$(25$ pts$)$ Consider a steady, two$-$dimensional, incompressible, irrotational velocity field specified by its velocity potentia function, $=3(x^2-y^2)+1\mathrm{.}5x-2\mathrm{.}5y.$

$($a$)$ Calculate velocity components $u$ and $v.$

$($b$)$ Verify that the velocity field is irrotational in the region in which $$ applies.

$($c$)$ Generate an expression for the stream function in this region.

Questions $1-3(25$ points$)$ You are given a tension spring with the following details.

$d=0\mathrm{.}072in,OD=0\mathrm{.}619in,N_a=22,A228$ music wire

$(10$ points$)$ Determine the spring constant k in units of $lb\frac{f}{i}n.$

$(10$ points$)$ and tensile load $F_y$ in lbf that would cause the tension spring to yield in the body of the spring $($not the hook ends$).$

$(5$ points$)$ Is this a standard wire diameter?