Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · 1910 · 165 citations · 0 references
Natural SciencesPhysicsDifferential EquationsFluid DynamicsFluid MechanicsContinuity EquationWave PropagationElastic Wave EquationsElastic WavesOne-dimensional Continuity EquationWave Propagation In Fluids
Abstract In the investigations which follow, we are concerned with the motion of an elastic fluid in one dimension, say, parallel to x. It is implied not only that there are no component velocities perpendicular to x, but that the motion is the same in any perpendicular plane, so that it is a function of x and of the time (t) only. If u be the velocity at any point x, p the pressure, ρ the density, X an impressed force, the dynamical equation for an inviscid fluid is du/dt + u du/dx = X - 1/ρdp/dx. At the same time the "equation of continuity" takes the form dρ/dt + d (pu)/dx = 0.