An Introduction to Engineering Fluid Mechanics by J. A. Fox (auth.)

By J. A. Fox (auth.)

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8r + - 88 = - - + 0 ar a8 27t r t{! = iL lo~ r + constant 27t or An Introduction to Engineering Fluid Mechanics 48 ¢'=3 -+------~---+----~~----r---+-------~¢'o=O ¢'=-4 ¢'=-3 Fig. /, _ Q () _ Q 21t - 21t tan 'l'source - -l(Y) :; omitting constants. These functions are illustrated in Fig. 16. 11 The Sink A sink is the opposite of a source, that is it is a point in space at which fluid disappears. Its stream function and velocity potential is simply obtained by using a negative value for the total flux Q.

6). The rate of change of the angle AOB will be au/ay. This is really a special case of the result obtained above and is obtained by giving av/ax the value of zero. B' B e f / y / I V 0 u x Fig. 4 Rotation ofa fluid element The rotation of a fluid element is illustrated in Fig. 7. In time to position OA', that is through an angle au ax ax'M/ax that is at OA rotates au ax at and line OB rotates to position OB' Le. i!. ax Ox 13 f 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 longer side is inclined at 60° to the vertical. (See Fig. 21). Calculate the magnitude, direction and location of the force acting upon one side of the plate due to water pressure. o I·OOm \:1 9~ Fig. 21 Area of plate = 2 m 2 = 0·5 + 1 cos 60° = 1·00 Force = area x pressure at centroid = 2 x 9810 x 1·00 Depth of centroid = 19·6 kilonewtons This force acts perpendicularly to the plate so it is acting in a direction which is 30° to the vertical. Location of centre of pressure-: X=x +kb/x i = O·S/cos 60° + 1 = 2·0 0·333 2·00 X= 2·00+--= 2·17 m 26 An Introduction to Engineering Fluid Mechanics Questions Questions throughout this book are set in both the British and the SI systems of units.

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