A Treatise on HydrostaticsMacmillan and Company, 1894 - 536 pages |
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Page 64
... curve , when placed in a vertical plane with G , the C.G. of the area , at a depth h feet in liquid ( when h is called the mean depth of the area ) , we divide up the area A into small elements AA , and denote by z the vertical depth of ...
... curve , when placed in a vertical plane with G , the C.G. of the area , at a depth h feet in liquid ( when h is called the mean depth of the area ) , we divide up the area A into small elements AA , and denote by z the vertical depth of ...
Page 66
... curve in the plane of A. Suppose the plane turned through the angle 0 , then the new depth of the element AA is h + y sin 0 + z cos 0 ; so that y , z denoting the coordinates of the new C.P. with respect to the old axes Gy , Gz , fixed ...
... curve in the plane of A. Suppose the plane turned through the angle 0 , then the new depth of the element AA is h + y sin 0 + z cos 0 ; so that y , z denoting the coordinates of the new C.P. with respect to the old axes Gy , Gz , fixed ...
Page 80
... curve EF ; and consider separately the horizontal thrust perpendicular to the plane By on the two portions of the surface BC into which it is divided by the curve of contact EF . But as the horizontal thrusts are in opposite directions ...
... curve EF ; and consider separately the horizontal thrust perpendicular to the plane By on the two portions of the surface BC into which it is divided by the curve of contact EF . But as the horizontal thrusts are in opposite directions ...
Page 87
... curve , and immersed in liquid , is the resultant of a force perpendicular to the plane of the base , and of a force represented by the weight of the liquid enclosed by the surface acting through its centre of gravity . 88 EXAMPLES ON ...
... curve , and immersed in liquid , is the resultant of a force perpendicular to the plane of the base , and of a force represented by the weight of the liquid enclosed by the surface acting through its centre of gravity . 88 EXAMPLES ON ...
Page 114
... curve becomes a similar hyperbola C , D ,, having the same asymptotes OA and OE ; and it is convenient for con- tinuity of measurement to choose W , so that the initial ordinate AC , of the new hyperbola is equal to the final ordinate ...
... curve becomes a similar hyperbola C , D ,, having the same asymptotes OA and OE ; and it is convenient for con- tinuity of measurement to choose W , so that the initial ordinate AC , of the new hyperbola is equal to the final ordinate ...
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Common terms and phrases
angle angular velocity atmospheric pressure axis B₁ B₂ balloon barometer barometric height Bernoulli's Theorem Boyle's Law cargo catenoid centre of pressure circular cm³ cone cross section cubic curvature curve of buoyancy curve of flotation curve of statical cylinder denotes depth diameter displacement distance diving bell draft dynamical stability ellipse equal pressure equation equilibrium feet filled FLOATING BODY fluid force free surface ft-lb ft-tons ft² ft³ given gravity heel height h horizontal plane hydrometer hydrostatic hyperbola immersed inches inclined kg/cm² lb/ft² lb/in² length mercury metacentric height parabola paraboloid parallel pendulum perpendicular piston plumb line position of equilibrium Prove pump radius rotation ship siphon solid specific gravity sphere spherical suppose surface of buoyancy surfaces of equal tangent temperature tension tetrahedron theorem thrust tons tube upright position valve velocity vertex vessel volume water line area weight
Popular passages
Page 53 - Pitcher, that so at least he might be able to get a little of it. But his strength was not sufficient for this. At last seeing some pebbles lie near the place, he cast them one by one into the Pitcher ; and thus, by degrees, raised the water up to the very brim, and satisfied his thirst.
Page 93 - Archimedes stated that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid.
Page 107 - The unit or standard measure of capacity from which all other measures of capacity, as well for liquids as for dry goods, shall be derived, shall be the gallon containing ten imperial standard pounds weight of distilled water weighed in air against brass weights, with the water and the air at the temperature of sixty-two degrees of Fahrenheit's thermometer, and with the barometer at thirty inches.
Page 133 - Bronze contains 91 per cent, of copper, 6 per cent. of zinc, and 3 per cent, of tin. A mass of bell-metal (consisting of copper and tin only) and bronze fused together is found to contain 88 per cent. of copper, 4-875 per cent, of zinc, and 7-125 of tin.
Page 7 - When this continuous alteration of form is only produced by stresses exceeding a certain value, the substance is called a Solid, however soft it may be. When the very smallest stress, if continued long enough, will cause a constantly increasing change of form, the body must be regarded as a Viscous fluid) however hard it may be.
Page 204 - ... horizontal: if 2a be the vertical angle of the cone, and /3 the angle between the plane base and the shortest generating line, shew that cot /3 = cot 4a - } cosec 4a.
Page 103 - The weight in vacuo of the platinum weight (mentioned in the First Schedule to this Act), and by this Act declared to be the imperial standard for determining the imperial standard pound, shall be the legal standard measure of weight, and of measures having reference to •weight, and shall be called the imperial standard pound, and shall be the only unit or standard of weight from which all other weights and all measures having reference to weight shall be ascertained.
Page 280 - Defence of the Doctrine touching the Spring and Weight of the Air . . . against the Objections of F.
Page 185 - When a small movable load is placed at ff the bridge is depressed uniformly: when the load is placed at a point C the end A is unaltered in level; when at D the end B is unaltered in level : and when at P the point Q of the roadway is unaltered in level. Prove that AG.
Page 103 - Act), and by this Act declared to be the imperial standard for determining the imperial standard pound, shall be the legal standard measure of weight, and of measure having reference to weight, and shall be called the imperial standard pound, and shall be the only unit or standard measure of weight from which all other weights and all measures having reference to weight shall be ascertained.