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Unformatted text preview: Page 1 Midterm Exam #1
CE 11 — Engineered Systems and Sustainability
University of California at Berkeley Spring 2010 NAME: g0 0 W5 Instructions: answer the questions that follow directly on these pages in the spaces
provided. Use the back of the page if you need more room for your answer. If you
believe there is insufficient information provided to answer a question completely, state
reasonable additional assumptions and proceed from there. The exam is closed—book/CIOSed—notes. You may use a calculator. Please write your name in the space provided above! Time: 50 minutes. Question: Score: Out of:
1 _ I 10
2 ____ 10
3 10 TOTAL 30 Page 2 1. GROUNDWATER Suppose thoroughly treated wastewater is being injected into the ground to recharge an
aquifer using a single injection well. Given: water injection rate of 1000 m3/day, aquifer
permeability K=50 m/day, injection well radius of 0.1 m (10 cm), and water table height
is 33 m above a confining bed at the edge of the injection well. (a) Sketch the well field looking down from above (i .e., map or plan view). Show both
equipotential lines (dashed) and streamlines (solid) on your plot. Also indicate direction
of flow on the streamlines. No calculations are necessary for this part,just sketch. (b) Sketch the water table height as a function of distance away from the well on the
cross—section (side View) diagram below. Again, no calculations necessary. Ci—I‘on we ll 4,. 'i #1516 rowan? 3 // Page 3 (0) Estimate the height of the water table above the confining bed at a distance of 25 m
east of the injection well. . m‘ae
mt ﬂf .._ aﬂiz‘ + Q M :5)
1 ‘ TrK (m
_ 9. ‘28—
1 (339m)?” + ("4)? (9.37 m f 26‘“ "“ ivsgtwl 3L§m >‘t:
VJ
H Page 4 2. ALGAE GROWING IN A LAKE An oftenwused chemical representation of algae is C106H2630110N16P (this is an empirical
molecular formula, not an actual structure). Suppose there are 0.10 mg of nitrogen (N)
and 0.04 mg of phosphorus (P) available for algal production per liter of lake water. (a) Assuming adequate amounts of nutrients other than N and P, What mass of algae
could be produced (answer in mg of algae formed per liter of water). Mill/M3“. : Inéxlz—i— awn/'4 lmwé+ (éx'/l7t+3[ 2353733; ml
,_ léX/HL :9 W = 9’ :1 0.0087
WM“. :1 0:069 0.5%.? L. (b) If the nitrogen source could be cut by 50%, how much algae could be produced? m we 37% M, N 044/; ﬂan/Mag,
?Mdljm :: O‘CJSWMA. 2 @ (c) If the phosphorus source could be cut by 50%, how much algae could be produced? (IA/0 W 35W pig ,M{4 m arm‘s“; W'W L W [Kile/v
% [Wham 3. VERTICAL PRESSURE PROFILES (a) Estimate atmospheric pressure at z = 10 km altitude, assuming an isothermal
atmosphere with T = 288 K. At sea level, P0 : 10? Pa. _2/H
F’Cz): 890 e MHA H‘ﬂﬁf
5M
3
ED: (0 Pa L}: {any (PaM3 x 233K
623 m x ooml‘ﬁ
Say We!
(Pa‘mg : 12; mg 1" N+m=
__ rogue;
FC‘OEWL) ‘1 Po 8, 2 Page 5 Page 6 (b) In fact the real troposphere has T( z) = a — bz, assume a = 288 K and b 2 0.0065 K/m.
Calculate the pressure at z = 10 km for this more realistic vertical temperature profile. Useful integral: fabeZ=—%ln(a—bz) F: : {OSBL all? 2:0
QE 2: w Pa ' = —~ m
ol % (i rerr 3’
Fl “Z.
rig z: — 3M .3E:_m
P R i a,  5%
Fe 0 Mg) 4—: pg [Mam]? V aim/LR E : firinch?
P0 CPI/“~67
$1212
1 _223K
9288K @
""3 Q‘ZCP ...
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 Spring '09
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