1 Chapter 4 Physical Processes 4 1 A pond is used to treat a dilute municipal wastewater before the liquid is discharged into a river The inflow to the pond has a flow rate of Q 4 000 m3 day and a BOD concentration of Cin 25 mg L The volume of the pond is 20 000 m3 The purpose of the pond is to allow time for the decay of BOD to occur before discharge into the environment BOD decays in the pond with a first order rate constant equal to 0 25 day What is the BOD concentration at the outflow of the pond in units of mg L Solution dm min mout mrxn dt 0 QCin QCout VkCout 0 4000 1 m3 mg m3 25 4000 Cout 20 000 m3 0 25 Cout day L day day Cout 11 mg L Solutions Manual prepared by Ziad Katirji and Heather E Wright Wendel Environmental Engineering Fundamentals Sustainability Design James R Mihelcic and Julie Beth Zimmerman John Wiley Sons New York 2009 2 4 2 A mixture of two gas flows is used to calibrate an air pollution measurement instrument The calibration system is shown in Figure 4 18 If the calibration gas concentration Ccal is 4 90 ppmv the calibration gas flow rate Qcal is 0 010 L min and the total gas flow rate Qtotal is 1 000 L min what is the concentration of calibration gas after mixing Cd Assume that the concentration upstream of the mixing point is zero Solution Qcal Ccal Qtotal Cd L L L L 0 010 0 0 010 4 90 ppmv 1 000 Cd min min min min Cd 0 049 ppmv 49 0 ppbv 1 000 Solutions Manual prepared by Ziad Katirji and Heather E Wright Wendel Environmental Engineering Fundamentals Sustainability Design James R Mihelcic and Julie Beth Zimmerman John Wiley Sons New York 2009 3 4 3 Consider a house into which radon is emitted through cracks in the basement The total volume of the house is 650 m3 assume that the volume is well mixed throughout The radon source emits 250 pCi s A picoCurie pCi is a unit proportional to the amount of radon gas and indicates the amount of radioactivity of the gas Air inflow and outflow can be modeled as a flow of clean air into the house of 722 m3 h and an equal air flow out Radon can be considered to be conservative in this problem a What is the retention time of the house b What is the steady state concentration of radon in the house units of pCi L Solution a V 650 m3 0 90 h m3 Q 722 h b dm min mout mrxn dt 0 QCin E QC 0 0 because mrxn 0 C E Q 250 and QCin 0 pCi s 3600 3 pCi s h 1 25 103 pCi m 1 25 3 3 m m L 1 000 L 722 h Solutions Manual prepared by Ziad Katirji and Heather E Wright Wendel Environmental Engineering Fundamentals Sustainability Design James R Mihelcic and Julie Beth Zimmerman John Wiley Sons New York 2009 4 4 4 You are in an old spy movie and have been locked into a small room volume 1 000 ft3 You suddenly realize that a poison gas has just started entering the room through a ventilation duct You are safe as long as the concentration is less than 100 mg m3 If the ventilation air flow rate in the room is 100 ft3 min and the incoming gas concentration is 200 mg m3 how long do you have to escape Solution Assume the gas is conservative dC Q in C in Q out C out 0 dt integrate to solve for t dC Q C C in dt V let y C C in V then dy dC d C in dt dt dt C in is a constant therefore dC in 0 dt dy dC dt dt now integrate so C C in 1 e Q t V ft 3 m in t 1000 ft 3 100 mg mg 200 3 1 e 3 m m t 6 9 m in 100 Solutions Manual prepared by Ziad Katirji and Heather E Wright Wendel Environmental Engineering Fundamentals Sustainability Design James R Mihelcic and Julie Beth Zimmerman John Wiley Sons New York 2009 5 4 5 In the simplified depiction of an ice rink with an ice resurfacing machine operating shown in Figure 4 19 points 1 and 3 represent the ventilation air intake and exhaust for the entire ice rink and point 2 is the resurfacing machine s exhaust Conditions at each point are C indicates the concentration of carbon monoxide CO point 1 Q1 3 0 m3 s C1 10 mg m3 point 2 emission rate 8 mg s of nonreactive CO point 3 Q3 C3 unknown The ice rink volume V is 5 0 x 104 m3 a Define a control volume as the interior of the ice rink What is the mass flux of CO into the control volume in units of mg s b Assume that the resurfacing machine has been operating for a very long time and that the air within the ice rink is well mixed What is the concentration of CO within the ice rink in units of mg m3 Solution a From the Figure note that CO enters the C V through the flow at point 1 and by direct emission at point 2 The Zamboni emission must be considered in a mass balance on CO in the rink air since it adds CO to the air min Q1C1 Emission 2 min 3 0 m3 mg mg mg 10 3 8 38 s m s s b Assume steady state and mrxn 0 since CO non reactive Q3 must equal Q1 since there are no other airflows dm 0 min mout mrxn dt mg mg 0 38 Q3C3 Q3C3 38 s s mg mg mg 38 38 38 s s s 13 mg C3 m3 Q3 Q1 m3 3 0 s Solutions Manual prepared by Ziad Katirji and Heather E Wright Wendel Environmental Engineering Fundamentals Sustainability Design James R Mihelcic and Julie Beth Zimmerman John Wiley Sons New York 2009 6 4 6 Poorly treated municipal wastewater is discharged to a stream The river flow rate upstream of the discharge point is Qu s 8 7 m3 s The discharge occurs at a flow of Qd 0 9 m3 s and has a BOD concentration of 50 0 mg L Assuming that the upstream BOD concentration is negligible a What is the BOD concentration just downstream of the discharge point b If the stream has a cross sectional area of 10 m2 what would the BOD concentration be 50 km downstream BOD is removed with a first order decay rate constant equal to 0 20 day Solution a Qu s 0 Qd Cd Qtotal Cdown 0 9 m3 mg m3 m3 50 8 7 0 9 Cdown s L s s Cdown 4 7 mg L b first order decay Ct Co e kt t distance 50 000 m 1 day 52 083 s …