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# Sol 4 - P156 A deliver}r vehicle carries a long sign on top...

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Unformatted text preview: P156 A deliver}r vehicle carries a long sign on top, as in Fig. P156. If the sign is very thin and the vehicle moves at 65 mith, (a) estimate the force on the sign with no crosswind. {b} Discuss the effect of a crosswind. Fig. FILEE Solution: For air at 2119C, talte p: 1.2 kgx’m3 and n: LEE—5 leg/“ms. Convert 65 mifh = 29.06 nits. [a] If there is no crosswind, we ma}r estimate the drag force by ﬂat—plate theory: 1.2[2Q.DE) [3} [1.1181 _ [1.03] Re = =1.55ET torﬁulent , {2' = _ — a [1.20291 1 ise—s E } D self [1 .555)” PM = mg] Watts sides] = D.UD291[ %] (cans)E (as) (a) (2 sides] =14 1v Ans. [a] {b} A crosswind will cause a large aide force on the sign, greater than the ﬂat—plate drag. The sign will act like an airfoil. For example, if the 29 mfs wind is at an angle of only 5“ with respect to the sign. from Eq. (Till), CL n:- 2;:rsin [5“]!{1 + 3.025} a [1112. The lift on the sign is then about Lift = CL Lora) vzat .1.- [ooa (twanzsosﬁosna) a so N Ans. {b} Test] a heavy sphere attached in a string shculd hang at an angle 6' when immersed in a stream at velccity U. as in Fig. Pisa. Derive an eapresaicn for H as a functicn cf the sphere and ﬂew preperties. What is E if the sphere is steel {56 = 136} cf diameter 3 cm and the ﬂaw is sea-level standard air at U = 40 rats? Neglect the string drag. Sciatica: 3Fer sea-level air take p: I 225 kgr‘rn3 and Jat: l. TEE—5 kgfm- s The sphere shculd hang sc that string tensien balances the resultant cf drag and net weight: wast Bras rand: , er H=tan'l[ ta— pigtm'ﬁlﬂ?’ {aﬁlﬂn atria:1 J Symbolic answers Fer the given numerical data. first check Re and the drag ceefiicieat. then ﬁnd the angle: 1 223%}{03‘3} ReD=—=B3ﬂl]ﬂ. Fig. alas: cu =a.s l .TSE—ﬁ F=%{c.5xt.225}(4cﬁe.e3f - {1.346 N: w: [asstaasi— 1.2251(931 igteaaii - the N a= tan'lﬂ .D‘JMJ‘lﬁ} - '12- Arts. 100 A piekug truck has a clean drag-area Cy! of 35 ft. Estimate the hersep-ewer requiredtudrive the lruekil 55 miﬂnia} clean and [b] with the 3- by 6-0 Sign in Fig. P103 installed if the rolling resistance is l50 lhf at sea IeveL Solution: For; sea-level air. lake p: 0. 00233 slugfﬂg’ and y: 17213—1 aluyﬂ- 5. Carmen V— - 55 mii'h: 30. Ir" W5. Calculate the drag witlmut the sign: F= Fm“; “snag v1 =15e+ aﬁemzamnﬂﬂﬁf =421 Ihf Fig. em Hemmer = (421K30.T}+550 - 62 hp {clean} Arts. (a) With a Sign added. 11111 = 2.0. read CD = 1.19 from Table 13. Then 0.00233 F = 421...," +1 . Ie[ Jar-.1}: {61(3 1 = 53? lhf. Fewer = FV = 00 hp Arts. {In} 114 Show that the onto-dimensional laminar-thatr pattern with dpttttt = t} u= Uﬂti —eC‘—") u= uIt a u is an exact solution to the bottom-layer equations {7.19}. Find the value of the constant C in terms of the floutr parameters. Are the bmndary cmditions satisﬁed? 1What Flg. F114 might this ﬂowr represent? Solution: Substitute these {our} into the :It-momcntum equation (1 19!?) with é‘ufﬂx = D: or: C: pvnftt = constant c I] If the constant is aagathc, 1.1 does not go to m and the solution represents laminar boundary-layer ﬂour past a ﬂat plate 1with wall suction, tr“ 5 U {see ﬁgure). It satisﬁes at 3 = t]: u = {1 {no slip} and it = cu {suction}: as 1.: —} an, o —} LL, {freestrcam} The thickness :1 where u = H.99Um is deﬁned by cspwvnﬁ'ﬂ}: 0.01,, or H: -4.6,tn'pvﬂ. ...
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Sol 4 - P156 A deliver}r vehicle carries a long sign on top...

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