P$5\mathrm{.}57$ The simply supported $1040$ carbon$-$steel rod of Fig. P$5\mathrm{.}57$ is subjected to a crossflow stream of air at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $1$ atm $.$ For what stream velocity $\backslash ($ U $\backslash )$ will the rod center deflection be approximately $1$ cm $?$

P$5\mathrm{.}57$