Q$1.$ Consider steady, incompressible, two$-$dimensional flow through a converging duct $($See the

figure below$).$ A simple approximate velocity field for this flow is

vec$(V)=(u,v)=(U_0+bx)i-byj$

Where is where $U_0$ 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 $a_y$ and $(2)$ as acceleration vector vec$(a).$

Q$2.$ For the above problem, consider $U_0=3\mathrm{.}56f\frac{t}{s}$ and $b=7\mathrm{.}66s^{-1},$ plot several streamlines from

$x=0ft$ to $5$ ft and $y=-2ft$ to $2$ ft $.$ Be sure to show the direction of the streamlines.