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共 120 题- ENCYCLOPAEDIA BRITANNICA
- ELEVENTH EDITION
- VOLUME XIV, SLICE II
- Hydromechanics to Ichnography
- ARTICLES IN THIS SLICE:
- HYDROSTATICS
- When the density [rho] is uniform, this becomes, as before in (2) § 9
- From the gas-equation in general, in the atmosphere
- GM = GG1cot[theta] = mc(P/W), (1)
- The righting couple of the wedges of immersion and emersion will be
- W.BB1 = wAk² tan [theta], (5)
- BM = BB1 cot [theta] = Ak²/V, (6)
- FK = (k² - hV/A)/FQ sin QFF´ (2)
- HYDRODYNAMICS
- The components of acceleration of a particle of fluid are consequently
- X = -dV/dx, Y = -dV/dy, Z = -dV/dz; (1)
- Eliminating H between (5) and (6)
- Putting
- Putting
- In plane motion (4) reduces to
- H = p/[rho] + z + q²/2g = P/[rho] + h, (8)
- In the equations of uniplanar motion
- Interchanging these values
- V²[psi]´ + 2R = 0, (7)
- 29. _Example 1._--Liquid motion past a circular cylinder.
- Consider the motion given by
- U1/U = (a² - b²)/b²; (5)
- Then, if the outside cylinder is free to move
- 2[rho]mUd[theta] (1 - a²b^(-2) cos 3[theta] cos [theta]), (9)
- Consider the streaming motion given by
- At infinity
- With [beta] = 0, the stream is parallel to x0, and
- 32. Next consider the motion given by
- Inside a cylinder
- Similarly, with
- The polar equation of the cross-section being
- A relative stream line, along which [psi]´ = Uc, is the quartic curve
- In this symmetrical motion
- 2[zeta]/y = -y^(-2)[nabla]²[psi] = dH/d[psi] (4)
- In the absolute path in space
- The velocity past the surface of the sphere is
- With n = 2, a state of motion is given by
- Again, since
- In a fluid, the circulation round an elementary area dxdy is equal to
- When the motion is such that
- Thus, for example, with
- Inside the sphere
- P = [Omega]1 + [xi], Q = [Omega]2 + [eta], R = [Omega]3 + [zeta]. (7)
- Thus
- P² = 4(a² + [lambda]) (b² + [lambda]) (c² + [lambda]). (10)
- If we can make
- In a state of steady motion
- It is convenient to introduce the function
- Then
- 0 > u > a´. (35)
- Along a jet surface, q = Q, and
- A system of confocal ellipsoids is taken
- Thence
- Along the normal itself
- P² = 4(a² + [lambda])(b² + [lambda])(c² + [lambda]), (18)
- The velocity of the ellipsoid defined by [lambda] = 0 is then
- Similarly, the inertia parallel to Oy and Oz is
- A + B + C = abc/½P, A0 + B0 + C0 = 1. (28)
- For a sphere
- The relative path of a liquid particle is along a stream line
- 46. Between two concentric spheres, with
- For a doublet at S, of moment m, the Stokes' function is
- The corresponding expression for two orthogonal cylinders will be
- With a2 = [oo], these reduce to
- P = lx1 + mx2 + nx3, (6)
- F²(X² + Y²) = y1² + y2² + y3² - G², (21)
- N³ = -8(a + b), (29)
- For the body alone the resultant of the components of momentum
- F·OO´·sin FOO´ = FVt sin ([theta] - [phi]), (4)
- Wk2²[omega] = M - M´, W´k´²[omega] = M´, (1)
- Wk2² + W´k´²[omega] = M, (2)
- C2 = Wk2² + W´k´² = (W + W´[epsilon])k2², (3)
- C1p[mu] sin [theta] - C2[mu]² sin [theta] cos [theta]; (4)
- A0 + 2B0 = 1, (14)
- W = 1/6 [pi] d^3 x (i - f^3) [sigma], (20)
- If [rho] denotes the density of the air or medium
- W´ = 1/6 [pi] d^3 x [rho], (23)
- U´ = Q cos ([theta] - Rt), V´ = Q sin ([theta] - Rt), (2)
- M + [alpha]M´ = c1, M + [beta]M´ = c2, C + [epsilon]C´ = C3, (13)
- The integral of (14) and (15) may be written
- FIG. 24.--_Rathkea octonemalis._]
- FIG. 25.--_Aeginura grimaldii._]
- FIG. 27.--_Stomotoca divisa_, one of the _Tiaridae_ (Anthomedusae).]
- FIG. 48.--Free Actinula of _Tubularia_.]
- SYSTEMATIC REVIEW OF THE HYDROMEDUSAE
- 3. Hydranth with a single circlet of tentacles.
- FIG. 52.--_Tiara pileata_, L. Agassiz.]
- FIG. 58.--_Octorchandra canariensis_, from life.]
- FIG. 64. _Olindias mülleri._]
- FIG. 65.--_Aglantha rosea_ (Forbes), a British medusa.]
- FIG. 67.--_Solmundella bitentaculata_ (Quoy and Gaimard).]
- In the siphosome the following types of appendages occur:--
- FIG. 71.--Upper surface of _Velella_, showing pneumatophore and sail.]
- The following are some of the forms of cormidia that occur:--
- FIG. 73.--_Physophora hydrostatica._
- FOOTNOTES:
- W = Vw0; or w0 = W/V. Also
- FOOTNOTES:
- FOOTNOTE:
- FIG. 8.--Ichneumon Fly (_Rhyssa per-suasoria_) ovipositing.]
- Followers of Luther
- Patrick
- FOOTNOTES:
- It is not essential that the theory shou
- And swims | or sinks | or wades | or creeps | or flies | --
- FOOTNOTE:
- FOOTNOTES:
- FOOTNOTES:
- FOOTNOTES:
- FOOTNOTES:
- Edition by A. Müller (Königsberg, 1884). (G. W. T.)
- HISTORY
- ANCIENT LITERATURE
- RECENT LITERATURE
- FOOTNOTES: