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Unformatted text preview: PGE 322K — TRANSPORT PHENOMENA
Fall 2008
EXAM 2
Oct 22, 2008
Except where noted, do all calculations in SI units
BEWARE OF UNNECESSARY INFORMATION.
DO NOT SPEND TOO LONG ON ANY ONE PROBLEM.
DO NOT LEAVE ANY PROBLEM BLANK!
YOU CAN START ANWERS FROM EQUATIONS IN BSL, JUST GIVE THE
EQUATION NUMBER
Total:100 pts NAME goLdTLm—l 564’ Fall 2008 1. (30 pts) Below are three velocity ﬁelds. For each velocity ﬁeld determine if it satisﬁes
the equation of continuity. Assume constant density and that b is a constant. Show your work. a) VX = by; vy = —bx; vZ = 0 Q g assayed“: 50
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0 Fall 2008 2) (30 pts) There are two tanks connected by two cylindrical conduits. The large conduit
(inner diameter of 20 mm, length = 0.5 m) is packed to a porosity of 0.4 with a sand of
average grain diameter of 0.9 mm. It is 0.1 m off the bottom of the tanks. The small
conduit (inner diameter of 2 mm, length = 0.5 m) is just an open cylindrical tube attached
to the bottom of the tanks. The tanks are closed to the atmosphere, are partially full of
water (to the heights given) with a water viscosity of 10'3 Pas, and density of 1000 kg/m3.
You can use a gravitational constant of g = 10 m/s2 to make your calculations easier. The tanks are large enough so that one can assume the ﬂow within the tanks is negligible. P = 2.4 x10‘1 Pa P = 2.5 x104 Pa sandpack 0.5 m cylindrical tube a) Calculate the permeability of the sand pack in SI units (m2).1 ‘7» \ (QM) \_ l "6)
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7 SE? X 10 M1 m“Mia—XMMNMWVWWmmm“m..mtm"WWW”.WNW.W~NMWW w b) Are the sandpack and cylindrical tube in parallel or in series? WW PAW—L WMWMMMMW”.mm«WWW.M.tm«_ww.mmwmmwwcm F all 2008 wkngmwtmm.new“. c) Calculate the head drop across the sand pack, and the head drop across the cylindrical tube. NM AM, ”A @Wﬂk so we MEAD
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(AMT «(Pym « HQ: PyWﬁ‘ia : 3‘3’“°\( l" ‘0 {”3 (0'13 2 3\?X\0\( I AH : 1.2 No" 43 no" . ”(03 («04M «em <0 «MT (1) Calculate the total volumetric ﬂow rate between the tanks. Qsmoencu: AoWWMK QR 2&1. Jun L
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5cm \ Side View of gutter 10 cm ,
Cross section of gutter full of water 3) (40 pts) At the end of my roof is a gutter to catch the water from coming off the roof.
The gutter drops 5 cm for every 1 meter of gutter length (or, if you prefer is angled 87.1
degrees with respect to vertical. The gutter in cross section is shaped like a U (see ﬁgure)
with 10 cm on each side. We will assume the following graph depicts the friction factor
of the gutter, with a gutter roughness of s/D = 0.01. Your job is to calculate the maximum amount of water the gutter can carry without overﬂowing. I will help lead you through
the problem. You can use a viscosity of 10'3 Pas, a density 1000 kg/m3, and a gravitational constant of g = 10 m/s2 to make your calculations easier. a) Calculate (AH/L) for the gutter assuming that the water level in the gutter is constant.
Hint: Find the head drop over a l m length of gutter. i“? @4993 :0... 90¢ EJHW in» 3(— (3011de 5“ ' (Mo‘él H‘suw‘xcoan 52m} k1 \M
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’7) L A I“ Fall 2008 .. mm......c_rm.mﬂw,wmmmﬁw”m“...ma.a..s......wwm....mw»mmmwwm.w.mwmm b) Calculate the hydraulic radius of the gutter when it is running full. 'L
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\i ‘0 3L0“ {‘J WW 3 atom, c) First assume that the ﬂow is highly turbulent (Re> 107, usually a reasonable
assumption for ﬂow in these large cross sectional ﬂow dimensions), estimate the gutters
average velocity when it is running full. If you do not trust your answers for parts a) and b), please use a hydraulic radius of 5 cm, and a head drop of 103 Pa/m. Mww WﬂvamK use Huew 9M’V‘OQ
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P L 6 {ms (LOUG‘HJESS Fall 2008 d) Is the assumption of highly turbulent ﬂow correct? If not, ﬁnd the appropriate average velocity.
CAL CULA’VG. QGYQOLo'S ti: :
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\‘T‘ ‘5 TQRQU‘NKJr‘T 99.39 1‘qu (”1st us we. same (’QACJUO'4 G‘QC’VDK 4$ QOK 09¢ch M A—SSUHPTUMA, 50 smug MT“ (vv 2. wt} “/3 6) Estimate the total volumetric ﬂow rate in the gutter when the gutter is running full. 1 4L .3 E
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 Spring '08
 dicarlo

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