http://worldcat.org/entity/work/id/137204035

The effect of acceleration on a sphere filled with a compressible, inviscid liquid

To study the effect of large acceleration on a fluid filled sphere, the equations of motion of a compressible non-viscous fluid, expressed in spherical coordinates with axial symmetry, were linearized under the assumption of small perturbations from rest. The equations were solved for the flow in a sphere which is suddenly accelerated from rest at constant value of the acceleration. Line of constant density and pressure were calculated for the sphere at several values of the time, and the streamlines were sketched by the method of isoclines. All the streamlines pass through the stagnation points located on the surface of the sphere at the ends of that diameter which is parallel to the acceleration. The maximum pressure in the sphere is about equal to the hydrostatic value at a depth equal to the diameter for a fluid in a steady state gravitational field defined by the magnitude of the acceleration and occurs at the base of this diameter, while the minimum pressure occurs at the opposite end. By means of the convolution integral, the pressure on the inside surface of the sphere being accelerated sinusoidally was computed. The reaction force produced by the motion of the fluid against the driving acceleration was also calculated. (Author).

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