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Solution of Assignment-1

May 29, 20141
Solutions of Assignment ONE (CHAPTER TWO)
(οΈ€ mol )οΈ€
(οΈ€ 20000 )οΈ€
1. A quantity π‘˜ depends on the temperature 𝑇 : π‘˜ cm
= 1.2 × 105 exp − 1.987
3 ·s
𝑇 . The units of the quantity
20000 are cal/mol, and T is in K (kelvin). What are the units of 1.2×105 and 1.987?
mol /cm3 · s and c a l / mol·K
2. How many significant figures are present in the following? (a) 12200 (b) 12200.0 (c) 0.003040 (d) 1.34×105
(a)3 (b)6 ( c )4 (d)3
3. Find the equivalent of 1 mg/L in (a) kg/m3 (b) kg/L.
1 mg/L = 0.001 kg/m3
1 mg/L = 1 e -06 kg /L
4. A resident in Kathmandu produces 0.5 kg of solid waste. If the volume of this waste is 1.5 L. Determine the
density of the solid wastes in (i) kg/L and (ii) ton/m3 . Based on this information, determine the volume (in
m3 ) and weight (in tons) of the solid wastes generated in Kathmandu Valley assuming the population to be 9
D e n s i t y = 0.33 kg /L
D e n s i t y = 0.33 t o n /m3
Volume = 13500.00 m3
W e i g h t = 4500.00 t o n
5. Colloids are particles of size 10−7 cm to 10−8 cm in size. Give these sizes in nm. Compare the sizes with the
size of a bacteria (1 πœ‡m).
Low = 0.1 nm
H i g h = 1 nm
B a c t e r i a s i z e = 1000.00 nm
C o l l o i d s have the s i z e of
0.0001 t o 0.001
times the s i z e of b a c t e r i a .
6. Convert the following concentration in to g/m3 (a) 500 ppm (b) 0.08 ppm. Assume that the density of the
solution is 1 kg/L.
500.0 ppm = 500.00 g /m3
0.08 ppm = 0.08 g /m3
7. Per capita water consumption in Kathmandu Valley is 180 liters per day. Estimate the quantity of wastewater
being discharged to Bagmati river in (a) MLD and (b) m3 /s (c) crore lpd, assuming 25% of the wastewater is
lost by evaporation and population of Kathmandu to be 9 million.
Net w a t e r d i s c h a r g e = 202.50 MLD
Net w a t e r d i s c h a r g e = 14.06 m3 / s
Net w a t e r d i s c h a r g e = 121.50
crore lpd
8. Estimate the volume of snow in the Mountains of Nepal. Assume that 17% of the surface area of Nepal is
covered by snow and average depth of snow is 1 m. Report the figure in appropriate unit.
Assuming the area of Nepal as 147181 km2 ,
v o l u m e o f snow = 25.02077 km3
9. Estimate the rural and urban water demand in your home district. Assume that the rural and urban water
demands are: 45 lpcd and 120 lpcd.
Assuming the population of urban region as 5 million and that of rural region as 5000,
r u r a l w a t e r demand = 2.2 e +05 l p d
u r b a n w a t e r demand = 6 e +08 l p d
10. Dhulikhel campus of Kathmandu University has about 1800 undergraduate students and 450 students
graduate every year. Supposing that everyone enrolled at the university graduates eventually. What is the
approximate retention time (the time the students spend) of the students at Dhulikhel campus?
May 29, 20142
r e t e n t i o n t i m e = 4.00
11. A power plant emits 80 kg of flyash per hour up the stack. The flow rate of the hot gases in the stack is
850 L/s. What is the concentration of the flyash in πœ‡g/m3 ?
c o n c e n t r a t i o n = 2.61 e +07 πœ‡g /m3
12. (a) How much milk is consumed in Nepal everyday? (Make reasonable assumptions). (b) One gram of table
salt is put into a glass of 400 mL. What is the concentration of salt in mg/L ?
Assuming that 2 crore people drink milk in Nepal, and that each person drinks 200 mL of milk everyday,
m i l k c o n s u m p t i o n = 4.00 MLD
1 g /mL = 2500.00 mg/L
13. What is the concentration in (a) ppmv and (b) percent by colume of carbon monoxide with a concentration
of 103 πœ‡g/m3 ? Assume a temperature of 25 ∘ C and pressure of 1 atm.
( a ) ppm𝑣 o f CO = 0.09 ppm.
( b ) p e r c e n t by v o l u m e o f CO = 0.000009 p e r c e n t .
14. Formaldehyde is commonly found in the indoor air of improperly designed and constructed buildings. If the
concentration of formaldehyde in a home is 0.7 ppmv and the inside volume is 800 m3 , what mass (in grams)
of formaldehyde vapor is inside the home? Assume 𝑇 = 298 K and 𝑃 = 1 atm. The molecular weight of
formaldehyde is 30.
Mass o f f o r m a l d e h y d e = 0.7 g .
15. Mobile combustion of N2 O in 2004 emitted 42.8 Tg CO2 e. How many Gg of N2 O was this?
Mass o f N2O = 143.6 Gg.
Solutions of Assignment ONE (CHAPTER THREE)
1. A household needs 50 kg of consumer goods (food, magazines, newspapers, appliances, furniture and associated packaging). Of this amount, 60 percent is consumed as food. Half of the food is used for biological
maintenance and ultimately released as CO2 ; the remainder is discharged to the sewer system. Approximately
1 kg accumulates in the house. The household recycles 30% of the solid wastes generated. Estimate the amount
of solid waste they place at the curb each week. π‘€π‘‘π‘œπ‘‘π‘Žπ‘™ = 𝑀𝑓 π‘œπ‘œπ‘‘ + π‘€π‘Žπ‘π‘ + π‘€π‘Ÿπ‘’π‘π‘¦π‘π‘™π‘’ + 𝑀𝑛𝑒𝑑 π‘€π‘Žπ‘ π‘‘π‘’
S o l i d w a s t e = 13.3 kg . Answer.
2. A sewage lagoon that has a surface area of 10 ha and a depth of 1 m is receiving 8640 m3 /d of sewage
containing 100 mg/L of biodegradable contaminant. At steady state, the effluent from the lagoon must not
exceed 40 mg/L of biodegradable contaminant. Assuming the lagoon is well mixed and that there are no losses
or gains of water in the lagoon other than the sewage input, what biodegradation reaction rate coefficient (d-1)
must be achieved for a first order reaction? 𝐢𝑖𝑛 𝑄𝑖𝑛 = πΆπ‘œπ‘’π‘‘ π‘„π‘œπ‘’π‘‘ + π‘˜ πΆπ‘œπ‘’π‘‘ 𝑉
k = 0.13 d−1 . Answer.
3. The Bagmati river has a discharge of 500 million m3 at Chobhar. Assuming that all the wastewaters
generated in Kathmandu is discharged to Bagmati at Chobhar after collection, determine the DO of river water
after mixing. Assume DO of Bagmati at Chobhar as 4 mg/L and DO of wastewater as 0.5 mg/L. Take the
wastewater generation rate of 100 lpcd for 1.5 million population in Kathmandu. 𝐢𝑖𝑛 𝑄𝑖𝑛 + πΆπ‘‘π‘Ÿ π‘„π‘‘π‘Ÿ = πΆπ‘œπ‘’π‘‘ π‘„π‘œπ‘’π‘‘
Downstream DO = 4.00 mg/L. Answer.
4. A stream flowing at 10.0 m3 /s has a tributary feeding into it with a flow 5.0 m3 /s. The stream’s concentration
of chlorides upstream of the junction is 10.0 mg/L and the tributary chloride concentration is 40.0 mg/L. Treating
chlorides as a conservative substance, and assuming complete mixing of the two streams, find the downstream
chloride concentration. 𝐢𝑖𝑛 𝑄𝑖𝑛 + πΆπ‘‘π‘Ÿ π‘„π‘‘π‘Ÿ = πΆπ‘œπ‘’π‘‘ π‘„π‘œπ‘’π‘‘
Downstream c h l o r i d e c o n c e n t r a t i o n = 20.00 mg/L. Answer.
5. A wastewater treatment plant with an output of 38400 m3 /day discharges the liquid effluent with a BOD
of 20 mg/L into a river. If the BOD of the river upstream of the discharge point is 0.2 mg/L, at a maximum
May 29, 20143
flow of 20 m3 /s, compute the BOD of the river downstream of the discharge, assuming complete mixing.
𝐢𝑖𝑛 𝑄𝑖𝑛 + 𝐢𝑑𝑝 𝑄𝑑𝑝 = πΆπ‘œπ‘’π‘‘ π‘„π‘œπ‘’π‘‘
Downstream BOD = 0.63 mg/L. Answer.
6. Each day 3780 m3 of wastewater is treated at a municipal wastewater treatment plant. The influent contains
220 mg/L of suspended solids. The clarified water has a suspended, solids concentration of 5 mg/L. Determine
the mass of sludge produced daily from the clarifier. 𝐢𝑖𝑛 𝑄𝑖𝑛 = 𝐢𝑀 𝑄𝑀 + 𝐢𝑠 𝑄𝑠
Mass o f s l u d g e = 812.70 kg / d . Answer.
7. A Sanitary landfill has available space of 16.2 ha at an average depth of 10 m. Seven hundred sixty-five
(765) cubic meters of solid waste are dumped at the site 5 days per week. This waste is compacted to twice its
delivered density. Draw a mass-balance diagram and estimate the expected life of the landfill in years.
E x p e c t e d l i f e o f t h e l a n d f i l l = 16.29
y e a r s . Answer.
8. A stream, (shown in the following figure) flowing at 150 L/s and 20 mg/L suspended solids, receives
wastewater from three separate sources: What are the flow and suspended solids concentration downstream at
the sampling point?
Downstream f l o w r a t e = 600.00 L/ s . Answer.
Downstream SS c o n c e n t r a t i o n = 80.00 mg/L. Answer.
9. The Star Tribune and the St. Paul Pioneer Press and Dispatch represented 75% of the newspaper circulation
in Minnesota. The Star Tribune had a circulation of 2973100/d and weighed about 0.5 kg/issue, while the St.
Paul Pioneer Press and Dispatch had a circulation of 1229500/d and weighed 0.4 kg/issue. Of course, not all
of what the consumer receives is recyclable newsprint; 17% of the weight is nonnewsprint material for glossy
advertisements and magazines, and 1% is ink. Also, 5% of what is printed is overissues and never reaches the
consumer, while 3% of the newsprint delivered to the press becomes newsroom scrap and is not printed.
A.Find the mass of newspaper that reached consumers in Minnesota each day. How much of this was
recyclable newsprint, including ink but excluding glossy pages?
Mass o f n e w s p a p e r = 2637.80 t o n n e s / d . Answer.
Mass o f r e c y c l a b l e n e w s p r i n t = 2189.37 t o n n e s / d . Answer.
10. For the following conditions, determine whether a CMFR or a PFR is more efficient in removing a reactive
compound from the waste stream under steady-state conditions with a first-order reaction: reaction volume =
280 m3 , flow rate = 14 m3 /d, and reaction rate coefficient = 0.05 d−1 . 𝐢𝑖𝑛 𝑄𝑖𝑛 = πΆπ‘œπ‘’π‘‘ π‘„π‘œπ‘’π‘‘ + π‘˜ πΆπ‘œπ‘’π‘‘ 𝑉
πœ‚π‘ƒ 𝐹 𝑅= 63.2 % and πœ‚πΆπ‘€ 𝐹 𝑅 = 50.0 %. Answer.
Hence PFR i s more e f f i c i e n t t h a n CMFR. Answer.