By J. A. Fox (auth.)

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Through an angle au - ay 'Oy 'Ot/'Oy au ay 'Ot that is - aa" y Sy S, l -- B'~-------r~ B \ \ o u - -- ~ 8x 8, a" A Fig. 7 Note that for line OB to rotate as shown in Fig. 7 the value of au/ay must be negative (point B moving in the x direction at a smaller velocity than point 0). The diagonal OC will rotate through an angle of ~ (au _ au) 'Ot 2 ax ay and its rate of rotation will be ~ (au _ au) 2 ax ay Thus Q, the mean angular velocity is Q= ~ (au _ au) 2 ax ay 38 An Introduction to Engineering Fluid Mechanics Vorticity (which will be dealt with later) is usually denoted by the symbol (zeta) and has a value of twice the angular velocity so ~ au au ~ = ax - ay Thus a fluid for which the vorticity is zero is one in which all the fluid elements have zero angular velocity, that is they are not rotating.

7) A spherical vessel of radius 12 ft [4 m] is filled wi th water. The pressure at the highest point is atmospheric. Calculate the magnitude and direction of the resultant force acting on the half of the sphere created by the intersection of a vertical plane through the centre of the sphere and the sphere itself. Also locate the point of intersection of the resultant with the surface of the sphere. Answer: Force: 407 x 10 3 1bf, angle: 33'7° to horizontal, point of intersection: 6·6-Ctbelow horizontal diametral plane [Force: 2·39 MN, angle: 33·7°, point of intersection: 2·23 m below horizontal diametral plane].

Water at ordinary temperatures has a value of u of 0·075 N/m. The value of u decreases with increasing temperature and becomes zero at the critical point-in this state a liquid and its vapour become indistinguishable. 11 Manometry The body of techniques that exists for measuring pressure and differential pressures is called manometry. h Fig. 11 A device that measures pressures is called a piezometer. The simplest of these consists of a vertical tube (see Fig. 11). calculated from p=wh, where w is the specific weight of the fluid.