$(15$ points$)$ The velocity field for a flow is given by$,u=2t,v=z,$ and $w=y$ where the velocities are in $f\frac{t}{s}.$ You must justify your answer using the appropriate equation$($s$).$

Show that conservation of mass is satisfied.

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}+\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{y}}+\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{z}}=0+0+0=0$

because this equals zero, the conservation of mass is satisfred

What is the local acceleration at point $x=2ft,y=4ft,$ and $z=0\mathrm{.}5ft$ at time, $t=10$ seconds?

What is the total acceleration in the x $-$direction at the same point and time?

$a_x=$

Is the flow rotational or irrotational? Be sure to show your answer!

$(1-1)hat()=0,$ Irrotational

Because vorticity is zero, it's irrotational