The lift and moment on a flat plate 
From (73), the coefficients are given by 
2 
So = Fy S06 a $8, = (z,) sec a tan a, 
NG 
a |r sec a(sec? a + tan” a), 
4 
Gy = (3) sec a tan a(5 sec? a + tan? a), 
8, = 77/48d?; 83 = 7774/1920d?, 
with a = 7(b—a)/2d. 
193 
(76) 
It may be verified that if we make b and d infinite, or a and d infinite, 
these expressions reduce to the former results for a semi-infinite stream 
bounded, respectively, by an upper free surface or by a lower rigid plane. 
For the particular case, a = b = dd, we obtain 
/), 2 (9n\2 
ijl = 1-5 (F)sina +5 (+ (1 + 18sin?) 
»\3 
4 (sin #— 14 sin?) 
+) (11+ 882 sin? — 3712 sin? @) + 
and M/M,=1- 
2p) 4 2p 
| sind +2, rae “(1 +36sin2 0) 
aS 
a sin’ @) 
‘a l + 3 sin® 12 
The follo W Ing numerical V alues may be compared with 
previous sections: 
6 = 10°; 2p/d = 0-2 
ald 0-3 0-4 0-5 0-6 
De 0-924 0-942 0-953 0-956 
M/M, 0-928 0-943 0-949 0-951 
(77) 
(78) 
those in the 
0-7 
0-960 
0-948 
Tn this case the relative variation near the middle of the channel is much 
less than when the boundaries are of the same kind. 
454 
