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 .
Step 1 of 3</p>
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,
Where is the horizontal speed at x=0.
Step 2 of 3</p>
For the two dimensional flow, the streamlines in the x-y plane is given by,
From equation 1,and
Using in above equation,