Show that the potential function Φ = ax(x2 + y2 ) represents the flow generated by a doublet. In which direction is the doublet oriented? A cylinder of radius 4 cm is held with its centre at the point...

Show that the potential function Φ = ax(x2 + y2 ) represents the flow generated by a doublet. In which direction is the doublet oriented? A cylinder of radius 4 cm is held with its centre at the point (0, 0) in a fluid stream. At large distances from the cylinder the fluid velocity is constant at 30 m s−1 parallel to the x axis and in the direction of x increasing. Calculate the components of the fluid velocity at the point x = −4 cm, y = 1 cm.