A Treatise on Hydrostatics and Hydrodynamics |
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Page 39
... displaced by the solid . 45. PROP . To find the resultant pressure on any surface of a fluid at rest under the action of any given forces . Let p be the pressure , determined as in Chapter II . , at any point ( x , y , z ) of a surface ...
... displaced by the solid . 45. PROP . To find the resultant pressure on any surface of a fluid at rest under the action of any given forces . Let p be the pressure , determined as in Chapter II . , at any point ( x , y , z ) of a surface ...
Page 45
... displaced , and acts in a vertical line through its centre of gravity . Hence it follows that the weight of the body must be equal to the weight of the fluid displaced , and that the centres of gravity of the body , and of the fluid ...
... displaced , and acts in a vertical line through its centre of gravity . Hence it follows that the weight of the body must be equal to the weight of the fluid displaced , and that the centres of gravity of the body , and of the fluid ...
Page 46
... displaced . When there is equilibrium the area APQ is to ABC in the ratio of the density of the prism to the density of the fluid , and therefore for all possible positions of PQ the area APQ is constant ; hence PQ always touches , 46 ...
... displaced . When there is equilibrium the area APQ is to ABC in the ratio of the density of the prism to the density of the fluid , and therefore for all possible positions of PQ the area APQ is constant ; hence PQ always touches , 46 ...
Page 49
... displaced is IIg 9 ( 2 + 2 ) € Χδα , k k and the whole weight of air displaced = S " IIg k _g ( 2 + x ) € Xdx Пд IIg - = € k k - h € Xdx . 0 0 The form of the balloon being given , X is a known function of x , and if W be the weight of ...
... displaced is IIg 9 ( 2 + 2 ) € Χδα , k k and the whole weight of air displaced = S " IIg k _g ( 2 + x ) € Xdx Пд IIg - = € k k - h € Xdx . 0 0 The form of the balloon being given , X is a known function of x , and if W be the weight of ...
Page 50
... displaced = [ ' guzZdz . a Let be the depth of the centre of gravity of the solid and Vits volume , then V z = = [ ' Zzdz ; therefore the weight of displaced fluid = guz V , and if p be the density of the solid , its weight = gpV ...
... displaced = [ ' guzZdz . a Let be the depth of the centre of gravity of the solid and Vits volume , then V z = = [ ' Zzdz ; therefore the weight of displaced fluid = guz V , and if p be the density of the solid , its weight = gpV ...
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Common terms and phrases
angle angular velocity axes axis vertical Cambridge centre of gravity centre of pressure co-ordinates cone constant curve cylinder D'Alembert's principle density depth determine direction disc displaced fluid distance dy dx dz dy elastic fluid equal pressure equilibrium filled with fluid floats fluid at rest fluid displaced fluid pressure force free surface function given Hence homogeneous horizontal plane immersed incompressible fluid inelastic latus rectum length mass of fluid mercury obtained orifice oscillations parallel particles perfect differential perpendicular piston portion position of equilibrium quantity of fluid radius ratio resultant pressure rotation shew solid specific gravity sphere spherical spheroid string suppose surfaces of equal temperature tension tube University of Cambridge vapour vertex vertical plane vessel vibrations volume wave weight whole pressure аф
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