Solution Found!
Converging duct flow (Fig. P4?17) is modeled by the
Chapter 4, Problem 33P(choose chapter or problem)
Problem 33P
Converging duct flow (Fig. P4‒17) is modeled by the steady, two-dimensional velocity field of Prob. 4‒17. Generate an analytical expression for the flow streamlines.
PROBLEM: Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P11–15). 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 ax and ay and (2) as acceleration vector .
Questions & Answers
QUESTION:
Problem 33P
Converging duct flow (Fig. P4‒17) is modeled by the steady, two-dimensional velocity field of Prob. 4‒17. Generate an analytical expression for the flow streamlines.
PROBLEM: Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P11–15). 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 ax and ay and (2) as acceleration vector .
ANSWER:
Solution
Step 1 of 3
For the given velocity field, we need to derive an analytical expression for the flow streamlines by considering the flow to be steady in the two dimensional in x-y plane.
The steady two dimensional velocity field is given to be,
………...1
Where is the horizontal speed at x=0.