1. Which of the following functions could represent the velocity potential for the two- dimensional flow of an inviscid fluid? (a) x + 5y; (b) 3x² – 4y²; (c) cos(x – y); (d) In(x + y); (e) arctan(x/y); (f) arccosec (x/y).

A steady, incompressible, two-dimensional velocity field is given by the following components in the xy-plane: u = 0.205 + 0.97x + 0.851y                                                                                 ? = −0.509 + 0.953x − 0.97y Calculate the acceleration field (find expressions for acceleration components ax and ay) and calculate the acceleration at the point (x, y) = (2, 1.5).

Pravin bhai

1. For incompressible flows, their velocity field 2. In the case of axisymmetric 2D incompressible flows, where is Stokes' stream function, and u = VXS, S(r, z, t) = Uz = where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence 1 Ꭷ r dr 1 dy r dz Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads Y(R, 0, t) R sin 0 S(R, 0, t) UR uo Y(r, z, t) r = = -eq, and Up = = 1 ay R2 sin Ꮎ ᎧᎾ 1 ƏY R sin Ꮎ ᎧR -eq 2 (1) (2) (3)