A Collection of Problems in Illustration of the Principles of Theoretical Hydrostatics and Hydrodynamics |
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Page 2
... expression gpΣ ( Kx ) must be effected by means of the Integral Calculus . We have supposed above that the surface of the fluid is free from pressure : should this not be the case , we must consider x to denote the sum of the depth of K ...
... expression gpΣ ( Kx ) must be effected by means of the Integral Calculus . We have supposed above that the surface of the fluid is free from pressure : should this not be the case , we must consider x to denote the sum of the depth of K ...
Page 9
... expression is a maximum , or 3 cos - sin 0 = 0 , tan 0 = 3 , which determines the required position . 9. A rectangular board is immersed vertically in a fluid , one side of the board being coincident with the surface ; to find the ...
... expression is a maximum , or 3 cos - sin 0 = 0 , tan 0 = 3 , which determines the required position . 9. A rectangular board is immersed vertically in a fluid , one side of the board being coincident with the surface ; to find the ...
Page 17
... expression for P shews that the pressures on the first , second , third , & c . portions of the cylinder are proportional to 1 3 5 7 - P1 P2 P3 P1 4. To find the whole pressure on the horizontal base of a vessel full of fluid ...
... expression for P shews that the pressures on the first , second , third , & c . portions of the cylinder are proportional to 1 3 5 7 - P1 P2 P3 P1 4. To find the whole pressure on the horizontal base of a vessel full of fluid ...
Page 19
... expression Σ ( Kp ) . Eliminating p between the two equations , we have or , putting = λ , dp Ρ dp Ρ = = g dx , k λdx ; whence , C being an arbitrary constant , we obtain p = C. ¿ 12 . Hence the total normal pressure is equal to CΣ ( K ...
... expression Σ ( Kp ) . Eliminating p between the two equations , we have or , putting = λ , dp Ρ dp Ρ = = g dx , k λdx ; whence , C being an arbitrary constant , we obtain p = C. ¿ 12 . Hence the total normal pressure is equal to CΣ ( K ...
Page 20
... ( E - 1 ) . λ Supposing to be very small and h not very large , we see that , expanding " by powers of λh , and neglecting terms of higher powers than the first , the expression for the pressure 20 NORMAL PRESSURE OF FLUids .
... ( E - 1 ) . λ Supposing to be very small and h not very large , we see that , expanding " by powers of λh , and neglecting terms of higher powers than the first , the expression for the pressure 20 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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