Boundary Lyer Theory

148 VTI. Boundnry lnycr eqnations for two-dimensionnl flow; boundary lnyer on n plate
Fig. 7.1 1. Skin-friction coefficicnt,
of n flat, plat^ of finite
length at zero incitlcnco
(I) 'f'llrory aftrr 11. Illnsius,oqn.(7.34)
(2) l'l~cnry nncr A. 1'. Mrlrsitrr I 1RI)I.
rqn. (7.00)
A Tlirnry nrter Ih~lain (nolullor% of
Nnvier-Stnkrs cqoaLio~~a)
Here, the trailing edge has been ncco~rnted for, bnt not the displacerncnt effect.
The dingrnrn in trig. 7.11, rcprotlnccd from the work of It. E. Melnik nnd It. Chow [18a],
shows t,l~at t h vnlucs of c, computed with t h aid of eqn. (7.60) ngrec very well with tlie results
obtained frorn the complck: Navicr-Stokes equntions as well as with those of ~nensnrements down
to RI = 10. At Rl = 40 eqn. (7.60) leads to c, = 0.316 which is less than 2% in excess of the exact
vnlnc cl = 0.31 1.
Sertion 1Xj will ret.urn to the discnssion of exact soltltions of houndnry-layer equations of
srcoritl order.
References
111 13airntow, I,.: Skin friction. J. ltoy. Acro. Soc. 19, 3 (1025).
121 I%lnsius, M.: Grenzuchichtct~ in Fliimigkeiten mit kleiner JEcibnng. Z. Mnlh. J'hyn. .SF, 1-37
(1008). Engl. transl. in NACA TM 1256.
131 Bolcy, U.A., and Friedman, M.U.: On the viscons flow aro~rnd the lcading edge of a flat
plntc. JASS 26, 453-454 (1059).
141 Ihrgcrs, J.M.: The motion of n fluid in the borlndnry lnyer along a plane smooth surface.
l'roc. First Intcrn. Congr. of Appl. Meell., Delft 1924 (C.B. Biezeno and J. M. Burgers, ed.)
Delft, 1925, pp. 113-128.
[R] Carrier, G. I?., and I,in, C.C.: On t,tie nnturc of t,ll& bonndnry layer near t,lic leading edge
of a flnt plate. Qnnrt. Appl. Mnth. VI, 63-68 (lp48).
[ti] I)linwnn, S.: Direct n~crcqurcmenta of skin friction. NACA Rep. 1121 (1953).
[7] Van Dyke, M.: Higher npproxi~nntiona in boundnry layer theory. Pnrt 1: General analysis.
JI'M I4, lti1- 177 (1962). I'nrt 2: Application tm lending edges. JFM 14, 481-495 (1!)62).
I'nrt 3: l'nrrrboln in uniform streani. JI'M 1.7, 145-IR!) (1964).
[R] Van Dyke, M.: I'crtnrbntion rnct,hodu in fluid mechanicu. Acnde~nic Pre-%,New York, 1964.
I91 Van 1)ykc. M.: Higher-order boundary Inyer theory. Annonl Iteview of F'luicl Mech. I,
2tiR 2!)2 (I!)(;!)).
[lo] Geraten, K.: Grenzschichteflkkte hiiherer Ordnung. Anniversnry volume com~ncmoratit~g
Professor H. Schlichting's 05th anniveranry (Sept. 30, 1972). lbp. 7215 Inst. f. Stromungumech.
Techn. Univ. at Brnunschweig, 29--53 (1972).
1111 Gersten, I