## An Elementary Treatise on Hydrodynamics and Sound |

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### Common terms and phrases

amplitude angle angular velocity axes axis becomes called centre of inertia closed curve closed surface coefficient const constant coordinates cosh coth mh cross section current function D'Alembert's Principle density determine direction distance doublet dynamical element of fluid elliptic cylinder equal equation of continuity equations of motion fixed flux method free surface frequency Green's Theorem heat Hence horizontal impressed forces infinite liquid integral irrotational irrotational motion kinetic energy Laplace's equation lemniscate of Bernoulli lines of flow mass membrane molecular rotation moving neglected normal obtain origin parallelopiped perpendicular pipe plane pressure problems produced prove quantity radius respect satisfied shearing stress shows sinh solid solution sound sphere spherical steam jet stream lines string Substituting suppose surface of separation tension theorem theory unit vanish velocity of propagation velocity potential vertical vibrations viscosity vortices wave length zero

### Popular passages

Page 177 - ... every pressure, but the movement is extremely minute. When relieved they return at once to their normal positions, and they exert a 'strong effort of restitution, in virtue of a property which is termed elasticity. We are now dealing with gases, and may define their elasticity as follows : — Def. The elasticity of a gas under any given conditions is the ratio of any small increase of pressure to the cubical compression thereby produced. The term cubical compression denotes the ratio of the...

Page 174 - It is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.

Page 174 - It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature ; or heat cannot of itself (that is, without compensation) pass from a colder to a warmer body.

Page 169 - The First Law of Thermodynamics. — When work is transformed into heat, or heat into work, the quantity of work is mechanically equivalent to the quantity of heat.

Page 23 - The image in a sphere, of a doublet whose axis passes through the centre of the sphere, can also be found by elementary methods.

Page 120 - ... latter. 8. Prove that three infinitely long straight cylindrical vortices of equal strengths will be in stable steady motion, when situated at the vertices of an equilateral triangle whose sides are large compared with the radii of the sections of the vortices; and that if they are slightly displaced, prove that the time of a small oscillation is the same as that of the time of revolution of the system in its undisturbed state. 9. A straight cylindrical vortex column of uniform rotation f, is...

Page 55 - In the irrotational motion of a liquid, prove that the motion derived from it, by turning the direction of motion at each point in one direction through 90° without changing the velocity, will also be a possible irrotational motion, the conditions at the boundaries being altered so as to suit the new motion. Discuss the motion obtained in this way from the preceding example.

Page 32 - A solid sphere of radius a is surrounded by a mass of liquid whose volume is 47rc3/3, and its centre is a centre of attractive force varying directly as the square of the distance. If the solid sphere be suddenly annihilated, shew that the velocity of the inner surface, when its radius is x, is given by && {(3?

Page 34 - The motion of a liquid is in two dimensions, and there is a constant source at one point A in the liquid and an equal sink at another point B ; find the form of the stream lines, and prove that the velocity at a point P varies as (AP.

Page 15 - Stokes, an important physical distinction in the character of the motion which takes place, according as a velocity potential does or does not exist. Conceive an indefinitely small spherical element of a fluid in motion to become suddenly solidified, and the fluid about it to be suddenly destroyed. By the instantaneous solidification velocities will be suddenly generated or destroyed in the different portions of the element, and a set of mutual impulsive forces will be called into action. Let x,...