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By A. B. Basset

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Show that air would be sucked vertical pipe of in through a small hole in the upper part of the pipe, and explain how this result is consistent with an atmospheric pressure in the cistern. 7. is A moving so that the velocity at any point the time, and the pressure is given by mass of liquid proportional to pip is = prove that this motion may have been generated from rest by finite natural forces independent of the time, with suitable boundary conditions and show that if the direction of motion at every point : coincides with the direction of the impressed force, each particle of liquid describes a curve which is the intersection of two hyperbolic cylinders.

Prove that if w be the impulsive pressure, , and after an impulse velocity potentials immediately before the potential of the impulses, &+pV -}- p (fi ) ' the acts, V = const. A mass of compressible fluid is arranged in concentric Show spherical layers round a point under its own gravitation. that if radial vibrations be set up, the displacement z of an element 12. z j dp %\dz_ ~ /2-7 p dp 1 , r the pressure and density being connected by the equation p = kpv, and p in the differential equation being the density of the element when at rest.

25), which shows that the left-hand side of (24) cfyr, whence 1 cty r w = --5 w a-cr where i|r is , u 1 = --is dz Stokes' current function. The existence of a velocity potential function involves 17. , 2f. will be explained in f, 77, f, for reasons which the case The we quantities the following chapter, are called the components of molecular rotation. They evidently satisfy the equation jf dx + * dy + de =0 dz (26) FORMULAE OF TRANSFORMATION. Formulae of Transformation 13 1 . The equations connecting the components 18.

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A Treatise on Hydrodynamics, Vol. 1 by A. B. Basset

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