A Collection of Problems in Illustration of the Principles of Theoretical Hydrostatics and Hydrodynamics |
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Page 1
... Pressure of Homogeneous Incompressible Fluids on the Surfaces of Immersed Solids . LET K denote any indefinitely ... centre of gravity of the surface of the solid below the surface of the fluid , then , A repre- senting the surface of the ...
... Pressure of Homogeneous Incompressible Fluids on the Surfaces of Immersed Solids . LET K denote any indefinitely ... centre of gravity of the surface of the solid below the surface of the fluid , then , A repre- senting the surface of the ...
Page 2
... centre of gravity are known , this corollary enables us at once to determine the 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 ...
... centre of gravity are known , this corollary enables us at once to determine the 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 ...
Page 4
... 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 will be ...
... 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 will be ...
Page 5
... centre of gravity of the surface , which is evidently the middle point of the axis , being equal to ( h + h ' ) , it follows that the whole pressure on the cylinder must be equal to πgpr ( r + l ) ( h + h ' ) . 3. An isosceles triangle ...
... centre of gravity of the surface , which is evidently the middle point of the axis , being equal to ( h + h ' ) , it follows that the whole pressure on the cylinder must be equal to πgpr ( r + l ) ( h + h ' ) . 3. An isosceles triangle ...
Page 6
... pressure on the lower portion of the triangle will be seven times as great as that on the upper . 4. To find the pressure which a diver sustains when the centre of gravity of the surface of his body is 32 feet under water . " The ...
... pressure on the lower portion of the triangle will be seven times as great as that on the upper . 4. To find the pressure which a diver sustains when the centre of gravity of the surface of his body is 32 feet under water . " The ...
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Common terms and phrases
ABCD Albert Girard altitude angular velocity aperture axis axis of revolution axis vertical base Bernoulli Bossut Traité Cambridge centre of gravity centre of pressure cone constant quantity cos² Daniel Bernoulli denote the density denote the length denote the radius depth determine distance dx dy Edition elastic equal equation filled with fluid floating fluid displaced free surface given hemisphere Hence humidum inclination incompressible fluid integrating James Bernoulli John Bernoulli lamina latus rectum mass motion oscillation parabola paraboloid of revolution parallel particles Phoronomia portion position of equilibrium position of rest problem ratio represent right angles sesquialterum sin² small orifice solid cylinder specific gravity sphere supposed Traité d'Hydrodynamique Treatise triangle tube vertex volume w³y² weight whole pressure
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