By W. H. Besant
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Additional info for Elementary Hydrostatics with Chapters on the Motion of Fluids and on Sound
32. THE points of the pressure of a liquid at rest is the same at all same horizontal plane. Take a thin its axis cylindrical portion horizontal, and its AB of the liquid, having ends A, B vertical, and consider the equilibrium of this portion. We have then a body AB kept at rest by the fluid pressures on its curved surface, all of which are perpendicular to the axis of the cylinder, by the pressures on the two ends, which are horizontal, and by the weight of the body. If p and p' be the measures of the pressures at A and B, and a the area of each end, which is taken to be very small in order that the pressure may be sensibly uniform over the whole of either end, the pressures on the ends are pa.
If is the volume of the column described. it = WZK, It will be seen that this is independent of the form of the vessel containing the fluid. This result may also be obtained in the following manner. K Draw through surface, vertical lines to the the boundary of and consider the equilibrium of the portion of fluid The pressure of the surrounding fluid is entirely horizontal, and therefore the pressure on the base must be enclosed. equal to the weight of the fluid If the vessel be of the form indicated by the dotted line enclosed.
42. If two liquids that do not mix together meet in bent tube, the heights of their upper surfaces above their common surface will be inversely proportional to their intrinsic weights. w t A and B be the two surthe common surface, and w', the intrinsic weights of the Let faces, C liquids. Let horizontal planes through A, B, b, and and C meet a vertical line in a, c, and take C' in the denser fluid same horizontal plane as C. in the a TWO 32 The pressure and these are G=w at by equal, be, . and the pressure at Art.