A Treatise on Hydrostatics and Hydrodynamics |
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Page 11
... dx , and therefore dp , is in- definitely diminished , p will be the density at P , and we obtain By a similar process , But dp dp dx dp SIS dy = pX * . = pY , = dp dz pZ . dp = d dx + dp dy + de d = ; dx dy dz : dp = p ( Xd + Ydy + Zdz ) ...
... dx , and therefore dp , is in- definitely diminished , p will be the density at P , and we obtain By a similar process , But dp dp dx dp SIS dy = pX * . = pY , = dp dz pZ . dp = d dx + dp dy + de d = ; dx dy dz : dp = p ( Xd + Ydy + Zdz ) ...
Page 11
... dy = pXdx . Proceeding to the limit when dr . and therefore definitely diminished , p will be he iensity at 2.ada dp = By a similar process , dx 32 22 But dp = = dp dp = the equation which deter 17. It that o fr Ax τρί fore essential ...
... dy = pXdx . Proceeding to the limit when dr . and therefore definitely diminished , p will be he iensity at 2.ada dp = By a similar process , dx 32 22 But dp = = dp dp = the equation which deter 17. It that o fr Ax τρί fore essential ...
Page 12
... dx dy dZ dY dX dz = = dy dx dy dz ' dz = dx ' which are in this case always satisfied , and therefore the equili- brium of a homogeneous fluid under the action of such forces is always possible . 19. If the fluid be elastic , an ...
... dx dy dZ dY dX dz = = dy dx dy dz ' dz = dx ' which are in this case always satisfied , and therefore the equili- brium of a homogeneous fluid under the action of such forces is always possible . 19. If the fluid be elastic , an ...
Page 14
... dx dy dz which are proportional to the direction cosines of the normal at the point ( x , y , z ) of the surface A , are equal to dp , dp dp dx ' dy ' dz ' respectively , i.e. to pX , pY , pZ , and are therefore proportional to X , Y ...
... dx dy dz which are proportional to the direction cosines of the normal at the point ( x , y , z ) of the surface A , are equal to dp , dp dp dx ' dy ' dz ' respectively , i.e. to pX , pY , pZ , and are therefore proportional to X , Y ...
Page 15
... dx do dp de dy + de dz = 0 dy dz . ( B ) . These then are the differential equations of surfaces which by their intersections determine curves of equal pressure and density . From ( B ) we obtain dx dy dp y dp X dp dz Z dy Y dz - z dp ...
... dx do dp de dy + de dz = 0 dy dz . ( B ) . These then are the differential equations of surfaces which by their intersections determine curves of equal pressure and density . From ( B ) we obtain dx dy dp y dp X dp dz Z dy Y dz - z dp ...
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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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