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Assignment 11 Solutions

# Assignment 11 Solutions - Problem 7.30(In Excel 7.30 The...

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Unformatted text preview: Problem 7.30 (In Excel) 7.30 The diameter. d. of the dots made by an ink jet printer de- pends on the ink viscosity. p. density. p. and surface tension. 0'. the nozzle diameter. D. the distance. L. of the nozzle from the paper surface. and the ink jet velocity. V. Use dimensional analysis to ﬁnd the [1 parameters that characterize the inkjet's behavior. Given: That dot size depends on ink viscosity, density, and surface tension, and geometry Find: [‘1 groups Solution: We will use the workbook of Example 7.1, maﬁﬁed for the eta-rent problem The numberofparmneters is: n =7 The number of primary dimmsions is: r = 3 Thentunberofrepeatparametersis: m=f=3 Thenumberofl'lgroupsis: n—m=4 Enter the dimensions (H, L, t) of the repeating parameta's, and ofup to four other parameters (for up to four H groups). The spreadsheet will compute the exponents a, b , and c for each. REPEATING PARAMETERS:Choose p, V,D l'] GROUPS: Hence D V D H L t d 0 l 0 U]: = C— " L t o l 0 -2 113: a: b: c: 2=—‘.J—_9p_m n3: 02 pVD it: pV D Note that groups 1'11 and 11.. can be obtained by inspection 93¢:- II N [3] H Problem 7.56 mm: m «Swag. WM‘aQ-mag‘mi mﬁ‘o‘tL‘M a. mm. in u. umMM‘. muum ‘. :3“ f; . \A.’ -d_gd§’\$._ \ mmlk m 'o m: “as m \$\$L~ 6&9“: can kf-Qréo ‘E‘f\u\i\\ ck. \- 236:: a.“ M:- Mcw_'§ gxskohndﬁukhum “35k Autotxk. Vu‘xt‘a kn“: M1. QAAM'QS» \155 '5‘: \‘W Mar :2 wom- (¢_\ ruUuA-zd. (OM 59.15» C!“ «95.9. c».\=,(‘9,~\\us‘¢,g‘}h m a. atm‘ku‘o. ‘th _ true-s %M%Wﬁ~ﬁwn‘ (at «21 and. “are; no. nae-AA exg-LX'c-ou MW «at!» ‘1. 3“}Li((£§‘us\%)% “‘5’ {-53 r [ISL—i Problem 7.58 [2] 7.58 A model test is performed to determine the ﬂight character- istics of a Frisbee. Dependent parameters are drag force. F9. and lift force. FL. The independent parameters should include angular speed. to. and roughness height. it. Determine suitable dimension- less parameters and express the functional dependence among them. The test {using air} on a i-hscale model Frisbee is to be geo- metrically. kinematically. and dynamically similar to the proto~ type. The prototype values are V, = 5 mfs and mp = 100 rpm. What values of V," and mm should be used? Given: Model of Frisbee Find: . Dimensionless parameters; Model speed and angular speed Solution: The ﬁtnctional dependenoeisF = F(D,V,Lo,h,p,p.) whereFrepresmtsliﬁordrag From Buckinghaml'l F 2 = f[p-—v2,ﬂ,£] p-Vz-D [1. V D p N -D p -V -D p D For dynamic similarity M = w vm = “flu—RE vm = 5.2 x (1) x [i] x (1) Vm = mg pm Pp pm Dm up 3 1 s “’m‘Dm “’p'Dp Dp Vm (4 [20] A] = -_- ._._ = 100. .. __ = 1600 so Vm Vp “’m wpovp “’m 1‘me 1x 5 tom rpm EH3 iﬁﬁi n:- a 3 ii .... ‘ i NJNON‘L Problem 7.76 [2] Guilt: 10W mink/'19 'ﬁ gag-Mlﬁyaimihr mods! Mf- of moﬁlfuwﬂow: . ' , variable. H'ohm Mm, mum Rue. 4p . 29.3131 WWW“ 0. 1:25m‘fmn Mai-7 ( mkglm' ‘Hﬁkeim' Mam-5W . w :53 mm - Mm]: Dmefu D 150mm so mm Fm): Missing mlmﬁm dig/mm (can, gm)” «Maw. .Somtaéa: AW, AWW 77‘— "MW. Assume «0- ﬂag. «no: G AP 9 P w 0 n -5 Mmctms ® Choose. manta: {Wm/1m 0'me ® gt 13.7: "f; '% L P *3 primary Jammy. ® term-gown erapMﬁr'ng mam. m-rss CS) mm n—m-s-a .z dbmnbnw paramount result (QM; 7"- - ¢“~‘D°AP -!€-J(¢rwg. - How M:dﬂ-o 4..., - ' {Jr-til L : ‘uh‘l'C"! Io dg—nz} 1T: 1: i‘ n; I: WTF'fljv' if —b-2 ‘0 {9: "Z PW‘D H l- s 7r!- “Fa“‘Dca ' @ﬂé) {L)°% - _ H'L't' “‘4'0 41-0 La 1 “ﬁat-“1+3 -0 was}? =51... 111-;§-5-£t3v ”ms. 77‘, '- fhl'ﬁ) ‘Frr #:th é:¥-«.a—ﬁéa. Flow: m‘gdqﬂ'Mf'Pldéﬂgﬁl'mfw. mm ImMﬁé. .SQMJ/u:b. 771m ﬁr Jamming Sinatlaxﬁly, If 755'": “than 1730, qup. am I Vgﬂq‘ﬁ—ES‘IEp'Ege-ﬂi am‘ap(:%% )3 0.07930? a," 2 0.0793, 3.234;"; a 0.0m: M‘s/M nil ADM m F - - 7!? - ' App ”Pm "" FM}. ‘ P (paw; ’ ‘ 92 ‘83 l t _ ’ ‘ I .5 #1” APm(49-r)(m)('-3) - '7’“ ”3““ 52 m {This mqu-ﬁ Maggi: meﬁct of wicoélwg. } ...
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Assignment 11 Solutions - Problem 7.30(In Excel 7.30 The...

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