This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1888 Excerpt: … w, into a single straight line in the plane of w, we must put /g-lV’ A-Jw + B or gfl + Vft’-! (12), where fl = cos a H. When the velocity of the stream at infinity is equal to F, which will be supposed to be the case in what follows, we must change f into fF, and (12) becomes (13). In the plane of z let O be the origin, OB the axis of x; along AB £ must be real and equal to w1, and at A and B %–F1. Hence at all points of the lamina we must have fl 1, and at A and B, fl =–1 and + 1 respectively. Let I be the breadth of the lamina, then since along AB Kf = a and df/dx = u, the limits of integration being determined by fl = cos a +–= + 1.-!£_-l–K-o. sina.,., 4 + Tt sin a–……..-…… which determines the resistance which the lamina offers to the stream, and shows that it depends partly upon the square of the velocity and partly upon the angle which the stream makes with the lamina. The moment of the pressure is The odd terms in /3 contribute nothing to the integral, and therefore The distance of the middle point of the lamina from the origin is cos a/ VK sin4 a; hence the distance of the centre of pressure from line middle point is 3 cos at-32 cos a 4jK”Fsin4a 4 (4 + Tt sia a) If ir a 0, the negative sign shows that the centre of pressure is on the upstream side of the middle point; hence if the lamina be free to turn about an axis parallel to its edges whose distance from the middle point is 32 cos a,1fi,………………… ( it will be in equilibrium. If a = 7r, « = 0; and the lamina will set itself transversely to the stream. When a = 0, x is a maximum and is equal to 32/16, in which case the axis divides the lamina in the ratio 11: 5. 139. The results of equations (15 and 16), which are due to Lord Rayleigh1, may be stated in…
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