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Aersp_311_Exam_II_08

# Aersp_311_Exam_II_08 - Aerospace Engineering 311 Exam H...

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Unformatted text preview: Aerospace Engineering 311 Exam H 11/6/08 Problem 1 [6 Points! Which of the following must be fulﬁlled by the ﬂow of any fluid, real or ideal? 1. Newton’s law of viscosity 2. Newton’s second law of motion / 3. The continuity equation / 4. 1: = (u + 11) dU/dy 5. Velocity at boundary must be zero relative to boundary 6. Fluid cannot penetrate a boundary/ A. 1,2,3 (4 Pa.) B. 1,3,6 (4134's-) Problem 2 (4 Points} What are the velocity boundary conditions at a solid wall for a viscous ﬂuid? A. Only the velocity component normal to the wall is zero. B. On] theveloci 'cou nnent :aentto thewallis zero. I C. All the compoennts of the veloci atthe are zero. D. All the components of the velocity at the wall are non- zero. Problem 3 (4 Points} What four characteristics must a flow exhibit in order for Bernoulli’s equation to be valid everywhere in it? (4 Pa) 1. lﬂmi'-'Lprﬁesii31¢ (lg-H 2.- irrohairmnal 011+.) 3. 143136;}? (1 W.) ‘l . . - , I - It- :‘WiéuéH sx- H11; 2J5- bz'l'i'y" I’m} {1 [ALB Problem 4 [11 Points] Compute the strain rate tensor in terms of a, b, c, and e for the velocity field given below. ‘7 (ax + by)? + (cx + 3):); _. w” LIA ‘ ' \$13 _ Ji<\$f +£iés') = 5‘591'1 ra'lx; 475\$}er (2 P453 3 61': \$11 \$111,. :2 \$154 6w; 5%% 62} S232. 523 6N)! 6v? SYE. 65k 632. 63% 5324 621/ 6529 Problem 5 35 Poim‘s Total A water jet impinges on the plate inclined at 30" to the x-axis as shown below. L 9" A: WSW In solving this problem, it is reasonable to neglect any eﬂ‘ects due to gravity and to assume the pressure is everywhere atmospheric. a) Relate the velociﬁw (V1, V; and V3) and areas (A1, A; and A3) using conservation of mass and Bernoulli’s equation along a streamline. (’9’ ‘7 re) om v5 c.....1r~1...: {{ ;&§AV+{£ga.aas-=o v 5 Y / -\f.lqu+\/z nz+V5q5 3-0 C1345} [1) Determine the force that must be exerted by the support strut to keep the plate in-place in terms of the given areas, velocities and angles. (25 Points) Conaogﬂomerrﬁm} fggwﬁzlﬂjyc‘sv'e gégﬁij ﬁ}:i.\$-— —' —@/de< + “;ZAV. E: P‘e-C-Oﬁlﬁtggm‘; 40 L553“ (l mini: {131- 63;}: “Lil'NL— 1306'3ff7ti'f‘é) to n5. 01 MOM?! 'L-HJM ..‘- Ft} “(Dam €V3A3' (Vigil/0550;} " 5: VIZA'. =‘ :3 V2. A2<V1 wb 50° = Fm (.3 POUL‘Lé) {3 POE-.1 i5} (3 RJIQ'LEI) (Z ?01_.L{'5> R 2 may? E” =- £33, \$0430“) + A; ax: (30°31 Y—chr“. 6 V3 ﬁsi‘igéméff) - 6V2 1312<JVLélll5O°j 2 Fr}; (3 Pap-Lit) (3 Eat-2,1295 {2 1? :49 Fr}:- 6WZ am. 60°) Eds—H H; c) What condition is required for the jet to exert no force on the plate in the y-direetion (other than V1: 0 or A1: 0)? (5'Points) 3 Fri), ; €\/.2ewarf%0°J E115“- H431 : O (} Patti") A2 = A3 {:2 '13: la 3 Problem 6 [20 Points Total} Given: 1. Johnny Smith loves canoes and his father runs a gas station on top of Jones’ peak where g: 9.1 mls2 and the temperature is 10°C. Since oil is so abundant, Johnny plays with his prototype canoe in a tank of oil. Johnny visits his grandmother who lives close to sea level in Death Valley where the temperature is 50°C Johnny couldn’t take his prototype canoe when visiting his grandmother, and being a scientiﬁc type, knows he must build a model of his canoe in order to conduct dynamically similar tests in the water tank at grandmother’s house The length and velocity of the prototype canoe are 3.0 m and 5.0 mls, mpeclively Knowing: 1. That the eﬂ'ects of surface tension forces, pressure forces, and forces due to compressibility can be ignored Determine: 1. The two (2) nondimensional parameters that must be matched (between model and prototype) for dymamic similitude. (5 Pts) 2. The length of the model (in meters). (5P3) u, U J , r- L134 “” LP (ﬁg; 1%“) (213mm) {3) 4%“me (I) u“ "E WJE‘UE (2 Poinﬁ) (4) ﬁrm (23 L1, .a I m ” UHDJ—g E “1% WE: ('5) i-mmiQB (g) mica (\$5 LH= LPEJE (\$3 <2 PM‘) L3‘: 133% (5’?) Ln“ = LY<3§ y3(gn_)% Z (3'40 B<wigH/_Q_:)/5 0.50'xloh‘W'; 2/3 H/s.Z [mo-4H5}, Ln ='- 0.0an (ZPom-bs) .5 3. The velocity of the model (in metersfsecond). (9 Pts) UH: UP [33 lg (3 Foinﬁ‘) ’2’ _. 93H?- 1 U” '- EOH/‘J ‘1. (mg? W< 3. 0n H) UH: 0-88 We. (2 Penis) Problem ’7 (20 Points Total} You are given the sourceslsinks shown below where Q [mzfs] represents the souredsink strength. Note that the flow fromlinto a sourcclsink is entirely radial. (3) Determine the velocity components u and v at (-3, 3) due to 01 only. [SPoints) . ' Ur: 3:? 5 %[%{%]: 2%? (2 Foam ”Tl _._\J| = if”; ._: An; (ZPmrLl-s) .35 4.5 2175“) g” 5 LL[ :0 (I \$tm¢l> -3.3 (b) Determine the velocity components u and v at (-3, 3) due to Q2 only. (5 Points) Ur 3 iér CZ 93"" ‘1‘”) Ha Ut'l -_.-_ Li! '_'.: fjrlfg, . __ﬂ _—--’l'__ “f; {/2 Hilal’.) grifﬁn} Jam? 9 x \J’; n .5“; 3'30,._.__.;) ‘4’; (c) Determine the 03 that is necwsary at location (0, 5) to generate a velocity vector at (-3, 3) of V’ = 02' + 0.3051} Note that the velocity vector is in units of 11115 and that Q3 is located at (0, 5) . (10 Points) A” a :1 Earls a Oi 430.3051;- _'='_-. 1".“- +US)4 + (3W+VS)J Us ‘2‘: —:'— :: areas (3 3:..qu V:IC)CG‘L ”Qt-”(Jag V3 2 0.509 E“— W3 32; war-omcos 3T:- - 0093‘? {:5 Fonds) U "'—' a z: .— st, aria-M O. ”974 (3 Panda) 0: —o.u¢'r4(2-rr3(3.bu) a :- — 33 M2 0 P934114.) Useful Material for Exam [1 ”I; _‘”’+‘ﬁlﬁ-W= 0 High” *ﬁsﬂfﬁ'ﬁhs =-ﬂpm + IIId-ﬁy “a: 10 pm- = 1000 kg/m" and ”mm = 1.013110“3 Nos/m2 at 20° C Pam. = 101,000 Pa 11 ...
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