By J. A. Fox (auth.)
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Extra resources for An Introduction to Engineering Fluid Mechanics
27 Definitions and Hydrostatics Rood surface 15' 15' [5mJ [5mJ 100' [33m] Fig. 22 40' [13m] ~I (6) A rectangular leaf gate is fitted into a side wall of a reservoir mounted in a vertical position. Its width is 4 ft [1·3 m] and its height is 10 ft [3 m] . Its upper edge is hinged to the reservoir wall and its lower edge is equipped with a retaining device that holds the gate vertical against the forces applied to its upstream face by the water. Its downstream face is at atmospheric pressure. Calculate the force on the hinge and the force on the retaining device when the water surface is 20 ft [7 m] above the level of the gate hinge.
Ax u=-=-- ay 46 An Introduction to Engineering Fluid Mechanics v y x Fig. 10 The source Certain idealised fluid motions can be considered which can in fact not occur in the real universe but which when compounded with other motions give resultant fluid situations that are of very great significance. These are the source, the sink, the doublet and the vortex, and uniform flow. A source is a point in space from which fluid is emitted at constant rate. This concept cannot of course represent a real situation.
8y 8x u x Fig. 3X 3y ax 3X) 3y + u3x - u3y - (U + ay au au ax ay ~=-- using the convention that circulation anti clockwise around the element is positive. This result is the same as that obtained previously. Before continuing to describe how these concepts of stream function, velocity potential, circulation and vorticity can be used to analyse some flow situations it is necessary to give the expressions for velocities in terms of the derivatives of the velocity potential and stream function expressed in cylindrical coordinates.
An Introduction to Engineering Fluid Mechanics by J. A. Fox (auth.)