By J. A. Fox (auth.)
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Extra resources for An Introduction to Engineering Fluid Mechanics
9. y v x Fig. 9 Between these streamlines a fluid flux occurs and as no flow can cross a streamline (by definition) this flux oQ must be made up of flow across AB which in turn must be the same as the sum of the flow across CB and that across AC. The flow across CB is -u ox (ox is negative). Thus oQ = - vox + U oy But at/J -=-v ax and 43 Hydrodynamics 51/1 = - v 5x + u 5y so 5Q=51/1 Thus streamlines, which have been defmed as lines of constant value of the stream function, must also be lines of constant flux; the flux between a streamline of stream function 1/1 and one having a value for its stream function of zero is numerically equal to 1/1.
11). calculated from p=wh, where w is the specific weight of the fluid. The tube must be sufficiently large for surface tension effects to be negligible. Obviously such a device can only be used to measure the pressure of a liquid. Pressure gauges A mechanical device, a Bourdon gauge, is available for measuring pIessures. It consists of a curved tube which tends to straighten when placed under pressure (see Fig. 12). The movement of the free end of this tube is used to drive a multiplying mechanism which rotates a pointer over a dial.
Next consider Fig. 5. The deformation of the element is due to shearing effects. Shear strain cannot be resisted by a fluid and cannot produce shear stresses. Shear stresses can be produced however by rates of shear straining (Newton's law of viscosity) and these are defined as follows. The angle AOB will become A'OB' in time ~t. This reduction in the angle is au ay au ax - ay at/ay + - ax at/ax and the rate of change of this angle is au au ay ax -+Denoting the rate of shear strain by 'Y then .