All Mcq Quiz4

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Your Answer Correct Answer « Correct. Assume that the flowrate, Q, of a gas from a smokestack is a function of the density of the ambient air, p,, the density of the gas, o, within the stack, the acceleration of gravity, g, and the height and diameter of the stack, h and d, respectively. Use p,, d, and g as repeating variables to develop a set of pi terms that could be used to describe this problem. 0 =¢<& fi) asgl? pad
Show Attempt History Your Answer Correct Answer A 1/10™ scale model of an airplane is tested in a wind tunnel at the same Reynolds number as that of the full scale airplane. (FIA) pV? 2 " The drag coefficient of the model is then 1/100% that of the full scale airplane. 1/10™ that of the full scale airplane. the same as that of the full scale airplane. 10 times that of the full scale airplane. 100 times that of the full scale airplane.
Your Answer Correct Answer « Correct. Water sloshes back and forth in a tank as shown in the figure below. The frequency of sloshing, w, is assumed to be a function of the acceleration of gravity, g, the average depth of the water, h, and the length of the tank, |. Develop a suitable set of dimensionless parameters for this problem using g and | as repeating variables.
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Your Answer Correct Answer « Correct. Because of surface tension, it is possible, with care, to support an object heavier than water on the water surface as shown in the figure below (see the Video). The maximum thickness, h, of a square of material that can be supported is assumed to be a function of the length of the side of the square, | the density of the material, p the acceleration of gravity, g, and the surface tension of the liquid, o. Develop a suitable set of dimensionless parameters for this problem. ——t—— |} [
v VTRt A cylinder with a diameter D floats upright in a liquid as shown in the figure below. When the cylinder is displaced slightly along its vertical axis it will oscillate about its equilibrium position with a frequency, w. Assume that this frequency is a function of the diameter, D, the mass of the cylinder, m, and the specific weight, y, of the liquid. Determine, with the aid of dimensional analysis, how the frequency is related to these variables. Cylinder diameter = D = CL xD? D w=c—~L m = Cn 22 14 w=CD1/l m D? »=Cr——= NV
« Correct. Because of surface tension, it is possible, with care, to support an object heavier than water on the water surface as shown in the figure below (see the Video). The maximum thickness, h, of a square of material that can be supported is assumed to be a function of the length of the side of the square, | the density of the material, p the acceleration of gravity, g, and the surface tension of the liquid, o. Develop a suitable set of dimensionless parameters for this problem. i | [— by _ M2 [ p h =g L) Igp 2 wes(£) g B, (0o 7= lg o h o 1(65) gp
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« Correct. The pressure drop, Ap, along a straight pipe of diameter D has been experimentally studied, and it is observed that for laminar flow of a given fluid and pipe, the pressure drop varies directly with the distance, |, between pressure taps. Assume that Ap is a function of D and |, the velocity, V, and the fluid viscosity, 1. Use dimensional analysis to deduce how the pressure drop varies with pipe diameter. Select the correct answer. . 1 Apufi 1 A —_ P o< o Ap xD Apo<\/5
Show Attempt History Your Answer Correct Answer « Correct. Assume that the flowrate, Q, of a gas from a smokestack is a function of the density of the ambient air, p,, the density of the 8as, Og, within the stack, the acceleration of gravity, g, and the height and diameter of the stack, h and d, respectively. Use p,, d, and g as repeating variables to develop a set of pi terms that could be used to describe this problem.
« Correct. A 1/10% scale model of an airplane is tested in a wind tunnel at the same velocity as that of the full scale airplane. The drag coefficient of the model is the same as that of the full scale airplane. The force on the scale model is then pV? 2 1/10,000t" that of the full scale airplane. 1/1000t that of the full scale airplane. * 1/100%" that of the full scale airplane. 1/10 that of the full scale airplane. the same as that of the full scale airplane.
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« Correct. The height, h, that a liquid will rise in a capillary tube is a function of the tube diameter, D, the specific weight of the liquid, y, and the surface tension, 0. Perform a dimensional analysis using both the FLT and MLT systems for basic dimensions. Note: the results should obviously be the same regardless of the system of dimensions used. If your analysis indicates otherwise, go back and check your work, giving particular attention to the required number of reference dimensions. E_ o by =\ 02 h_, (2 D_(p 7 h yo 5=¢(57) h_ (e D yD? he _ (V7 Dy ~ yD?
« Correct. Because of surface tension, it is possible, with care, to support an object heavier than water on the water surface as shown in the figure below (see the Video). The maximum thickness, h, of a square of material that can be supported is assumed to be a function of the length of the side of the square, | the density of the material, p the acceleration of gravity, , and the surface tension of the liquid, 0. Develop a suitable set of dimensionless parameters for this problem. f——t—— |
Solution h=fp.g0) h=L I=L p=FL?*T? g=LT" o=FL" From the pi theorem, 5 — 3 = 2 pi terms required. Use |, g, and p as repeating variables. Thus, 0, = hi‘g"p¢ and (O @ (LT72) (FLT) = FLOT° sothat c=0 (for F) l+a+b—4c=0 (forl) —2b+2c=0 (forT) Itfollows thata = —1,b = 0,¢ = 0,and therefore h m=7 which is obviously dimensionless. ForIly: Tl = ol'g"p* (FL™) @ (LT72) (FL™T?) = FOLOT° I+c=0 (for F) —l+a+b—4c=0 (forl) —2b+2c=0 (for T) Itfollows thata = —2,b = —1,¢ = —1,and therefore [ M= — * T P Check dimensions using MLT system: I (M12) Pgp (12) (LT-2) (ML~ h I i=(%) MOLOTO ok
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Your Answer Correct Answer « Correct. The pressure drop, Ap, along a straight pipe of diameter D has been experimentally studied, and it is observed that for laminar flow of agiven fluid and pipe, the pressure drop varies directly with the distance, |, between pressure taps. Assume that Ap is a function of Dand, the velocity, V, and the fluid viscosity, . Use dimensional analysis to deduce how the pressure drop varies with pipe diameter. Select the correct answer. ApxD CApx 1 e p o< o Ap /D
“Ap0jaA NS € 10y Y say I 1842 SMOJ[0J SNU) 3| JUBISUOD BWIOS S| 3} 2U3UYM a,__a > 1 adv w0y ay3 Jo g 3snwi (T) b3 ey 05 7 30 dy ‘walqod ay) JO JUBWILIE]S 2] WO a Al ([)(1)4)7 =ady SnUL "SS3]UOISUBLIIP AISNOIAGO S1 UoIYM +( Buiue3uo9) I ] 404 (1-27) (1-21-70) (D (gL - TI) LT BUIsn P3YD (a7) (Le7d) A D (1) ady +(dy Buuteuo) 111105 ‘vondadsul Ag Yo A0 0 LoTod Bil “panbassuLEyd g = ¢ — G ‘Wa10y) 1d B3 wosy L 1d=1 L1T=A T=1 1=d 14=4V AT f=dy uonnjos, “sejoweip adid yam satien doup 2nssa.d a4} Moy 3onpap 0 sisA[eue [euoisuawip 3sn ‘rl A}ISOISIA PN AU PUE ‘A A}10[aA 33 ' pUE g 4O uonduNy € 51dy Jey suinssy sde) 2anssaJd USBIBQ | ‘DIURISIP AU YaIM ARdR.Ip SaLeA doIp 2anssad ayy ‘adid pue piny UBAIS € Jo Mol JeUIWE] O} JeU) PAAIBSGO S1 31 PuE PaIpNIS AjjejuauLadke udaq sey g Ja1welp o adid 1ysiens e Buoje ‘dy ‘dosp ainssaid ayL wajgoid ‘2[0S 0} U3AIS U33q aneY NoA walqoad ay) uj 350y} 23eW 30U Aew SaNJeA 353U "SAN[EA JO 335 Je|Nfed SUO YHM Waqoad 3y3 03 UORIN|OS 343 SMOYS UORN|OS SIY} 930N a5eald Tonnos
‘wa|goJd sy} 2q112S3p 01 Pasn aq pjnod Jewy sui) Id 4o 3as e dojanap 0 sajqeLien Suneadal se 8 pue ‘p °0 asn AjpAIadsa1 ‘P PUE Y HOEIS 3U) JO JIaUIEIp PuE 1yBIaY 34} pue ‘5 KIIARIS JO UONEIBI2ITE B} HOBIS B UM £0/‘sed ay3 Jo ANSUBP a1 0l U1e JuBIGUIE 343 JO A}ISUSP 3] JO UOHOUN B S| 3IBISHOWIS B WOJ SeS € JO D) ‘DIBIMOY 3U3 1By BWINSSY Paudy A
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‘snyL 210j2U3Y pUE‘() = 2 '[— = §'() = DIeY) SMOJ[0} 3] (L103) 0=9t- (1103) 0=2+q+vg—1 (Wao)) 0="» oL T = (L) (D, (=TI (D) 2P = 11 1€]q 404 “ssa|UOISUBWIP AISNOIAGO S| UDIYM v 5= 210j2U3Y pUE() = 2°() = §']— = DIeY) SMO[0} 3] ar (L10y) 0= (T40) 0=o+q+vg—¢ (i 104) 0=r+1 oLgToW = (-2 ) oD, T0) (o TI) 0% =1 :T1og AU L Tpd = ————— = oLoTod 1 ] s10j0101 pue & — | (L103) 0=22-1- (1403) 0=2+q+vg—¢ (Wao)) 0="» e os oLoTolW = (o-27) D, () (1-1¢7) pue ‘sny_ "sa|qelJen Suneadal se § pue p*"d asn ‘painbal suuiay d ¢ = ¢ — 9 ‘waloayy 1d a3 woig T=PT=Y, 1= IN="9 IN="d 1150 (prysidd) = §
Your Answer Correct Answer « Correct. A 1/10™ scale model of an airplane is tested in a wind tunnel at the same velocity as that of the full scale airplane. The drag coefficient > of the model is the same as that of the full scale airplane. The force on the scale model is then pV 2 1/10,000t" that of the full scale airplane. 1/1000%" that of the full scale airplane. = 1/100" that of the full scale airplane. 1/10t" that of the full scale airplane. the same as that of the full scale airplane.
Your Answer Correct Answer « Correct. The pressure rise, Ap, across a pump can be expressed as Ap=f(D,p,w,Q), where D is the impeller diameter, p the fluid density, w the rotational speed, and Q the flowrate. Determine a suitable set of dimensionless parameters. eTextbook and Media
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Solution Please Note: this solution shows the solution to the problem with one particular set of values. These values may not match those in the problem you have been given to solve. Problem The pressure rise, Ap, across a pump can be expressed as Ap =fD,p,», Q) where Dis the impeller diameter, pis the fluid density, w is the rotational speed, and Q; the flowrate. Determine a suitable set of dimensionless parameters. Solution Ap=FL?D=Lp=FL*T?w=T"'Q=01T" From the pi theorem, 5 — 3 = 2 pi terms required. Use D, p, and w as repeating variables. Thus, 0, = ApD*pl o’ and (FL2) @ (FL72)" (17)° = FOLOT so that 1+b=0 (for F) —2+a-4b=0 (forl) 2b 0 (for ) Itfollows thata = =2,b = —1,¢ = =2, and therefore I, = Check dimensions using MLT system: A MLTTE L opeqog D2p? (L (ML) (1~ ForIly: 1L, = QD p’of (L1 @ (FLAT2) (17) = FOLOT° b=0 (for F) 34+a-4b=0 (forl) ~142b—c=0 (forT) Itfollows thata = —3,b = 0,c = —1,and therefore Check dimensions using MLT system: o . 1! = = MLOT" ok Diw (L (1) Thus,

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