A Collection of Problems in Illustration of the Principles of Theoretical Hydrostatics and Hydrodynamics |
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Page 13
... - ing through the circumference of the required circle to a line drawn vertically upwards from the centre of the sphere ; then cos = 1 − √2 . 29. A hollow segment of a sphere rests on its NORMAL PRESSURE OF FLUIDS . 13.
... - ing through the circumference of the required circle to a line drawn vertically upwards from the centre of the sphere ; then cos = 1 − √2 . 29. A hollow segment of a sphere rests on its NORMAL PRESSURE OF FLUIDS . 13.
Page 14
... segment , and r the radius of the sphere , the required pressure will be equal to 4πgpr3 sin2 β 4 ( 1 cos a cos2 4 30. The axis of a given hollow cone filled with fluid is in- clined at a given angle to the horizon ; to find how much of ...
... segment , and r the radius of the sphere , the required pressure will be equal to 4πgpr3 sin2 β 4 ( 1 cos a cos2 4 30. The axis of a given hollow cone filled with fluid is in- clined at a given angle to the horizon ; to find how much of ...
Page 33
... segment of a parabola cut off by a chord passing through the vertex , the tangent at which lies in the surface of the fluid , and inclined at an angle of 45 ° to the axis . The axis of the parabola and the tangent at its vertex being ...
... segment of a parabola cut off by a chord passing through the vertex , the tangent at which lies in the surface of the fluid , and inclined at an angle of 45 ° to the axis . The axis of the parabola and the tangent at its vertex being ...
Page 37
... a 15π 4. A segment of a parabola , cut off by a double ordinate to the axis , is immersed in a fluid the density of which varies as the depth ; the tangent at the vertex of the THE PLANE SURFACES OF IMMERSED SOLIDS . 37.
... a 15π 4. A segment of a parabola , cut off by a double ordinate to the axis , is immersed in a fluid the density of which varies as the depth ; the tangent at the vertex of the THE PLANE SURFACES OF IMMERSED SOLIDS . 37.
Page 38
... segment , the required depth will be equal to zh .. 5. A segment of a parabola , cut off by a double ordinate to the axis , is immersed in a fluid , the density of which varies as the depth ; the base of the segment lies in the surface ...
... segment , the required depth will be equal to zh .. 5. A segment of a parabola , cut off by a double ordinate to the axis , is immersed in a fluid , the density of which varies as the depth ; the base of the segment lies in the surface ...
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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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