An incompressible, irrotational, two-dimensional fl ow hasthe following stream function in polar coordinates:ψ = A rn sin (nθ) where A and n are constants.Find an expression for the velocity potential of this fl ow.

Consider the steady, two-dimensional velocity field of :                                  V-›= (u, ? ) = (0.5 + 0.8 x) i-›+ (1.5 − 0.8 y) j-›                                                      where lengths are in units of m, time in s, and velocities in m/s. There is a stagnation point at (−0.625, 1.875) as shown in Fig. Streamlines of the flow are also plotted in Fig. Calculate the various kinematic properties, namely, the rate of translation, rate of rotation, linear strain rate, shear strain rate, and volumetric strain rate. Verify that this flow is incompressible.

The locus of fluid particles that have passed sequentially through a prescribed point in the flow is called a (a) Pathline (b) Streamtube (c) Streamline (d ) Streakline (e) Timeline