By Jonas M. K. Dake B.Sc (Eng.) (London); M.Sc.Tech. (Man.); Sc.D. (M.I.T.) (auth.)
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Extra resources for Essentials of Engineering Hydraulics
Sample text
2 The Basic Physical Laws of Mass, Energy and Momentum Transport The transport of mass, energy and momentum associated with the motion of fluids is observed in nature to obey a basic physical law which Daily and Harleman have called an 'observational' law. Mass transport follows the principle of conservation of matter, heat energy transport obeys the conservation of energy or the first law of thermodynamics and momentum transport is according to Newton's second law of motion. To summarize the laws of conservation, let X be any scalar quantity being transported (mass or energy).
34 Essentials of Engineering Hydraulics ~-- Fh F. v 0 (b) Fluid displaced by surface (a) Flu id above surface Fig. 22 Two cases, one in which the liquid is really held up above the surface and the other when it is imagined to be held up, are shown in Fig. 22. The vertical component acts through the centroid of the volume of fluid held up or dis-placed. The location of the lines of action of the horizontal and vertical components of the forces enables the line of action of the resultant itself to be determined graphicallx or otherwise.
Pressure is always normal to the solid surface. If the pressure corresponding to angle () is p, the pressure force on a small segment made by o() is (pa[j())1 where a is the radius of the cylinder and I is the immersed length of the cylinder. The component of the pressure force in the direction of motion is (paIS()) cos (). The total drag on the cylinder is the sum of the pressure force on all such elemental segments 21T drag =f drag = 2al . 0 From symmetry, pal cos () d() f: p cos 8 d8 Now fp cos () d()is the area under a plot of p cos () against ().