By J. A. Fox (auth.)
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Extra resources for An Introduction to Engineering Fluid Mechanics
As before As wair is very much less than Wf the value of Wair/Wf is very much less than 1. For instance, if water is the working fluid Wair/Wf = 1/780. p Fig. 15 Micromanometers A number of devices are available for the measurement of extremely small pressures. In the range of small, but significant pressures, the slant tube manometer can be used (see Fig. 16). The value of 1m can be converted to the eqUivalent head reading by mUltiplying by sin O. F or small pressures multi-fluid manometers can be used (see Fig.
3). x y Fig. 3 These body forces are usually denoted by X for the body force, that is force/unit volume, in the x direction y for the body force, that is force/unit volume, in the y direction Z for the body force, that is force/unit volume, in the z direction Then the force in the x direction due to pressure forces and body forces is " ax 3x ) 3y 3z + X 3x 3y 15z (- ap This must cause an acceleration of the element of du/dt. ap ax - - 3x 3y 3z du dt + X 3x 3y 3z = p 3x 3y 3z - ap du --+X=pax dt Now, by defmition of a total differential d a dx a dy a dz a ax dt ay dt az dt at -=--+--+--+dt 33 Hydrodynamics so au au au au ax ay az at ap (au au au au) --+X=p u-+u-+w-+ax ax ay az at du -=u-+u-+w-+dt By an exactly similar process equations can be developed that describe the forceacceleration relationships in the y and z directions, that is ap au au au ) --+y = p (au u-+u-+w-+.
The wid th of the bridge is 30 ft [10 m]. g' [3m] 100' [30m) Fig. 24 level on both sides of the bridge is level with the road surface. Also calculate the resultant force acting on one half of the underside of the bridge from springing to crown in magnitude and direction. Answer: 2·21 x 10 6 lbf, 1·16 x 10 6 lbfat 18'2° to the horizontal - - [11·5 MN, 6·11 MN at 20·3° to the horizontal]. (11) A cubical tank, square in plan, with vertical sides contains water to a depth of 3 ft [1 m] overlain by a layer of oil of specific gravi ty 0·9 of 9 ft [3 m] thickness.