A Collection of Problems in Illustration of the Principles of Theoretical Hydrostatics and Hydrodynamics |
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Page 1
... whole surface of the solid will be equal to gpΣ ( Kx ) , where denotes the summation of a series of terms , of which Kx is the general type , the limits of the summation being defined by the boundary of the immersed surface . COR . 1 ...
... whole surface of the solid will be equal to gpΣ ( Kx ) , where denotes the summation of a series of terms , of which Kx is the general type , the limits of the summation being defined by the boundary of the immersed surface . COR . 1 ...
Page 2
... whole pressure upon it . COR . 2. Suppose that the area A is divisible into a finite number of areas of known magnitudes , A ,, A , A , & c . , the positions of the centres of gravity of which are known , then the pressure on ( 4 ) will ...
... whole pressure upon it . COR . 2. Suppose that the area A is divisible into a finite number of areas of known magnitudes , A ,, A , A , & c . , the positions of the centres of gravity of which are known , then the pressure on ( 4 ) will ...
Page 4
... whole pressure upon it . Let a , b , be the lengths of two unequal sides , and h the depth of its centre of gravity , that is , of its middle point , below the surface of the fluid ; then , by COR . ( 1 ) , the whole pressure upon it ...
... whole pressure upon it . Let a , b , be the lengths of two unequal sides , and h the depth of its centre of gravity , that is , of its middle point , below the surface of the fluid ; then , by COR . ( 1 ) , the whole pressure upon it ...
Page 5
... whole cylinder , remains constant , the whole pressure on the cylinder will be invariable , however the inclination of its axis to the surface of the fluid may be varied . We have solved this problem by means of COR . ( 2 ) . It might ...
... whole cylinder , remains constant , the whole pressure on the cylinder will be invariable , however the inclination of its axis to the surface of the fluid may be varied . We have solved this problem by means of COR . ( 2 ) . It might ...
Page 7
... whole pressure on the plane surface . Let OA , OB , ( fig . 2 ) be the two tangents to the parabola HABK , and let OA , OB , produced indefinitely , be the axes of x , y , respectively . Let a , ß , be the inclinations of OA , OB ...
... whole pressure on the plane surface . Let OA , OB , ( fig . 2 ) be the two tangents to the parabola HABK , and let OA , OB , produced indefinitely , be the axes of x , y , respectively . Let a , ß , be the inclinations of OA , OB ...
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Common terms and phrases
Albert Girard altitude angular velocity aperture axem axes axis vertical base Bernoulli body Bossut Bossut Traité Cambridge centre of gravity centre of pressure coinciding cone cos² cube Daniel Bernoulli denote the density denote the length depth determine distance dx dy Edition efflux elastic equal equation filled with fluid floating fluid displaced force free surface given hemisphere Hence humidum Hydrodynamique immersed vertically inclination incompressible fluid James Bernoulli lamina late Fellow latus rectum motion parabola parallel particles portion position of equilibrium position of rest problem quæ ratio required pressure resultant pressure right angles sesquialterum sin² small orifice solid cylinder specific gravity sphere supposed tangent Treatise triangle Trinity College unit of pressure University of Cambridge vertex vertical line vessel volume weight whole pressure
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