Converging duct flow is modeled by the steady, two dimensional velocity field of Prob. 4–17. As vertical line segment AB moves downstream it shrinks from length η to length η + Δη as sketched in Fig. P4–55. Generate an analytical expression for the change in length of the line segment, Δη. Note that the change in length, Δη, is negative.

Data from Problem 4-17.

Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P4–17). A simple approximate velocity field for this flow is

where U₀ is the horizontal speed at x = 0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field. Calculate the material acceleration for fluid particles passing through this duct. Give your answer in two ways:

(1) As acceleration components a_x and a_y 

(2) As acceleration vector a(vector)

n OA 3,+ An B'O