A Collection of Problems in Illustration of the Principles of Theoretical Hydrostatics and Hydrodynamics |
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Page 7
... curve , and then 0 to x = a , we have from x = ffx dx dy = fx dx.y b 2 Ꮖ -6 fxdx . { 1- ( ) } = a 2 = = b 6 fxdx { 1 ( + સ્ટો as - = b ( } a2 − fa2 + } a2 ) = žab . Similarly we have Sfy dx dy = b2a . Hence NORMAL PRESSURE OF ...
... curve , and then 0 to x = a , we have from x = ffx dx dy = fx dx.y b 2 Ꮖ -6 fxdx . { 1- ( ) } = a 2 = = b 6 fxdx { 1 ( + સ્ટો as - = b ( } a2 − fa2 + } a2 ) = žab . Similarly we have Sfy dx dy = b2a . Hence NORMAL PRESSURE OF ...
Page 8
... curve is 22 = a2 cos 20 , the axis of the loop being the prime radius vector , and the vertex being the pole . Hence , the depth of an elementary polar area rde dr below the surface of the fluid being r cos 0 , the pressure on the loop ...
... curve is 22 = a2 cos 20 , the axis of the loop being the prime radius vector , and the vertex being the pole . Hence , the depth of an elementary polar area rde dr below the surface of the fluid being r cos 0 , the pressure on the loop ...
Page 9
... curve surface to 2πr2 . Also the depth of the centre of gravity of the base below the highest point of the rim is equal to r sin 0 , and the depth of the centre of gravity of the curve surface , which is at the middle point of the axis ...
... curve surface to 2πr2 . Also the depth of the centre of gravity of the base below the highest point of the rim is equal to r sin 0 , and the depth of the centre of gravity of the curve surface , which is at the middle point of the axis ...
Page 27
... curve , and an ordinate at right angles to the axis , supposing the ordinate to lie in the surface of the fluid . Let a denote the portion of the axis between the foot of the ordinate and the vertex of the parabola , and b the length of ...
... curve , and an ordinate at right angles to the axis , supposing the ordinate to lie in the surface of the fluid . Let a denote the portion of the axis between the foot of the ordinate and the vertex of the parabola , and b the length of ...
Page 29
... curve r = a ( 1 + cos 0 ) , is immersed vertically in a fluid , the prime radius vector being coincident with the surface ; to find the depth of the centre of pressure . The required depth being denoted by x , we must determine from the ...
... curve r = a ( 1 + cos 0 ) , is immersed vertically in a fluid , the prime radius vector being coincident with the surface ; to find the depth of the centre of pressure . The required depth being denoted by x , we must determine from 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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