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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¢ (lgH
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 $154 6w; 5%%
62} S232. 523 6N)! 6v? SYE. 65k 632. 63% 5324 621/ 6529 Problem 5 35 Poim‘s Total A water jet impinges on the plate inclined at 30" to the xaxis as shown
below. L 9"
A: WSW In solving this problem, it is reasonable to neglect any eﬂ‘ects due to
gravity and to assume the pressure is everywhere atmospheric. a) Relate the velociﬁw (V1, V; and V3) and areas (A1, A; and A3) using
conservation of mass and Bernoulli’s equation along a streamline. (’9’ ‘7 re)
om v5 c.....1r~1...: {{ ;&§AV+{£ga.aas=o v 5
Y / \f.lqu+\/z nz+V5q5 30 C1345} [1) Determine the force that must be exerted by the support strut to keep the plate inplace in terms of the given areas, velocities and
angles. (25 Points) Conaogﬂomerrﬁm} fggwﬁzlﬂjyc‘sv'e gégﬁij ﬁ}:i.$— —' —@/de< + “;ZAV. E: P‘eCOﬁlﬁtggm‘; 40 L553“ (l mini: {131 63;}: “Lil'NL— 1306'3ff7ti'f‘é) to n5. 01 MOM?! 'LHJM
..‘ 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 PapLit) (3 Eat2,1295 {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 ydireetion (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) immiQB
(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 [mo4H5},
Ln =' 0.0an (ZPombs) .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: 088 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; (ZPmrLls)
.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; waromcos 3T:  0093‘? {:5 Fonds) U "'—' a z: .—
st, ariaM O. ”974 (3 Panda) 0: —o.u¢'r4(2rr3(3.bu) a : — 33 M2 0 P934114.) Useful Material for Exam [1 ”I; _‘”’+‘ﬁlﬁW= 0 High” *ﬁsﬂfﬁ'ﬁhs =ﬂpm + IIIdﬁy “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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 BRUNGART,TIMOTHY

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