A Collection of Problems in Illustration of the Principles of Theoretical Hydrostatics and Hydrodynamics |
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Page 1
... equal to gpΣ ( Kx ) , where denotes the summation of a series of terms , of which Kx is the general type , the ... equal to gpДx , that is , to the weight of a column of the fluid the base of which is equal to the surface of the solid ...
... equal to gpΣ ( Kx ) , where denotes the summation of a series of terms , of which Kx is the general type , the ... equal to gpДx , that is , to the weight of a column of the fluid the base of which is equal to the surface of the solid ...
Page 2
... equal to that exerted upon an equal area in the surface of the fluid . This amounts to supposing the depth at any point of the fluid to be x + H instead of x . The principles of the determination of the pressure of fluids , on plane ...
... equal to that exerted upon an equal area in the surface of the fluid . This amounts to supposing the depth at any point of the fluid to be x + H instead of x . The principles of the determination of the pressure of fluids , on plane ...
Page 4
... equal to gp ab h . This result shews that , so long as h remains constant , the pres- sure on the parallelogram will remain the same at whatever inclination it may be placed to the horizontal surface of the fluid . 2. A solid cylinder ...
... equal to gp ab h . This result shews that , so long as h remains constant , the pres- sure on the parallelogram will remain the same at whatever inclination it may be placed to the horizontal surface of the fluid . 2. A solid cylinder ...
Page 5
... equal to 2π2 + 2πrl = 2πr ( r + 1 ) , and the depth of the 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 ...
... equal to 2π2 + 2πrl = 2πr ( r + 1 ) , and the depth of the 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 ...
Page 6
... equal to gp . 2πr sin 0.rd0 . r cos 0 πgpr3 sin 20d0 . = Hence the required ratio will be equal to sin 20d0 6 NORMAL PRESSURE OF FLUIDS .
... equal to gp . 2πr sin 0.rd0 . r cos 0 πgpr3 sin 20d0 . = Hence the required ratio will be equal to sin 20d0 6 NORMAL PRESSURE OF FLUIDS .
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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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