Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4–17. For the case in which U₀ = 5.0 ft/s and b = 4.6 s^-1, consider an initially square fluid particle of edge dimension 0.5 ft, centered at x = 0.5 ft and y = 1.0 ft at t = 0 (Fig. P4–86E). Carefully calculate and plot where the fluid particle will be and what it will look like at time t = 0.2 s later. Comment on the fluid particle’s distortion.

Data from Problem 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)

Transcribed Image Text:

Initially square fluid particle at t = 0 FIGURE P4-86E ? Unknown shape and location of fluid at later time t particle