1.1-1.7 The solutions for these problems are the solutions for problems 1.1-1.7 in the 2

1.1-1.7 The solutions for these problems are the solutions for problems 1.1-1.7 in the 2 nd

edition Solutions Manual.

1.8 The washing machine is a batch reactor in which a first order decay of grease on the

clothes is occurring. The integrated form of the mass balance equation is:

kt CC -

e =

First, find k:

1-

min 0.128 0.88 1 ln min 1 1

0.88 ln min 1 1 ln 1 ==== C C C C t k

Next, calculate the grease remaining on the clothes after 5 minutes:

()

( )( )

g 0.264 eg 0.500 e 1-1 min .005min 128.0--

=== kt mm

The grease that is not on the clothes must be in the water, so

g/L 0.00472

L 50.0

g 0.264 - g 0.500

w==C (Introduction to Environmental Engineering and Science, 3e Gilbert Masters Wendell Ela) (Solution Manual all Chapters) 1 / 4

Q0, C0Qs, CsQb, C0 farm PlateauCreek C.V.Qf/2, C f 1.9

Qf, C0

• A mass balance around control volume (C.V.) at the downstream junction

yields

()( )( )( )( )

() mg/L 0.112 /sm 4.5 mg/L 0015.0/sm 4.0 mg/L 00.1/sm 0.5

/2

3 33 s 0bff s = + = + = Q CQCQ C

• Noting that Qb = Q0 – Qf and Q s = Q0 – Qf/2 the mass balance becomes

• Qf/2)Cf + (Q0 – Qf)C0 = (Q0 –Qf/2)Cs

and solving for the maximum Qf yields

() ( )()

/sm 0.371 mg/L 2 0.04

0.0015 -

2 1.0 mg/L 0.0015 - 04.0/sm 5.0

2 - 2 -

3 3 s

f 0s0 f = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = C C C CCQ Q

• / 4

1.10 Write a mass balance on a second order reaction in a batch reactor:

Accumulation = Reaction

2

• ere wh kmr(m)Vr(m)

dt dm V==

∫∫

= tm m dtk m dm t

2 -

so, kt mm t - 1 - 1

=

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 0t 1 - 11 k mmt calculate m t=1 based on the equation’s stoichiometry that

• mole of methanol yields 1 mole of carbon monoxide

()OHCH g 114.3 OHCH mole OHCH g 32 CO mole 1 OHCH mole 1 CO g 28 CO mole CO g 100 3 3 33 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

so, g 85.7 g 114.3 - g 200

• tOH,CH

3 == =C

and 1-1- gd 0.00667 g 200 1 - g 85.7 1 d 1 1 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =k

• / 4

1.11-1.13 The solutions for these problems are the solutions for problems 1.8-1.10 in the 2 nd edition Solutions Manual.

1.14 Calculate the pipe volume, Vr, and the first-order rate constant, k.

()( ) 1- 1/2 3 2 p min 0.0578 min) (12 2ln

t 2ln and ft 24,033 4 ft 3400 ft 3.0 ====kV π

For first-order decay in a steady-state PFR

() () ()Lmg2.82 ft 0.134 gal gal 10 min ft 033,24min0578.0expmg/L 1.0 e 34 31-

/=⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ == −kt CC

• / 4