#### Sentence Examples

• 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.