# irrotational

ir·ro·ta·tion·aladjective

Not rotating or involving rotation.

- If w vanishes throughout the fluid at any instant, equation (I I) shows that it will always be zero, and the fluid motion is then called
**irrotational**; and a function 4) exists, called the velocity function, such that udx+vdy-{-wdz =-d, (13) and then the velocity in any direction is the space-decrease or downward gradient of cp. - D - K dK dK _ dK dK dK ?dx n dyd °, udx dz - ° and K=fdp/o+V+2q 2 =H (3) is constant along a vortex line, and a stream line, the path of a fluid particle, so that the fluid is traversed by a series of H surfaces, each covered by a network of stream lines and vortex lines; and if the motion is
**irrotational**H is a constant throughout the fluid. - When the motion is
**irrotational**, dq_ _I d deId> G =o, a=-dxy dy, v dy ydx' v 21, ' = o, or dx + dy -y chi, '1/4724, 4 1 1+1 Rx2 = $Rc 2 (ch 2 a1 +I), +h+I Ry2 = 8Rc 2 (ch 2a 1 - I), (6) (7) b2)2/(a2 + b2). **Irrotational**Motion in General.-Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single-valued potential function; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be**irrotational**; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it any rotation.**Irrotational**Motion in General.-Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single-valued potential function; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be**irrotational**; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it any rotation.

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- irrotational
- irrotationality
- irrotationally
- irrubrical

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