A Treatise on the Application of Generalised Coordinates to - download pdf or read online

By Henry William Watson

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Let *bv be an element of the normal. K of the fluid at any point. , quantity. y, to rectangular axes. Let be a function of as, y, z satisfying the following conditions, viz. is V at every point on the surface, * ^ *<^ dx )+ dy^( dx and ^ ^ dy ) + |: dz ( v dz ) = at every point within the vessel *. Let u, v, w be the initial velocities Then a motion fluid. u satisfies = dV dx in , taken by a particle of the which v = dV , and dV w= - , dz dy the surface condition dV at every point on the surface, and also satisfies the equation of continuity, viz.

Quantity. y, to rectangular axes. Let be a function of as, y, z satisfying the following conditions, viz. is V at every point on the surface, * ^ *<^ dx )+ dy^( dx and ^ ^ dy ) + |: dz ( v dz ) = at every point within the vessel *. Let u, v, w be the initial velocities Then a motion fluid. u satisfies = dV dx in , taken by a particle of the which v = dV , and dV w= - , dz dy the surface condition dV at every point on the surface, and also satisfies the equation of continuity, viz. or dx^ dx ) + (/ + ^ dy dy dz () = ^ dz o v (2); at every point within the vessel, and is therefore a possible motion of the liquid subject to the given surface conditions.

Let be a function of as, y, z satisfying the following conditions, viz. is V at every point on the surface, * ^ *<^ dx )+ dy^( dx and ^ ^ dy ) + |: dz ( v dz ) = at every point within the vessel *. Let u, v, w be the initial velocities Then a motion fluid. u satisfies = dV dx in , taken by a particle of the which v = dV , and dV w= - , dz dy the surface condition dV at every point on the surface, and also satisfies the equation of continuity, viz. or dx^ dx ) + (/ + ^ dy dy dz () = ^ dz o v (2); at every point within the vessel, and is therefore a possible motion of the liquid subject to the given surface conditions.

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A Treatise on the Application of Generalised Coordinates to the Kinetics o by Henry William Watson


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