aer205_q2_2006_solutions - AER205S FLUID MECHANICS and...

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Unformatted text preview: AER205S FLUID MECHANICS and TRANSPORT PHENOMENA Quiz 2 27 October 2006 9:10 am - 10:00 am Closed Book, no aid sheets Non-programmable calculators allowed Instructor: J. W. Davis Family Name: \ \93 \ }C€«U :5 Given Name: o l Ulyst'I-LO’L “’35 Student #2 FOR MARKER USE ONLY Question Note: The following integrals may be useful. {coszede = i0 + lsin26 + C; [sinzfidfi = 1(E) — lsin20 + C J 2 4 2 4 Page 1 of 7 l) a) State and explain the importance of the continuum hypothesis. (Zmarks) 7L1 $2 6Q rawain Mic/chm} I‘M fimLMTC “(0 H1 MHH‘ Wed- m1 m a M tram allows aflwatuw u Calcufiju—lofbe CLF/fofci *icP‘ “QiouJS. b) Explain what is meant by the “no-slip” condition. (2 markS) Phil {mma—liflcimig "337' Oat/eel In wwle wild“ 0:. 90K; SM‘QaLE Mow-€25 wLJrlA @Gct‘llJ-S Hue Saw M0591 m gmijfiCC c) Explain the difference between surface forces and body forces. (2 marks) Sm‘gatf’ M03? FWLQ’SIQMLQA (Muff! (4.;th claim “Milan: 0C a fluid elem/«emf. EDA Cyrus. .~ :ché,gwlxm mew}. ‘ Who/L Cu! 3 40%“ M044 mi3 0 dame.le d) State the Hydrostatic Axiom, and explain in words What it means. mfimafi (3marks) A A :1 _ " 85' at? — * r "‘ ' 5,? — a.“ uh A: Oh 0L SMQOLC: gala/“5“; 5“ ourm SSr wail/M 0 war Am‘MAa/l ’le Causal“? YVfidésd—‘I‘fl Q0401 W ’\ cbg J t) carol“: 0AM V‘ I it) Q; in Magmilwif ll? 33,6604: (:55) L5 Cm? res/fiue_ Page 2 of 7 e) Define the following terms: streamline, streamtube, stream filament. (3 marks) [M men 601% WW ‘lp—l’lj 0405A: Sim“ (ram/Ll; we. : ShEaVMJrf/tloe: ‘l’tkhf’ gimmeci giveaM‘lwe’i CL clown/J CW6 in ‘l’lx upland \Elclg “Wham Rdamcwjr: 5 “WM: Small though stack awj WA—Sfié-“llo‘w Mans he (gm-\Clercd ?\:‘1vxa~“( 044i WQEWJiCu/Qar is: Chm—j f‘ltrflmlxwfi, f) A solid sphere, 50 cm in diameter, floats at the interface between water ( pw = 1000 kg/m3) and oil (poi, = 750 kg/m3), such that 80% of the sphere’s volume is in the water. What is the density of the sphere? (3 marks) Page 3 of 7 2) The discharge Q [m3/s] of a centrifugal pump is a function of the rotational speed of the pump, N, the diameter of the impeller, D, the pressure drop across the pump, Ap, the Viscosity of the fluid, ,u, the density of the fluid, p, and the acceleration due to gravity, g. Develop a suitable set of [7 terms for this problem. (8 marks) xxx ~39, E43 TFQ : 3.3 IUD _ a r}? mm = we - rT~~rLL>3\W> '=, )L='L 3:34 '1‘“ _ A; .5 TVA? .- wtblifi x..._../ K "s 3,. E C’b Em - WW = U“) m U” l “ 15% 5:7. 1”“ \QG 7T = 45. A a WS n x & Jblgi ; LTI = LT‘} lLVlHLIB) pLz'L (3:4 -b='-O I ‘3 " 773 ; MID Page 4 of 7 3) A rectangular channel of width 1m contains water to a depth of 1m. A gate at the end of the channel is a quarter circle of 2m radius as shown on the figure. Find the force F required to hold the gate closed. (12 marks) ////// // / —~,. m - “J C“ $9171: 5"— ? R) ? 9i 5F» ' W $5 5““ Page 5 of 7 4) A box of length and height L is closed at the top except for a slit in the upper right-hand comer, C, which is open to the atmosphere, Pa, as depicted in the diagram below. It is filled completely with liquid of density ,0, and with g = — g]; being the acceleration due to gravity, it is subject to an accelerationzfi = + in such a way that no liquid spills from the box. Determine the pressure distribution throughout the box, and in particular, find the pressure at the lower left—hand corner A. (10 marks) Po ~ l"? 1% Law a ilfié /_ “we” r? to a c..\~€_ ‘. z i—F - S'X a: 1" “ii” =9 reflex” its =7 watt» : C* 0.3.: 3-ssz mm a» rm: J ml“ W "C C: ?& 3 “p: Fiat + ZfiL “‘7; “La 2:: gag}, 5) 0d: x:?:=0 :9 $=TQ+ZQL Page 6 of 7 5) A Pitot tube is used to measure the water velocity at the centre of a 30 cm diameter pipe as shown in the figure. If h = 10 cm, what is the flow velocity? (5 marks) Page 7 of 7 ...
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aer205_q2_2006_solutions - AER205S FLUID MECHANICS and...

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