By Jonas M. K. Dake B.Sc (Eng.) (London); M.Sc.Tech. (Man.); Sc.D. (M.I.T.) (auth.)
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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 ().
16b, pressure at A is equal to pressure at B and pressure at c is equal to pressure at d because each pair is connected by a continuous column of mercury. On the other hand the pressure at a is not the same as pressure at b. Although they are at the same level they are not in the same continuous fluid column. In solving a manometric problem it is advisable to start from a point at which the pressure is known and work toward the point at which the pressure is desired. Add to this pressure in appropriate steps the changes in pressure calculated from ±'Yh, using positive for movement downward and negative for upward movement.
Thus Pl =Pa 27 Fundamental Concepts of Fluid Mechanics Resolving vertically P2 (BC) =Pa (AC) cos 0 + 'Y/2 (AB) (BC) where the last term on the right-hand side represents the weight of fluid in the prism. 15) The conclusion is arrived at that: 1. 2. the pressure at a point in a column of a fluid (liquid) equals the product of the depth from the liquid surface to the point and the specific weight offluid (liquid); and the pressure at a point in a fluid has the same magnitude in all directions. Thus pressure acts normally on any chosen plane through a point.