expected to be removed from the lake water by volatilization with a volatilization rate coefficient of 0.7 m/day. a. Draw a diagram of the lake and write the appropriate mass balance equation. b. Calculate the steady-state concentration of the contaminant in the lake c. Calculate the mass of chemical in the lake. d. Develop a mass budget for the lake and present as a diagram Ans. b) 10.0 pg/L; c) 400 kg; d) 80 kg/day (input), 10.0 kg/day (outflow), 70.0 (volatilization) 3. Two different reactor tank configurations with equivalent volumes are being considered to treat 1200 m/hr of wastewater with an influent concentration of 100 mg/L. The first in a square tank (width of 40 m, length of 40 m, depth of 2.5 m) that behaves as a CSTR. The second is a long, narrow tank (width of 10 m, length of 160 m, depth of 2.5 m) that behaves as a plug flow reactor. In both tanks, the contaminant is expected to be removed by a first- order reaction with a rate coefficient of 0.6 /hr. a. Draw a diagram and write the mass balance equation for the CSTR. b. Calculate the contaminant concentration in the effluent of the CSTR. c. Draw a diagram and write the mass balance equation for the plug-flow reactor d. Calculate the contaminant concentration in the effluent of the plug-flow reactor. e. For each reactor, calculate the percent removal of contaminant and briefly comment on the removal efficiencies for CSTRs and plug flow reactors. Ans. b) 33.3 mg/L; d) 13.5 mg/L; e) 66.7% (CSTR), 86.5% (plug flow reactor)

Answer 1

Dout > 182x109 m² year Min 1815 Xho I 16 m/year - Anea- 25.2 x 103 m² do 18.57m = 468 x 100 m Let c = steady state canc. assuming the love to be completely mixed applying mass balance we have ! - accumulation inflow - outflow - sedimentation at steady state accumulation so. 0= alin - Sout. C- C. Anea. sedimentation rate : ay 03 18150 x 103 - 182x109x5 - Cx252X109x16 (reg/year) (uglyen) 3.10x 10 x 10 x 106 C= 3.10X10s ng (kg/m3) (000 31 49/L - conc. of phosphones

mass budget nos 3 Parts load , outflow, settling load 18150 tlyn (given) outflow - Sout C = 3.1x105 x 182 x 109 x 103 outflow = 5644 tlyn (25640) settling = c.x Aneax settling rate - 3.1810 x 25.2x109 x 16 x 10-3 I setting = 12450 tlyn (~ 12500) outflow Ioad Lake S640 18150 1245o a) TP is removed more by settling.

2) loading in flow rate = sinh Cin = 80kg/day & Anea= 107m² depth = 4m. d = 100 m3/day • volatili Zation rate = 0.7m/day mass balance equation: accumulation = inflow - outflow - volatilization at Sh rate o accumulation conc.ac. . at ss we have : O in Cin- &* c- c. Area. Ur a, o= 80 - 106 XC - cx 107 x 0.7 = I xosug- 1xo xixio m3 6 [C= 10 mg/l 1) mass of chemical = volume conc. = 10tx 4x (1.0X105) M = noong Vol = Axd = 203x4 C.A.ver = 70 kg Id volania ze lod 80 kg/d outron sxc = 10 kg/d