1、#.tTEGINICAL IWDH3. .No. 84.-NEW DATA OH THE IJ$WS(N?FLUID RESISTANCE.%(G. IHeselsbergez.Taken frou%hysikalischeZeitsch=ift,l2921, vol. 22.Haroh, 1922. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS.T(JNI
2、CALNOENo, 84,NEW DATA ON THE LAVS 03FLUIDByC. Jieselsberger.-WMle very noteworthy Tesults aweREfiISTANOE.* .been obtained, esFeciailytn reoent years, iththe aid of the theory Of the rctcnless.fluid, this is the case in a mud smaller degree for the resultsOf the tkeorybased on ELfluid tih internal f?
3、irtion or viPcos-ity, The fuids with which we actually have to do always possess.some viscosity, which is the very reason for the res?.santeen-counteredby a oodymovingin a fluid. ,%ent!d.s ZeSi Elt3nGf? Ordrag has been reduoed to a.mintium by Stremlj.nulg the body,theeffect of the viscosity becomes
4、so small that the actual flmrverynearly agrees with that calculated,on the basi of the theory of :the frictionless or non-viscous fluid.* Thie is not ths oase$however, with shapes which aause a great resistance, since the vis”cosity of the fluid ierephys a decisive role. Thus far all at-tempts at th
5、e quantitative determination of the drag, on t.ebais,of the theory of viscGus f“luids,with the exception of a few sec-,ial oases, have met uith but slight suooess. For this reason,whenever a more .acou-r.ateknowlefi.geof the drag is desiable, it.* Fmm !lFhytiikalischeZeitgchrift,:l1921, Vol. 22, p,
6、321-328.* l?hrmam, Theorie und experimentelleUntersuchungyenan Ballon-.ViwisllenjDissart,J G for example, in the ease of aerofwil, the greacesprojected area. The dimensionless coefficient c is terw.sdthecoefficientof drag. For a long time the opinioa held, maiy onJ the stzength of l?ewtonsconception
7、 of the reistanceof the air, that for a given fluid this coefficientof drag is independentof the velocity and of the absolute size of the body and my ELC-oodinglybe regarded as a oonstantwhose value depends only onthe Seometricai.shape of the body. It was thought possible, frcnthe knowledge of the d
8、rag coefficient obtainedfor a singleve-looity of a given body by r,eansof the above drag formula), todetermine the drag for any other size of the body and for anyother velooity, geometrloal similarityof shape being assuued.,Provided by IHSNot for ResaleNo reproduction or networking permitted without
9、 license from IHS-,-,-a71-3-.In reality, as we shall see, the relations are not nearly sosimple.Ioreaccurate experiments on the mutual influence of theforces which produce the drag, have shown that the coefficient ofdrag remains constant only for geometrically similar flows. Thelatter do not however
10、 necessarily follow from geometric similazity of the bodies experimentedupon. The decisive conditions.for the production of geometrically similar flows were first de-% termined by O, Reynolds. If any desired ltnear dimension of tLebody (whichmust however be identical in the cases compared) isdesigna
11、ted by d and the kinetic viscosity by V = 11p(inwhich is the coefficient of viscosity), the two flows are ge-m= R is the sameometrically simiiar only when the quotient in both cases. The coefficient R is dimensionless and is calledReynolds number from its discovere.Consequently, it oamot be eected t
12、hat the coefficient ofdrag c (mhioh characterizesthe resistance of a body) will re-Smain unchanged in the transition to another Reynolds number, for.example, by dhangingthe velocity or thefact, a dependence of the coefficient ofaetei X# is observed for most bodies.size of the body. Indrag on Reynold
13、s para-The kind of ckange isdetermined by the geonetrioal shape of the body. The aboveexpression is usually employed for the drag, even in the cases wherec is not a constant. The least changes in the coefficient ofdrag occur for bodies with sharp edges, when the latter are perpen-dicular to the dtre
14、ction of flow. Thus, for example, according to .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-*y revious on-4?-sharp-edged.lgw,the coefficient of drag zexains constant for a tide rangef Reynolds num;ersand ha a value of about c = 1.1. On thecontary
15、, bodies with convex upper surfaces aay ,ggvevery differ-ent results. With Reynolds numbers (whichare small in compazisufiwith unity) the drag increases dizectly as the velocity, as wasfirs% demonstratedby Stokes for the case of falling syheres.a71a71 This flow is characterizedby the fact that here
16、the inertia oon-ithour syrnkok,)c = R (2.C02 - lzlrt).in which R represents the Reynolds number with reference to thediameter of the cylinder. This formula is derived from an approx- ;imation theory and is only applicable for values of R which azesmall with reference to unity. The values correspondi
17、ngtO th.iS* A detailed description of this arrangement,which has hitherto.been principally employed for testing aerofoils in a tvo-d-men-sional flow is given in lZeitschriftffirT?iugtechnikund l.%tor-titschiffaart,rf1919, p,95, and inlErge-ouisseder Aerodynanis-.then Ver8uchsarstalt,lrfirst report,
18、1921, pp. 54-53, pu-oishedby R. Oldenbowg,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-7-.fomiula ars zepzesentedby a dash.line in Fig. 1. It is evidentZh.atthe contlnla%ionof the curve passing through the experineri-tal points connects well witht
19、he oourse of the calculated ourve,so that the regim. in whiah the experlaenis can m longer be mr-ried out, is bridged over, with R (U23, them is a very not-iceable downward deviation, confirmedhowever from another side*From R = 15,GMl to R = 180,000, the quadratic law of drag isapproximately satisfi
20、edby the value of c = 1.2.b With R N 2OG,000, a very rapid fall of the c!kagcoefficient(from 1=2 to 0.3) takes place. A.vezy similar behavior had been .Previously observed in determining the resistance of spkeres* Iand afterwards also for many other bodies with convex upper sur-faces. The Reynolds n
21、unher correspondingto this transitionalregion is usually designated as the llcritioalReynolds numbe?.*!The decrease of tks Jrag ooef.ficientis 30 great in the ?egion,that even the ahsclute value of the drag for a cylinder ofgivendiameter, contzary tg all previous experienoe, decreases with in-.oreas
22、ing veiocity. The quantitative relations are shown by Fig.2,in which the drag in kg per meter length of a oylinderof 30 cm* E. F. Relf, ltDiscussionof the Results of Measurements of theResistance of Wires, with some Additional Tests on the Resistanceof Wices of Small Diemetez,tTechnical Report of Ad
23、visory Cormittee for Aeronautics, 1923-1914,p.47.* G, Eiffel, l)Surla Resistance des %heres clansItair en r;ouve-H.ent11Co further, Capt. G. Oons-%anzi,pllAl,cuneesper:enze di idroinamica,1!Rendiconti delle espez-ienze e degli studi nello stab, di esp. e constr. aeron. del genie,# Vol. 11, IJo.4,Rom
24、e, 1912; L. Frandil, Der LuftwiderstandvonKugeln Nachri C. Wieselsberger, ffirFlugteclmikund Motorluftschiffahzt,1S14, p,140,ZeitschriftProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8-*(iiametezis plotted against the velocity of tke air.:surface. I
25、t is seen that in the lattercritical number, which is here about Rcotinuous line was ob-aith a roughthe dashline, ,case, after passing te= 70,000 a rapid inceaseof the drag coefficientagain takes plac, so that even for”thisb region the quadratic law of resigtce is yTAOean obeyed with aconstant coeff
26、icientof drag. It will be an essential task.for ex-Frifin%l aezodynauics to find theexplanationof these peculiar phenomena,In concluding,thanks to Professorthis work.the wti,tierwishes to eress his ;ieartiestPrandtl for the active support he has 4oi_J.1. . -1 i +.:.,/.l-,; l,iy!+20 .,._ -, . ,_. i .
27、 - . cj p ./i ,L:mb,4 or lal - .4;. d. l- -1- - - - -b -l6. -“-”-” 1-“1 14. L.-. -c M- - k -t3.- “- +,2. i.-.- . +_ -1.5 - -:-,L.-._.-.“1.2- 1,0 1 i-.,.,_,_._- _ -,._, t-. .- -l- :jt l, t .- .- .-.”, .-.I ,.;.r- -,:;:ii:;:;1I =QK)d=$ t6)-e-= “ H I - ,- .-_. ._: - I-A- . -1-. 1-1 i-. .l”-”-”-“- “-l”-
28、” - - - “ “”1- “- - -”-,+ Oz,P.i!:. :.;_l;= . . ,04.1 .-.-J .“ -1j-L - “yi.j.i.1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.D(kti).3C2.Fig,“,. “,. ., 11 / .i s-(”- “=-_ -_.- : 0 :-.-”+- ;,R -.-.,b-1 IIi-3 -q- -: I I t 1-J - -.- . . .i“. -Fig.?.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
